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1. H S5 e Des SP_CROPALLOC xlsx Excel 2 amp D xXx HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys A Al yi fe Scenario Tree v A B C D E F G H J K Lja 1 Scenario Tree IT 2 a z Ca d H 8 9 10 11 12 Stage 0 Stage 1 Stage 1 13 initial Beginning End 14 decision 4random recourse 15 on area outcomes decision 16 on yields on crops 17 and final 18 computation LJ 19 20 Problem Statement Model Scenario Tree CH Il fr 388 CHAPTER 7 Optimization The SP_CROPALLOC Worksheet Before Optimization H S E De SP CROBALLOC alen Excel 7 D DS A ra FILE HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys v f H Al ab fe Farm Planting Decisions in Face of Crop Yield vy A B c D E F G HI J ta 4 Step1 LC 5 Data Note yield and price data are completely artificiallarbitrary wh Selling Cost Unit Quantity Planting Price Unit Shortfall B Yield Acre 6 Crops Required CostiAcre forExcess ought random Good 7 Wheat 150 170 Fair 8 Corn 230 150 6 Bad 9 Beans 260 q Very Bad 10 1 Total res 500 Step 2 12 Declare the area alloca 13 WBSF 14 Adjustables Area Quantity Quantity Purchase 15 Crops Allocated Harvested Sold d Declare the yield of eac 16 Wheat 0 in WBSP_ 7 Com D 0 18 Beans D D Declare the sold and pu 19 ShortfalliPurchased WBSF 20 Excess Sold WBSF 71 Objective Maximize Profit Amount Obtai
2. Omit_CreateError Error setting omit cells 176 CHAPTER 4 Remarks Cells that are in an omit range can t be referenced by any cell outside of an omit range Example To define an omit range D10 H20 using the range name Report enter WBOMIT Report D10 H20 To Remove If you wish to delete a WBOMIT range name using VBA instead of the Delete button on the Omit dialog box you can use ActiveWorkbook Names WBOMITReport Delete This statement removes the WBOMIT range name thereby returning the adjustable cells contained in the former range to normal status wbResetOptionsToDefault For further discussion of the functionality provided see the section entitled Options Reset To Default This procedure has no arguments and resets all of the workbook options to their default values Syntax wbResetOptionsToDefault Error Code Description ResetOptionsToDefaultError Error in reseting options to default wbSetFunctionSupport This routine can be used to set the What sBest function support option seen in the Function Support dialog box There is only one argument required For additional discussion of the options available through this routine see the section entitled Advanced FunctionSupport Syntax wbSetFunctionSupport AdvFunctionSupport Argument Required Default Description AdvFunctionSupport Yes 0 False AdvFunctionSupport is a True False flag indicating whet
3. 330 CHAPTER 7 Product Mix File name PRODMIX XLSX TYPE LINEAR OPTIMIZATION PMIXMAC XLSM Application Profile In product mix problems the objective is to find the most profitable allocation of a set of limited resources over a set of desired products or activities Virtually every manufacturer faces this situation in some form or another This example involves the conversion of raw materials into manufactured goods An agricultural example might involve the use of land seed water labor and fertilizer so as to maximize farm output Product mix problems often serve as the building blocks for more complex applications The Problem in Words You are a manufacturer producing six products from six materials with each product requiring a different combination and amount of raw materials Background You know the profit per unit of each product and the quantity of each raw material required for a single unit of each product For instance each unit of product 2 contributes 45 to profit and uses 4 units of steel 5 of wood 3 of plastic etc in its manufacture Objective of Optimization The objective of optimization is to maximize the profits that can be realized from manufacturing products using only the current inventory of raw materials SAMPLE MODELS 331 The Worksheet Let s look at the PRODMIX sample file The PRODMIX Worksheet Before Optimization x ld 8 gt fe Il PRODMIX xlsx Microsof
4. 358 CHAPTER 7 The Constraints worksheet contains constraint formulas that ensure each employee works no more than one shift in any 24 hour period A Determine Adjustable Cells The adjustable cells in this model are cells D3 J5 D8 J10 D13 J15 and D18 J20 of the Assignments worksheet These are the schedules for the individual staff members B Define Best The best solution maximizes the total staff preference E4 of the Model worksheet which is the sum of the individual preference totals Individual totals are the product of the shift assignment variables 0 or 1 and the preference values assigned to each shift C Specify Constraints The constraints in this problem are Staffing requirements for each shift must be met Each staff member must work exactly the prescribed number of shifts during the week no more and no less After working one shift a staff member can t be assigned to the next two consecutive shifts or work more than one shift in a single day To assure that the staffing requirements for each shift are met the constraint formulas in D8 J8 of the Model worksheet require the number of people assigned to each shift to be greater than or equal to the number required On the Monday Days shift Model D8 for instance the formula is WB ASSIGNMENTS D3 ASSIGNMENTS D8 ASSIGNMENTS D13 ASSIGNMENTS D18 gt D7 This adds the shift assignment variables for the Monday Day shift for all four
5. MsgBox To the user Please unprotect all the sheets in your models using the Tools Protect command Else If Err gt 30000 Then MsgBox The error description is amp wbError Err Else MsgBox The error description is amp _ Err Description MACROS THE VBA INTERFACE 161 End If End If Exit Sub End Sub If you are running What sBest within a VB project you should use an alternative method for error handling This method will prevent possible What sBest errors from being transformed into unusable Visual Basic runtime errors The following Code Sample Two can be used as a workaround for the Visual Basic project file WB_VB sln available in the WB directory CODE SAMPLE TWO Sub VBABuildxyYz Omitted code that created an Excel object named gobjExcel and opens the problem to be solved Dim intError As Integer gob JExcel Run wbAdjust C5 D5 intError If intError gt 0 Then GoTo Quit End If Omitted code similar to above for wbBest wbConstraint and wbSolve as well as code for displaying the results of solve Exit Sub Quit Dim strError as String gob JExcel Run wbError intError strError MsgBox Error amp intError amp Description amp strError Exit Sub End Sub 162 CHAPTER 4 wbError The error numbers and the codes stored in the wbErr structure are as follows
6. ADDITIONAL COMMANDS 93 Distributions with one argument WBSP_DIST_DISCRETE_SH argument Discrete values with scenarios read horizontally WBSP_DIST_DISCRETE SV argument Discrete values with scenarios read vertically WBSP_DIST_CHISQUARE argument 1 Degrees freedom WBSP_DIST EXPONENTIAL argument 1 Rate WBSP_DIST_ GEOMETRIC argument 1 Success probabilities WBSP_DIST LOGARITHMIC argument 1 p Factor WBSP_DIST_ POISSON argument 1 Mean WBSP_DIST STUDENTS_T argument 1 Degrees freedom Distributions with two arguments WBSP_DIST_DISCRETE_ SH Wi argument Discrete values argument 2 Weight probabilities with scenarios read horizontally WBSP_DIST_DISCRETE SV Wi argument 1 Discrete values argument 2 Weight probabilities with scenarios read vertically WBSP_DIST_ BETA argument 1 Shape 1 argument 2 Shape 2 WBSP_DIST_ BINOMIAL argument 1 Sample size argument 2 Success probabilities WBSP_DIST CAUCHY argument Location argument 2 Scale WBSP_DIST_GAMMA argument 1 Shape argument 2 Scale WBSP_DIST_GUMBEL argument 1 Location argument 2 Scale WBSP_DIST_F DISTRIBUTION argument 1 Degrees freedom 1 argument 2 Degrees freedom 2 WBSP_DIST_LAPLACE argument 1 Location argument 2 Scale WBSP_DIST LOGISTIC argument 1 Location argument 2 Scale WBSP_DIST LOGNORMAL argument 1 Mean argument 2 Sigma WBSP_DIST_NEGATIVEBINOMIAL argument r Factor argument 2 Success proba
7. E F G XYZ COMPUTER CORPORATION PRODUCTION PLAN Product Standard Deluxe PROFIT Quantity to Produce 120 0 Profit per Unit 300 500 OONA WN A Product Component Requirements Components Quantity Required Total Number Dual Lower Upper Standard Deluxe Usage In Stock Value Range Range 1 0 120 lt 121 0 1 1E 30 0 50 0 50 1 30 1 120 300 120 1 Standard Tower Adjustable Cell Ranges In the XYZ Production example the adjustable cells refer to the production of Standard and Deluxe computer tower models The dual value of each of these adjustable cells is the amount by which the profit of producing the models would have to increase in order to make it profitable to put them into the solution The upper and lower range of the dual of an adjustable cell is the range over which the adjustable cell could change with its dual value remaining the same ADDITIONAL COMMANDS 121 We will use the example referred to earlier for the adjustable cell dual value where the number of hard drives in stock is reduced to 50 An upper and lower range value can be put in the model by selecting the cell to put the dual information in selecting Advanced Dual selecting the adjustable cells D5 to enter in the For cell range choosing Upper Range or Lower Range whichever is appropriate and clicking OK In the box below we used cells D6 and E6 for the lower and upper ranges respectively and then re solved
8. Formulas This shows the number of formula cells Constraints This shows the total number of constraint cells in the model ABCs 35 Nonlinears This shows the number of adjustable cells that appear nonlinearly in the model We say that a variable appears nonlinearly in a formula when that formula is nonlinear with respect to changes in the variable For instance consider the nonlinear expression X Y 2 This expression is nonlinear with respect to Y but it is linear with respect to X Thus Y would be included in the nonlinear count while _X would not Coefficients This shows the total number of coefficients in the best cell and all formulas dependent on adjustable cells Mathmaticians refer to this as the number of nonzero elements Obj Direction This shows the direction of the best cell Activity After the Verifying part this shows the stage of the solution process the solver is currently performing Extracting Data Check license copy file Extracting Data Reading file Extracting Data Storing relevant formulas Extracting Data Creating Instruction List Building the Model Solving Debugging Finding Infeasible Cells or Finding Unbounded Cells if Debugger requested Writing Solution During the last stage What sBest writes the solved values of the adjustable cells directly into your spreadsheet and writes the requested reports Elapsed Runtime This show
9. Suggestions Your license key has expired You may continue on running a trial version with limited capacity or you can contact LINDO Systems to obtain a new license LICKEY4 Pending Expiration of Option Trial Some versions of What sBest include trial licenses for some of the optional capabilities e g the global solver If the trial license for the options is about to expire the following warning message will be displayed on the WB Status tab Warning Message Pending Expiration of Option Trial Help Reference LICKEY4 Your trial period for the optional features will expire at the end of the day You can continue to use What sBest but some of the optional features may no longer be available Suggestions Some installations come with a free trial period for the optional solvers Nonlinear Global and Barrier In this case the trial period is about to expire What sBest will continue to operate but you will no longer have access to all the optional solver engines You may want to contact LINDO Systems to order a license upgrade that includes permanent access to one or more of the optional solvers 428 CHAPTER 8 LICKEY5 License Key Dongle Required Some versions of What sBest include a dongle key with the license The dongle key is in the form of a key to insert into a USB port of the computer If this dongle key is required and missing the following error message will be displayed on the WB Status tab
10. Warning Message License Key Dongle Required Help Reference LICKEY5 Unable to find or read a valid license key with dongle Run the WB License command to install a valid license key Suggestions Some licenses require a dongle key at the time of order to insert into a USB port of the computer If the dongle key is missing corrupted or does not match the license file so you will not be able to run What sBest What sBest can still continue to operate on a demo license capacity You may want to contact LINDO Systems to order a license upgrade that includes permanent access to one or more of the optional solvers including a dongle key LICOPT1 Global Solver Not Licensed If you attempt to use the global solver option without a license the following error message will be displayed on the WB Status tab Error Message ERROR Global Solver Not Licensed Help Reference LICOPT1 The license for your installation does not allow for use of the global solver option Suggestions The global solver is an optional feature You ve attempted to use the global solver with a copy of What sBest that does not have an appropriate license You will need to either disable the global option WB Options Global Solver or contact LINDO Systems regarding a license upgrade that includes the global option Note The global solver needs the nonlinear option and the mixed integer option to operate TROUBLESHOOTING 429 LICOPT2
11. eccceesceceeeceseeeceeeeeseeeecaeeeeaeeseeeeeseaeeesuaseneneeseaees 437 RUNTIME Runtime Limit Reached cece cccececccsseeecessseeuseeeseeesuueeeeseaaaeeeeeaneeas 438 SOLVERGOP Global Solver Use i a R eadal ieia da 438 SOLVERR EE Errore tenna aan a a a N r EA 439 SPCONFLICT Stochastic Conflicting Declarations 0 0 00 ceeeeeeeeeeeeeeeeeeeeeeeeneeeeeeaas 440 SPCORR Stochastic WBSP_CORR Fommat renn 441 SPDIST1 Stochastic WBSP_DIST 1 Fomet eect eee tener eraser taaeenaes 441 SPDIST2 Stochastic WBSP_DIST 2 Fomet nn 442 SPDIST3 Stochastic WBSP_DIST 3 Fomet nn 442 SPERR Stochastic EO a a aae a aa aa ae aa aa aait 443 SPHIST Stochastic WBSP_HIST Fomat n 444 SPRAND Stochastic WBSP_RAND Format cec ececceceeeeeeeeeecaeceeeeeeesecenaeeeeeeeeess 444 SPREP Stochastic WBSP_REP Fommmat nn 445 SPSTSC Stochastic WBSP_STSC Fommat nen 446 SPVAR Stochastic WBSP_VAR Fommmat rn 446 STRARG String Arguments Found 447 STRLUST String List Errors cits tases eege ees aia hides nae 447 STRRES String Result Of Formula cc ecccecceeeeeeeeeeeeeeeeeeeeaeeeeeeaeeeeeeaeeeseeaeeeeeenaeeeeneaas 448 SUMIF Unsupported Sumif Usage 448 TEMPFILE Error Managing Temp Files seeeseeeeeeeeeeserreserresrirrssrrrssrtrrsstrrrssrrrrssreens 449 UNBOUNDED Unbounded Model 449 UNDEFREF Undefined Reference snssessssessrrnnensstertttnnttestrrtrtnntnesttttnnnnnnenttn nn nnnn nent 450 WBCARDFORM Cardinal
12. Average 50 Count 2 Sum 100 Flog 100 1 O The dual value of adjustable cell D5 is now 100 This means the value of the best cell would be penalized in this case decrease by 100 for each unit increase in DS In other words forcing the number of Deluxe computers from 0 to 1 would return a new solution with a profit of 14 900 15 000 100 assuming a valid range on the dual value of at least one see the Valid Ranges for Dual Values section below 116 CHAPTER 3 In the window below we show the re solved model with the Deluxe adjustable cell forced to be 1 by putting the constraint WB D5 1 in cell D7 As you can see the dual value is now zero because the variable is in the solution The quantity of Deluxe computers to produce could also be forced to one by choosing Remove Adjustable in the Adjustable dialog box or the toolbar button to make D5 into a non adjustable cell and entering 1 as a constant value x H 5 e g0 XYZ xlsx Microsoft Excel lala Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o El X fe WB D5 1 B e ee e E G XYZ COMPUTER CORPORATION PRODUCTION PLAN 1 2 3 Product Standard Deluxe 4 PROFIT 5 Quantity to Produce 48 1 6 0 0 14 900 8 Profit per Unit 300 500 9 10 Product Component Requirements 11 12 Components Quantity Required Total Number 13 Standard Deluxe Usage In Stock 14 15 Standard Tower 1 48
13. J8 J10 I8 110 or wbConstraint Range Cells 8 8 Cells 10 8 lt Range Cells 8 10 Cells 10 10 Range Cells 8 9 Cells 10 9 wbConstraintPOSD For additional discussion of the functionality provided see the section entitled Constraints which refers to the dialog box that calls this procedure This routine is also called with appropriate arguments by the three toolbar buttons displayed above This routine inserts a constraint formula within the selected cell Syntax wbConstraintPOSD RangeMatrix Place_in_cell NoErrDialog Argument Required Description RangeMatrix Yes RangeMatrix is a cell reference for indicating the range of the matrix Place_in cell Yes Place_in cell is a cell reference to specify the cell in which to write the WBPOSD function NoErrDialog No Any argument passed causes all What sBest error dialog boxes from the wbConstraintPOSD routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to get any possible returned What sBest error number Useful in an embedded application of What sBest 158 CHAPTER 4 Error Codes Value Description Con_BadRangeMatrixArg Bad RangeMatrix argument Con_BadPlaceInCellArg Bad PlaceInCell argument Remarks RangeMatrix ranges must be a symmetric range more than one cell Example To enter the POSD constraint for the matrix A1 C3 and
14. T jl i 3 The holder of the option has the right to sell a specified stock mal 4 at any time the American feature between now and a specified 5 expiration date at a specified strike price 6 The holder makes a profit in the period of exercise if the 7 strike price exceeds the market price of the stock at the 8 time of sale Money is borrowed invested at the risk free rate 3 10 Step 1 Corelone scenario model 1 Initial Price 100 12 Strike price 99 S fension 13 Risk free rate 0 03 14 Step 2 information 15 Stock Price of Wealth Mark Stock 16 return this stock this this ify stage as random 17 Period period period Sell 1 period of Sell decisions and give sti 18 0 D 100 000 0 0 000 WBSP_VAR 13 4 0 08 92 000 0 0 000 WBSP_VAR WBSP_RAND 20 2 0 01 91 080 0 0 000 WBSP_VAR WBSP_RAND ER 3 0 01 90 169 0 0 000 WBSP_VAR WBSP_RAND 22 4 0 014 89 268 0 0 000 WBSP_VAR WBSP_RAND 23 5 0 03 91 946 0 0 000 WBSP_VAR WBSP_RAND 24 25 Number times sold 0 Step 4 Sample sizes 26 Can sell at most once lt WBSP_STSC Ste 27 4 Stage Scenario Ber 28 PV of final wealth 0 lt Maximize 1 4 W I Model Scenario Tree DI p 396 CHAPTER 7 H S e e Des SP_PUTOPTION xIsx Excel 2 P D xXx HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys D Al a ee Se v 10 1 12 13 14 Step 2 S information 15 Mark Stock returns 16 Specify stage as random parame
15. amer Coe MACROS THE VBA INTERFACE 163 Int_BadRefers_toArg 164 CHAPTER 4 MACROS THE VBA INTERFACE 165 30157 IntPreSolvOpt_BadFlowCoverCutsArg 166 CHAPTER 4 MACROS THE VBA INTERFACE 167 168 CHAPTER 4 30237 CleanUpFilesError 30238 AddWBMenuError 30239 ResetOptionsToDefaultError WBFREE For additional discussion of the functionality provided see the section entitled Free which refers to the dialog box that calls this procedure This routine builds WBFREE ranges which are areas of the worksheet where adjustable cells are allowed to be negative Syntax WBFREE FreeName Refers_to Argument Required Description FreeName Yes FreeName is a string that refers to the range being allowed to be negative Refers_to No Refers_to is the range or address of the cells to be allowed to be negative If omitted the default is the current selection Error Codes Description Free_BadRefers_toArg Bad Refers_to argument Free_ProtectedSheetError Unable to set free cells on a protected sheet Free_CreateError Error setting free cells Example To allow cell G8 to be positive or negative using the range name BuySell enter WBFREE BuySell G8 To Remove If you wish to delete a WBFREE range name using VBA instead of the Delete button on the Free dialog box you can use Active Workbook Names WBFREEBuySell D
16. number states the number of desired bins and cells must refer to any cells cell address Suggestions There is an incorrectly formatted Stochastic Histogram Report cell in the model A reporting cell must use the format WBSP_HIST number cells where number is a numeric number referring to the number of bins and cells is a reference to the cells you want to report the histogram The number can be left to 0 so the solver will decide the number of bins The cells reference can be any cells For more information on using the Stochastic Histogram values refer to section Options Stochastic Solver SPRAND Stochastic WBSP_RAND Format Using the stochastic feature the user has to associate a stage information to a random cell The WBSP_RAND function is used to specify the timing information If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message KT RPROR Stochastic WBSP_RAND Format Help Reference SPRAND A WBSP_RAND cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_RAND stage cells where stage is numeric and cells must refer to random cells Also verify the number of stages in the mode cell address additional message TROUBLESHOOTING 445 Suggestions There is an incorrectly formatted random function cell in the
17. value The cell reference should be to a variable cell For more information on using K Best Solution values refer to section Options Integer Solver INDICMOD Indicator Model Cell Reference If your model has references to WB constraint cells without being in a Slack mode the following warning message will be displayed on the WB Status tab Error Message WARNING Indicator Mode Cell Reference Help Reference INDICMOD The following cells directly refer to WB constraint functions being in Indicator mode rather than Slack mode You need to modify the range selection or to specify the Slack mode via the WB Options General menu cell addresses listed at bottom of tab Suggestions You should verify that the cells being referenced were actually intended to be in Slack rather than Indicator mode checking the option via the WB Options General command Otherwise you may need to change the range selection in the cells listed at the bottom of the status report Some other What sBest functions such as WBDUAL WBLOWER or WBUPPER for the dual values can have references to WB constraint cells without being in the Slack mode 418 CHAPTER 8 INFEASIBLE No Feasible Solution Found If the What sBest solver was unable to find a solution that satisfies all the constraints cells and any integer requirements in your model the following error message will be displayed on the WB Status tab Error Mess
18. x The solution of an SP model can produce a lot of information You are probably interested in only a small portion of these results These features allow you to specify the cells for which to report the values in the WB Stochastic and the WB _Histogram sheets Create Report Using the Function WBSP_REP The general format is WBSP_REP cells_to_be_reported e g WBSP_REP Sheet1 B 1 Sheet1 B 2 meaning the cells B1 and B2 of Sheet will appear in the Stochastic Scenario Report After solution a new tab WB Stochastic will be created It will have one column for every cell to be reported and one row for every scenario 98 CHAPTER 3 Select the checkbox to tell What sBest you would like a stochastic report created when the model is solved The next time you solve What sBest will generate a worksheet called WB _ Stochastic containing a listing of the cells and their locations and values of the variables solution or the random outcomes for the scenario path Click on the WB Stochastic tab to see the stochastic report Select button This button will open a new window To create the list of reporting cells specify the cell or cell range in the Select any cell to report field Once this is done pressing the Add button causes the selected cells to appear in the List of selected cells box You can decide to remove any selected cells by simply going to the list box select the cell reference to remove from the list of na
19. 1 What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit Stochasti 2 3 DATE GENERATED Oct 14 2014 09 39 AN 4 5 6 STOCHASTIC INFORMATION 8 CLASSIFICATION DATA Current Capacity Limits EI a career ran ener eevee eecOP rear mnE er ee eee 10 Adjustables 1800 Unlimited 11 Integers Binaries 0 Unlimited 12 Constraints 1599 Unlimited 13 Nonlinears a Unlimited 14 RANDOMS 1 15 STAGES 2 16 NODES 201 17 SCENARIOS 200 18 19 Expected Value EV 2 11E 03 20 Femected Value nf Wsit snd_Gee Madel Ohiectine FUNG 2 DDEAD3 LY D WB Status WEB Stochastic WB _Histogram Model Sa 4 Ip Any of the standard statistical tools in Excel can by used to analyze the scenario data MATHEMATICAL MODELING 235 The histogram generated on the WB Histogram tab is H o o ei D D SP_NEWSVENDOR Isx Excel 2 P D xXx HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys v Al fe What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A B Cc D E Z o 13 2201 622357 2201 62236 2201 62236 0 005 14 p e 15 700 973037 587 868656 644 420846 0 01 16 416 188067 61 676896 177 255585 0 025 17 188 07856 634 866908 411 472734 0 045 18 708 652903 1255 516689 982 084796 0 085 19 1279 344153 1838 842378 1559 093266 0 125 20 1848 826299 2414 888163 2131 857231 0 195 21 2431 076291 3002 818791 2716 947541 0
20. 13 0 11 0 Not Average Squared Downside Risk 4 4 gt gt DNRISK 27 al il IER A Determine Adjustable Cells The adjustable cells are the percentages of your capital to invest in each of the three assets in cells C4 E4 and the percentages of Downside Risk for each Scenario in cells G6 G12 B Define Best The best cell is the average of the sum of the squares of the downside risk percentages D19 The sum of squares is used to increase the relative penalty on outcomes that are far below the return threshold C Specify Constraints There are three kinds of constraints in this model The Forcing Constraints in 16 112 force the Downside Risk for each Scenario to be either the Threshold Return minus Scenario Return when the Scenario Return is less than the Threshold Return or zero when the Scenario Return is more than the Threshold Return For example the formula in I6 is WB G6 gt SE 16 F6 SAMPLE MODELS 297 Since G6 is an adjustable cell which is prohibited from returning a negative value and since this is a minimization problem it will return the smallest possible nonnegative value If E16 Threshold Return is less than F6 Scenario Return E16 F6 is a negative number so the constraint will be satisfied by zero which is greater than any negative number The constraint in H16 forces the sum of percentages invested in each stock to be 100 The constraint in C16 forces the average r
21. 30 1 Node Demand 1 2 4 6 Node Pressure 203 204 206 227 233 240 240 ad WB Status ARC RESISTANCE lt ARC FLOW PRESS BALANCE 3 Mau J gt t 0 85 0 15 2 85 7 00 0 25 0 13 0 10 12 63 0 23 8 15 6 99 A B cC D E F G H SAMPLE MODELS 277 A B C D E F G H 1 1 Note The pressure parameter equals 1 for incompressible fluids and electricity and 2 for gases The flow parameter equals 1 for electricity 1 852 for H2O and between 1 8 and 2 for other fluids WB Status lt ARC RESISTANCE lt ARC FLOW PRESS BALANCE 278 CHAPTER7 Bond Portfolio Optimization File name BONDS XLSX TYPE LINEAR OPTIMIZATION FLOWNET Application Profile This multi period model is an example of dynamic modeling Dynamic means that decisions made in this period affect not only this period s returns or costs but future decisions and returns as well For this reason multi period problems cannot be treated as if they were merely a collection of single period problems In many multi period modeling problems liquid or cash like assets are treated like other commodities so holding cash is just like keeping inventory The following illustrates the major features of multi period models in a financial context The Problem in Words You re a financial advisor for an investment firm Your client needs enough cash to cover commitments for the next
22. 9 750 3500 Total Value Total Weight Maximum of Load of Load Load Weight 10000 10000 TRUCK lt I al il on Count 6 Sum 3 SD 100 ln Note that What sBest has returned a value of 1 in the Proportions Loaded cells of Items 3 4 and 6 and a 0 for the remaining items This results in a total load weight of 10 000 pounds and a total load value of 27 250 This total load value is 3 250 greater than that achieved by rounding fractional answers Rounding versus Integer Solutions The important things to notice about the integer solution are that the truck s capacity is more fully utilized and more importantly that the value of the load is 3 250 higher As a rule rounding of fractional answers is effective when it results in large integers When the integers are small as in this problem rounding is less effective SAMPLE MODELS 383 Crop Allocation Under Uncertainty File name SP_CROPALLOC XLSX TYPE LINEAR OPTIMIZATION STOCHASTIC Application Profile The stochastic farm allocation model is an example of a single stage stochastic optimization problem In this problem a random event occurs at stage 1 of the process To handle this random event a decision has to be made at stage 0 This decision tries to optimize an objective function over all the possible realizations of the random event The Problem in Words A farmer can grow wheat corn or beans on his 500 acres of farm land He r
23. Although it is typically easier to use the What sBest commands constraints can be created in a What sBest model by copying or modifying existing constraints What s Best will treat copied constraint cells the same as any constraint cell created by the menu or toolbar Constraints command Note It is not recommended to lock or hide constraint cells on a protected sheet POSD SDP Constraint Range To allow the use of the Semi Definite Positive SDP capability with the LINDO Solver specify the selection of the range matrix to be constrained by a Positive Semi Definite function POSD as WBPOSD range The range defining the matrix should be symmetric with the adjustable cells typically set to be free type although not required and greater than one cell A sample case is provided with the file WBPOSDcase XLSX This case is based on a covariance matrix and shows the lower triangular matrix its constraints and the non default option keeping the quadratic recognition on to minimize the sum of squared differences Also the POSD feature is not compatible with nonlinear constraints and objective To retrieve compatibility the model needs to be convex quadratic with the adjustable cells set to be free type in the matrix and the Quadratic Recognition should be turned on ABCs 29 Usage Guidelines for Constraints In the real world decisions are always constrained in some fashion In the steel business for example you w
24. Each plant must receive its minimum steel requirement e Fach steel mill cannot ship more than its capacity The use of any raw material cannot exceed the starting inventory After you ve experimented on your own you re ready to solve The Shipping Worksheet After Optimization gig ae GG TR BLOCK xlsx Microsoft Excel lo File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V e o E ES SHIPPING COST REDUCTION F G H SHIPPING COSTREDUCTION Total Units From Total Units From Demand Demand Shipped Steel Mill 1 Cost Shipped Steel Mill2 Cost Constraint by Plant To To Plant A 800 2 Bant A 0 e 800 Plant B 400 3 PlantB 400 gt 800 Plant C 0 SG PlantC 800 gt 800 Output Capacity Output 1 200 P lt 1200 1 200 lt 1800 12 Costs 2 800 6 400 Shipping Costs 13 14 ISF Sa gengg PROFIT From ALL PLANTS less SHIPPING COSTS 16 Ir 18 19 21 WB Status Shipping Plant A lt PlantB lt PlantC 2 DEI IO s 338 CHAPTER 7 The Plant A Worksheet After Optimization mas ec ge Blockaxisx Microsoft Excel hs File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 o ER amp ID Product Resource Requirements Total Start Usage Inv 800 lt 800 1160 lt 1780 lt 1050 1050 1240 lt 1360 1240 The best possible answer to this problem is a total profit of 35 860 Note
25. Error Message WARNING Hidden Solvers Names Help Reference HIDSNAME There are hidden names in this workbook related to other model formats for solvers The interface can convert these names into a What sBest format via the menu Advanced Convert Model Format for the current selected worksheet This will create any additional Adjustable Best or Constraint cells to review Otherwise you may clean up these model names via the menu Options Reset To Default Suggestions These hidden names belong to the workbook They may have been created when the model was being built with other solvers These names are not visible via the Name Manager but can be detected They usually refer to variables constraints and objective cells from multiple models in a same workbook So select the sheet tab from which these names would be converted or removed e You may clean up these hidden model names via the menu Options Reset To Default e You can convert these names into a What sBest format via the menu Advanced Convert Model Format What sBest has found hidden names in this workbook related to non What sBest model format Try to Solve without Conversion Exit Help Where Convert and Solve will convert these names into a What sBest format for the current selected worksheet and try to solve This will create What sBest style Adjustable Best and Constraint cells in the workbook Try to
26. FORMULAS External Reference 0 ccc cccccccccceeeeeeeeeccessueecessaueeseeeeeeeseueeseeeauaeeeeeaaaeas 412 FUNCADDIN Failed to Access the Addin 413 FUNCMACRO Failed to Access the Macro u cccccccccecccceeeesesseeeeseeeeeseesuueeeeeeaaeeseneneea 413 FUNCSERVER Failed to Access the Gener 414 HIDSNAME Hidden Solvers Names 415 IKBREP K Best WBIKB_REP Format 417 INDICMOD Indicator Model Cell Reterence 417 INFEASIBLE No Feasible Solution Found 418 INFLARG Large Infeasibility cccesccccceeesccceeeecceceeeeeceeeeeeeceenenenaeeneeeeaeeneeeeaeeneeeenerenes 419 INTERRUPT Solver Interrupt ececeecce cece eeeeeecencaeeeeeeeseseaaaeaeeeeeeesesesnaeaeeseeeeeeeennaees 419 INVMOD Invalid Model 421 IRRECONST Irreconcilable Constrante 421 ITRLIM Iteration Limit Reached cee cccceeeceseeeeeseeeeessesaueueesesuuueeeeeeseesanaeeeeeaaes 422 LICCAP1 ConstraintieiMit sii 2otaes ech ieee a a Lol cain adi dead icin as 422 LICCAP2 Adjustable Cell Um 423 LICCAPS Integer Cell Limit 0 ccccccccccecceeeedeeseceeeeeeeeeedeteceeeeeneneeedeneeeeeneeeeeeedetenseedeteneees 424 LICCAP4 Nonlinear Adjustable Cell Limit 0 0 0 0 ie cccceeeeeeeeeeeeeeeeeeneeeeeseeeeeeseeaeeeeeeenaes 424 LICCAP5 Global Adjustable Cell Um 425 LICKEY1 Failed to Process License Key 426 LICKEY2 Pending License Expiration ccccecceeceeeeeeeeeeeeeeeeeeeeeeeeeeeseeeeeeeseenaeerteenaees 426 LICKEYS E
27. Nonlinear Solver Not Licensed If you attempt to use the nonlinear solver option without a license the following error message will be displayed on the WB Status tab Error Message KE RROR Nonlinear Solver Not Licensed Help Reference LICOPT2 The license for your installation does not allow for the solution of nonlinear models Suggestions The nonlinear solver capability is an optional feature You ve attempted to solve a nonlinear model with a copy of What sBest that does not have the option enabled You need to either reformulate the model to eliminate all nonlinear cells or contact LINDO Systems regarding a license upgrade that includes the nolinear solver option For more information on identifying nonlinear expressions see Overview of Mathematical Modeling LICOPTS Barrier Solver Not Licensed If you attempt to use the barrier solver option without a license the following error message will be displayed on the WB Status tab Error Message ERROR Barrier Solver Not Licensed Help Reference LICOPT3 The license for your installation does not allow for use of the global solver option Suggestions The barrier solver is an optional feature You ve attempted to use the barrier solver with a copy of What seet that does not have an appropriate license You will need to either disable the barrier option WB Options Linear Solver or contact LINDO Systems regarding a license upgrade that includes the barr
28. SUM TAN TRUNC VLOOKUP WBERLANG B WBLOGISTIC WBNORMSL Operators n Ka ob lt lt gt ACOS ASINH AVERAGE COS FALSE GAMMAINV INT LOGNORMDIST MMULT NORMSDIST OR PV ROUNDDOWN SIN SUMIF TANH WBERLANG C WBLOGISTICDENS WBTRIAINV gt gt ACOSH ATAN BINOMDIST COSH FDIST HLOOKUP LN MAX NEGBINOMDIST NORMSINV PI ROUNDUP SINH SUMPRODUCT TRANSPOSE WBEXPOINV WBLOGISTICINV WBUNIFINV AND ATAN2 CHIDIST EXP FINV HYPGEOMDIST MIN NORMDIST NOT POISSON SQRT TRUE WBINNERPRODUCT WBMULTINV WEIBULL The function is non smooth Its use may result in long solution times and if the Global Solver is not used non optimal solutions See the discussion of Smoothness in Overview of Mathematical Modeling 205 206 CHAPTER 5 These functions are supported only under certain conditions Refer to the sections Function SUMIF or Function VLOOKUP HLOOKUP for specifics WBINNERPRODUCT is a function supplied with What sBest This function is the equivalent of SUMPRODUCT but instead of multiplying terms row by row the terms are multiplied row by column TOG can support one argument assuming base 10 or two arguments Distributions Correlations for Stochastic Programming Refer to the section Options Stochastic Solver for additional explanation on using these functions Distributions WBSP_DIST_BETA WBSP_DIST_BINOMIAL WB
29. What sBest Version 13 0 User s Manual Taking your spreadsheet beyond What If 1415 North Dayton Street Chicago Illinois 60642 USA Phone 312 988 7422 Fax 312 988 9065 info lindo com www lindo com COPYRIGHT The What sBest software and its related documentation are copyrighted You may not copy the What sBest software or related documentation except in the manner authorized in the related documentation or with the written permission of LINDO Systems Inc TRADEMARKS What sBest and LINDO are registered trademarks of LINDO Systems Inc Other product and company names mentioned herein are the property of their respective owners DISCLAIMER LINDO Systems Inc warrants that on the date of receipt of your payment the enclosed computer media contains an accurate reproduction of the What sBest software and that the copy of the related documentation is accurately reproduced Due to the inherent complexity of computer programs and computer models the What sBest program may not be completely free of errors You are advised to verify your answers before basing decisions on them NEITHER LINDO SYSTEMS INC NOR ANYONE ELSE ASSOCIATED IN THE CREATION PRODUCTION OR DISTRIBUTION OF THE WHAT SBEST SOFTWARE MAKES ANY OTHER EXPRESSED WARRANTIES REGARDING THE DISKS OR DOCUMENTATION AND MAKES NO WARRANTIES AT ALL EITHER EXPRESSED OR IMPLIED REGARDING THE WHAT SBEST SOFTWARE INCLUDING THE IMPLIED WAR
30. With the exception of the best cell the ABC s in the BLOCK model are the same as in its PRODMIX and SHIPPING components A Determine Adjustable Cells The adjustable cells B6 B8 F6 F8 of the Shipping worksheet are the quantities shipped from each mill to each plant and the quantities to produce of each product from each plant B6 G6 of the Plant A B amp C worksheets B Define Best The best solution is the shipping and production decision that maximizes profit at all three plants less all shipping costs This formula is in cell A15 of the Shipping worksheet SAMPLE MODELS 337 C Specify Constraints The constraints are to ship at least the minimum amount of steel required by each plant 16 18 of the Shipping worksheet to ship no more steel than the capacity of each mill C11 G11 of the Shipping worksheet and to use no more raw material at each plant than has been shipped or is being held in stock 113 118 of the Plant A B amp C worksheets What If vs What sBest If you spend a few minutes working with the spreadsheet you ll quickly understand how complex this problem really is You must make six decisions on the quantities of steel to ship from each mill to each plant and eighteen decisions on the amount of each product you will produce at each plant six products times three plants As your spreadsheet recalculates your What If projections be sure to keep in mind the following guidelines
31. exceeds the limit ot integer limit The model has more integer cells than is allowed by your installation You will need to either reduce the size of your model or upgrade to a larger version Suggestions The model exceeds the integer cell limit for your installation The capacity limits of your version may be found by running the WB About What sBest command One option is to remove integer cells from the model until it satisfies the limit You should also check that there aren t any unintended ranges of integer cells in the model Integer cells are flagged by What sBest using range names that begin with WBINT and WBGIN Review all such range names to be sure that there are no unintended integer cell ranges Some classes of models will return naturally integer values If your model falls in this category you can remove the integer formatting and let What sBest solve the model as a continuous problem You may also want to review your demands for an integer solution For instance in some models you can simply round the solution to the continuous model with little or no ill effects For instance if a model calls for producing 1 247 288 33 pencils you could safely round the number up or down without significant impact On the other hand if the model calls for building 6 space stations rounding up or down will have a huge impact on the objective and feasibility of the constraints In which case rounding is not an op
32. 1 55 9 72 Sales 1000 s 10 00 14 00 12 00 19 00 14 00 21 00 19 00 26 00 WB Status SEASON J Predicted 9 31 14 10 12 85 18 81 14 44 20 93 18 40 26 14 Error 0 69 0 10 0 85 0 19 0 44 0 07 0 60 0 14 Seasonal Factors Spring Summer Fall Winter Average 0 83 1 10 0 89 1 18 1 00 al 1 00 ena 100 0 The spring seasonal factor is 83 In other words spring sales are 83 of the average season The trend of the solved model is 1 55 This means that after the effects of season are taken into account sales are increasing at an average rate of 1 550 per season SAMPLE MODELS _ 307 Actual sales compared to predicted sales are shown in the graph below 308 CHAPTER 7 Exponential Smoothing File name SIMXPO XLSX SMOOTH XLSX TYPE NONLINEAR OPTIMIZATION Application Profile Exponential smoothing is one technique that you can use to predict events in the future by studying events in the past By employing weighted averages to smooth past values it lets you forecast the value in the next period The basic model for exponential smoothing is Pa P ta Y P where a predicted value at period 4 1 P predicted value in period Y actual value at period amp alpha the smoothing constant
33. 339 376 Depth First 67 78 Derivatives 64 Design 267 Determine Adjustable cells 9 Determine Best 9 Determine Constraints 9 Devex 60 Direction 39 Disaggregation 72 Disclaimer 2 Disk space 3 Distribution 373 DNRISK XLSX 295 Downside risk 298 Dual 75 Dual dialog box 110 Dual Pricing 60 Dual Value 111 of a Constraint Cell 112 of an Adjustable cell 114 of Zero and Multiple Optima 117 Dual values 112 and Multiple Optima 117 in Integer Problems 117 in Nonlinear problems 117 in Nonlinear Problems 117 Valid ranges for 117 E Embedding in a Visual Basic project 145 Engineering Models 267 270 Error 304 308 Error Codes 160 Error from VBA code 406 Error messages Iteration Limit 422 438 no feasible solution found 221 solution status globally optimal 220 locally optimal 215 Undefined Arithmetic Value 409 Unexpected Operation 432 Error messages amp Warnings 406 Adjustable Cell Limit 423 Barrier Solver Not Licensed 429 Constraint Limit 422 Dual Cell Format 451 Error Managing Temp Files 449 Excel File Format 410 Expired License Key 427 External Reference 412 Failed to Access the Add in 413 Failed to Access the Macro 413 Failed to Access the Server 414 Failed to Process License Key 426 Formula Parsing 411 Global Adjustable Cell Limit 425 INDEX 469 Global Solver Not Licensed 428 Hidden Solvers Names 415 Integer Cell Limit 424 Invalid M
34. 344 PMIXMAC XLS 150 PMIXMAC XLSM 330 PORTCOST XLSX 292 Portfolio Minimizing Downside Risk 295 Scenario Model 298 Selection 288 With Transaction Cost 292 PORTSCEN XLSX 298 POSD 28 POSD SDP 28 Positive Definite 28 Positive Semi Definite function 28 Presolve 62 Pricing 59 PRICING XLSX 320 Primal 75 Primal Pricing 60 Probing Level 69 PRODMIX XLSX 330 Product Mix 330 Professional Version 134 Profit 295 320 334 Protect Sheet 23 28 146 Put Option 390 PUTOPTION XLSX 390 Q quadratic cone 252 Quadratic Recognition 62 QUAPREC 437 R RAM 3 Ranges 117 Reasonable Bounding Constraints 223 Recourse models 227 Reduced Cost 114 Refers to 44 Register 138 Relationships 224 Relative 74 Relative Limit 72 Relative Violation 67 Remove adjustable 23 Restrictions 224 Return 278 292 RHS 27 Right Hand Side 27 Risk 292 295 298 Runtime Concerns 44 Errors 407 RUNTIME 438 runtime limit 52 INDEX 473 S Sales 304 SAMPLEWB XLSX 317 Sampling 317 Savage S 2 Scale Model 59 Scaling the Model 223 Scheduling Model 349 353 360 SDP 28 SEASON XLSX 304 Seasonal Sales Factoring 304 Selective Constraint Evaluation 62 Semi continuous variable 48 Semi variance 298 Set Adjustable cells 16 Shadow Price 112 Shipping Cost Reduction 373 SHIPPING XLSX 373 SIMXPO XLSX 308 SIN 205 SINH 205 SLP Direction 62 Smooth vs Nonsmooth Expr
35. 424 LICCAPS 425 License key 4 License Key 136 INDEX 471 LICKEY 1 426 LICKEY 2 426 LICKEY3 427 LICKEY4 427 LICKEYS 428 LICOPT1 428 LICOPT2 429 LICOPT3 429 LICOPT4 429 LICOPTS 430 LICOPT6 430 Lifting 72 Lindo Systems Inc 465 Linear expressions 213 Formulas 213 regression 313 Linear Solver Options Dialog Box 58 Linear vs Nonlinear Expressions and Linearization 213 linearization 54 Linearization 207 214 313 LINEARZ XLSX 313 Linus Schrage 2 LN 205 Load 379 Local Optima 215 Local Width 67 Locally Optimal 220 Locate 132 Location of the Add in files and Update files 460 LOCKBOX XLSX 284 Locked cell 23 146 LOG 205 Logical operators 205 LOOKUP 431 Looping Macro 150 Lower Range 110 117 LP Solver 75 Macros 147 Macros in VBA 143 Make Adjustable 22 Make Adjustable amp Free or Remove Free 23 24 Markowitz Portfolio Model 288 MARKOWITZ XLSX 288 Mathematical functions 205 MAX function 205 207 Max Passes 71 Maximize Best 25 Media Buying 324 MEDIA XLSX 324 Menu bar 7 Menu commands 7 Microsoft Windows 3 MIN function 205 Minimize Best 25 Minimum and Maximum coefficients 38 MMULT 205 MOD 205 Model Reduction 59 Model Type 38 Models Non optimization 221 with Integer Restrictions 2 MODERR 432 Multi Period Inventory Management 327 Multi period Model 278 Multiple Optima 117 123 375 Multi stage 225 Multistart
36. C Specify Constraints The constraints in this problem 114 119 must reflect the requirement that total usage of raw materials remain less than or equal to the quantities of raw materials in stock This necessitates a separate constraint for each of the six raw materials For instance the constraint in 114 WB H14 lt J14 requires that the Total Usage H14 be less than or equal to the Starting Inventory J14 Total Usage H14 H19 is determined based on the Product Resource Requirements defined within the model B14 G19 For instance the formula in H14 for Total Steel Usage is SUMPRODUCT B14 G14 B 8 G 8 That is interpreted as the Steel requirement per unit of Product 1 Quantity Produced of Product I Steel requirement per unit of Product 2 Quantity Produced of Product 2 and so on What if vs What sBest Spend a few minutes working with the model to try to maximize Total Profit A3 by inserting and adjusting the Quantities Produced B8 G8 for each product As you go through these What If projections be sure to use no more of any raw material than you currently have in your Starting Inventory As you near exhaustion of any raw material look at the Product Resource Requirements table B14 G19 for products that require relatively little of that material Also remember to use Profit Unit B6 G6 as a guide to the effect of incremental production of each product Judge each of your hypothetical solutions by the T
37. Failed to Process License Key Help Reference LICKEY1 Unable to find or read a valid license key Run the WB Upgrade command to install a valid license key Suggestions You may need to reinstall your license key with the WB License command Also make sure the license file LNDWB80 LIC is installed in the directory along the What sBest add in files typically Program Files Microsoft Office Office10 Library You may need to contact LINDO Systems to obtain a valid license key LICKEY2 Pending License Expiration If your license key will expire in the next day the following warning message will be displayed on the WB Status tab Warning Message WARNING Pending License Expiration Help Reference LICKEY2 Your What sBest license key will expire at the end of the day Suggestions You have a temporary license key that will expire at the end of the day Note that you will still be able to use What sBest after the license expires but it will revert to a demonstration version with limited capacity You may want to contact LINDO Systems to obtain a new license key TROUBLESHOOTING 427 LICKEY3 Expired License Key When your What sBest license key has expired the following warning message will be displayed on the WB Status tab Warning Message WARNING Expired License Key Help Reference LICKEY3 Your license key has expired You may wish to contact LINDO Systems to obtain a new license key
38. If you wish the string arguments to be used click on the menu Advanced gt String Support gt On gt OK On the other hand if you want string arguments to be disregarded this warning can be turned off via the menu Options gt General cell addresses listed at bottom of tab Suggestions In many instances text arguments can be replaced by numeric arguments with the same end effect See if this is possible in the cell formulas listed as part of this error message STRLIST String List Error What sBest supports string cells and arguments under certain conditions If your string listing becomes unsupported the following error message will be displayed on the WB Status tab Error Message String List Error Help Reference STRLIST What s Best encountered an error while loading all the strings You may need to shorten the string length to save memory omit cells containing strings or simplify the format of these strings Suggestions What sBest may have encountered the following restrictions on the string support Too many strings to load to the current allowable memory String containing unsupported characters Illegal string operations The maximum length of the string is too large The return value of a formula cell should be numeric rather than text Omit string cells or sheets that are not relevant to the model 448 CHAPTER 8 Refer to the What sBest sample file VehicleRouting xls for an example of valid
39. Microsoft Ec eo File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ai o X D G MULTIPLE SHIFT ASSIGNMENT MODEL Preference Total 50 Mon Tue Wed Thu DAYS REQD 2 1 1 3 gt gt Mon Tue EVES REQD 1 1 gt gt Mon Tue NITES REQD 1 0 gt gt WB Status Assi Preferences The solution returns a Preference Total of 50 The scheduling requirements are tightly satisfied no overstaffing has occurred and each employee has been assigned to three or more preferred shifts 360 CHAPTER 7 Staff Scheduling Two Stage Fixed Shift File name FIXED1 XLSX FIXED2 XLSX TYPE LINEAR OPTIMIZATION Application Profile Many organizations staff their personnel according to a number of non overlapping daily shifts Manufacturing plants hospitals and banks usually have 2 or 3 shifts per day with prespecified durations and starting times For example a hospital might have 3 daily shifts each 8 hours in length with 8 00 am 4 00 pm and midnight as the starting times In this model you need to fill these shifts at the lowest cost i e with minimal overstaffing Another consideration is that worker preferences for certain shifts should be satisfied as much as possible In fact these may be not only preferences but requirements under union work agreements Here s a two stage model for this specific situation Stage 1 Cost Minimization T
40. Model sa 4 Ip Bi 398 CHAPTER 7 H S E A Zo SP_PUTOPTION xIsx Excel 0 0x HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys A1 vj fx What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A R CG D E 11 Bin Lovs Bin Highs Mid Points Bin Probabilities EIN 13 0 1 465069 0 732534 0 583984 14 2 880678 3 365033 3 122855 0 016602 15 4 248284 4 248284 4 248284 0 025391 16 5 442626 6 170251 5 806439 0 069336 TC 17 6 810232 8 1789 7 494566 0 174805 18 8 647193 9 986162 9 316677 0 020508 19 10 817707 11 277204 11 047455 0 046875 20 13 535677 13 535677 13 535677 0 0625 21 22 23 Histogram 24 25 0 8 26 Soe a S 04 27 H g 0 2 28 29 o an ab L ab A e A _ Q A hd D WB Status WB _Stochastic WB _Histogram Model So fa D READY 3 H The solver writes a series of solution in the created tab WB _Stochastic with the expected value and displays the first scenario on the spreadsheet 6 Troubleshooting Troubleshooting is divided into two major sections Frequently Asked Questions and Error Messages amp Warnings The Frequently Asked Questions and General Operational Problems section lists general problems and symptoms that may occur due to some operational problem especially in loading and running What sBest within Excel This can be reviewed as a Technical Support Erro
41. Reports Chance Constrained Specify any range for Chance Constrained with WBSP_CC_LT for Lower Than or WBSP_CC_GT for Greater Than a percentage WBSP_CC_LT v Percent 1 Objective weight 1 Refers to A 1 Place function in cell A 1 geck Specifications Optimization Method Seed for Random Generator Common Size per Stage I Sampling on Continuous Distribution Only tee o This page is useful to setup a stochastic model in Chance Constrained format which is the second major class of models in stochastic programming The goal in Chance Constrained Programming is to make an optimal decision prior to realization of random data while controlling the chance that constraints are violated in one stage Extensive explanation on Chance Constrained Programming are given in the Guidelines for Chance Constrained Modeling Specify Chance Constrained Using the Function WBSP_CC_LT or WBSP_CC_GT The general format is WBSP_CC_LT percent weight constraint cells where LT for Lower Than or WBSP_CC_GT percent weight constraint cells with GT for Greater Than 106 CHAPTER 3 Percent This is the amount by which the constraints assigned to this set must be satisfied in the scenarios Otherwise the scenario will be considered as unsatisfied according to to the direction function Objective Weight The amount by to give priority to the objective value Refers To Specify the constraint
42. SAMPLE MODELS 361 There may be many patterns consistent with an organization s work rules The first step in scheduling is to find a representative sample of patterns that correspond with organization rules or policies and meet other necessary criteria The example shown here displays 10 patterns Patterns 11 and 12 may be written in or any of the supplied patterns may be written over This process need not be repeated unless there is a change in the policies or rules Objective of Optimization The objective is to minimize staffing costs for a single shift The model creates the minimum cost schedule based on daily requirement figures average cost per employee category and the work patterns It chooses the best out of all work patterns that meet the staffing requirements It also specifies how many people to schedule according to each work pattern and if desired how many pool people to hire on a temporary basis to satisfy requirements The Worksheet The model is formulated on the left and far right of the worksheet FIXED The first screen A1 N20 contains the staffing and full time equivalent FTE requirements and coverage and cost information The FIXED1 Worksheet screen 1 Before Solving i x W9 e sy e RED T Microsoft Excel kala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o El X STAFF SCHEDULING Fixed Shift Scheduled Recommended TOTAL FTEs AND POOL DAYS Sun 0 N
43. Second you must account for pressure lost along each arc due to resistance These constraints are found in cells C5 H11 of the Pressure Balance worksheet The formula in C5 for instance requires that pressure applied equals pressure lost on the B gt A arc WB ARC RESISTANCE D14 C 13 ARC RESISTANCE C14 C 13 ARC RESISTANCE C5 ARC FLOW C5 C 14 Disregarding the exponents which in this case are 1 the formula is WB ARC RESISTANCE D14 ARC RESISTANCE C14 ARC RESISTANCE C5 ARC FLOW C5 Thus loss in pressure along arc B gt A pressure at B minus pressure at A must equal resistance along arc B gt A times flow along arc B gt A Note The Pressure parameter is 1 for incompressible fluids and electricity and 2 for gases The Flow parameter is 1 for electricity 1 852 for H O and between 1 8 and 2 for other fluids SAMPLE MODELS 275 Now you re ready to solve the model and determine the balance of flows After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning and No Best Cell warnings These warnings may be turned off from the General Options dialog box The three model worksheets now show the flows as shown below The FLOWNET Model After Solving Il ed SS g STT EGRET de Microsoft Excel cS File Home Insert Page Layout Formulas Data Review View Developer Team What sBest YV ei o ER X E EECH ARC RESISTANCE Destination C D E
44. True False False _ False True False False True To set one or more options named arguments should be used wbSetGeneralOptions goSolutionReport 1 goWmBlank 1 wbSetGlobalOptions This routine is used to set the What sBest global solver options seen in the Global Solver Options dialog box For additional discussion of the options available through this routine see the section entitled Options Global Solver All arguments are optional Syntax wbSetGlobalOptions GlStratGlobal GlMultistartAttempts GlOptimalityTolerance GlDeltaTolerance GI VariableBoundLimit GlUseBoundLimit GlBranchingDirection GIBoxSelection GlAlgebraicReformulation Argument Required Default Description GlStratGlobal No 0 False GlStratGlobal is a True False flag indicating whether or not to use this strategy GlMultistartAttempts No 0 Solver GlMultistartAttempts is a positive Decides number indicating the multistart attempts 0 Solver Decides 1 Off 2 or more number of attempts GlOptimalityTolerance No 0 000001 GlOptimalityTolerance is a number between 0 and 1 indicating the optimality tolerance GlDeltaTolerance No 0 0000001 GlDeltaTolerance is a number between 0 and 1 indicating the delta tolerance GlVariableBoundLimit No 1000000000 GlVariableBoundLimit is a positive integer indicating the variable bound limit GlUseBoundLimit No 0 Solver GlUseBoundLimit indicates the use
45. What If vs What sBest Work on a conventional What If spreadsheet solution to this problem by adjusting the Dollars Allocated shown in cells H9 H13 You ve reached a viable solution when cells B16 G16 return gt or gt Judge any solution that meets all the exposure requirements by minimizing Total Cost H18 When you arrive at a reasonable answer jot down your total cost figure Now let s solve the model with What sBest The MEDIA Worksheet After Solving i E We Gen D e MEDIAxlsx Microsoft Excel kalak Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o ER amp fe OPTIMAL MEDIA BUYING E E G H Exposure per Dollar by Market and Medium Thousands Target Markets Group1 Group Group Group4 Group5 Group6 Media Times 10 Mirror 10 Tribune Herald Post Exposures 25 41 538 40 14 362 Met Se P d gt E gt P OTAL Requirement 25 0 400 600 1200 400 11 0 _ M 4 m WB Status MEDIA 3 al w Ready 7 soo 100 C As you can see the What sBest solution has a total cost of 6 220 It results in surplus exposures in only two target markets Group 2 and Group 6 It proposes no media purchases from the Herald which offering only 15 total exposures per dollar is not a bargain D Dual Values Dual values can be applied to cells H9 H13 giving the cost penalty associated with using a media source when the optimiz
46. constraint display type in General Options as Indicator then the cells with unsatisfied constraints will display Not Not lt or Not gt Investigating their relationships to satisfied constraints may help you find the conflicts Next find all the constraints that are contradictory to the constraints identified in the first step Finally eliminate all the contradictory constraints except the ones that most accurately model your business situation If a nonlinear problem returns this error message and you suspect there is a feasible solution change the starting adjustable cell values to a feasible or near feasible solution and solve again Note that a very discontinuous problem may have a feasible solution that can only be found by starting at the solution point itself If you have the global solver option you may be able to use the multistart capability to automate the selection of alternate starting points You may also try invoking the global solver which assuming the model is not too large will always find a feasible point if one exists TROUBLESHOOTING 419 INFLARG Large Infeasibility If the infeasibility is too large the following warning message will be displayed on the WB Status tab Warning Message Infeasibility too large for a trusted solution Help Reference INFLARG Constraint violations exceeding tolerances were found Check the solution carefully before proceeding You may be able to resolve this err
47. handle computationally For instance a 2 stage model may have 30 stochastic parameters with two outcomes each This will correspond to a scenario tree with 2 1 0737e 009 scenarios Sampling is essential for models with scenario trees this big Guidelines for Chance Constrained Modeling The second major class of models in stochastic programming is Chance Constrained Programs CCP A CCP model is a similar to general stochastic programs in that the model contains random quantities with known distributions but b simpler in that the model has just a single decision stage and a single random outcome stage The goal in CCP is to make an optimal decision prior to realization of random data while controlling the chance that constraints are violated Consider an LP with random matrix E and random right handside w Min cx E Xi wii 1 m If we required all m realizations of E x w to be satisfied then we would get a very conservative expensive solution x or no feasible solution at all The distinctive feature of CCP is that we require that E x w be satisfied with some prespecified probability 0 lt p lt 1 as opposed to it being satisfied for all possible realizations of E w Defining a CCP Model in What sBest Simple Feed Mixer Example There is a relatively straightforward six step process for setting up an SP CCP model in What sBest All the information about the SP features is stored explicitly openly on the spread
48. installation ADDITIONAL COMMANDS 49 Lower Bound Upper Bound This field allows you to select the lower and the upper bounds of the Adjustable cells of the set You can select numeric values or cells references These references cannot be variable numbers Select Any Cells This reference field allows you to select any of the Adjustable cells that will be part of the set You can select multiple ranges by holding the Control Ctrl key Then click on Add to store them in the List of Selected Cells field List of Selected Cells This field will list all the cells that are part of a Semi continuous set You can modify the list by clicking on Add or Remove buttons Place the Function in Cells Specify the host range of cell you would like to see the SEMIC function to be placed in the spreadsheet What sBest automatically fills this box with the current cell selection If the selection already contains a WBSEMIC function then What sBest will display the cells argument into the List of Selected Cells 50 CHAPTER 3 Options The Options command allows you to customize the operating parameters of the What sBest solvers the user interface how What sBest runs and how your model is displayed There are several sub commands under the Options command on the WB menu They are ff OO General Linear Solver Nonlinear Solver Global Solver Integer Pre Solver Integer Solver Stochastic S
49. lt 60 16 Deluxe Tower 0 50 17 Hard Drive 1 50 4 gt WB Status xyz lt DEN m oO 100 gt Note Itis important to note that the dual value of a particular constraint or adjustable cell assumes all other information in the model remains unchanged That is given the dual information you cannot predict the effect on the best cell of simultaneously changing two or more constraints ADDITIONAL COMMANDS 117 Dual Value of Zero and Multiple Optima Dual values are generally positive for adjustable cells that have a zero value in the optimal solution An exception to this occurs when there are multiple optima i e more than one combination of adjustable cell values that yield the same optimal objective value because no penalty is incurred in moving from one optimal solution to an alternative one If your model yields zero dual values for any of the adjustable cells it s likely that there are multiple optima for your model Dual Values in Nonlinear Problems Dual values in a nonlinear problem can be interpreted usefully only for small changes in the right hand side It may not be possible to make assumptions about the effect of large changes in a nonlinear model You may want to investigate the effect of such changes manually by inserting proposed changes and re solving Users with knowledge of calculus can think of the dual value as a derivative the rate of change of the best cell value with resp
50. r bh amas c ils Zd Microsoft Excel T balm File Home Insert Page Layout Formulas Data Review View Developer Team What sBest YV ei o ER X D4 B c ME F e XYZ COMPUTER CORPORATION PRODUCTION PLAN Product Standard Deluxe Quantity to Produce 50 8 Profit per Unit 9 410 Product Component Requirements 11 12 Components Quantity Required Total Number Standard Deluxe Usage In Stock 15 Standard Tower 1 0 50 lt 60 16 Deluxe Tower 0 1 o 50 417 Hard Drive 1 2 50 lt 50 M 4 WB Status Average 32 5 Count 7 Sum 130 IEE 90 122 CHAPTER 3 The ranges for the number of Deluxe computer towers to produce are 25 upper and 5 lower That is the dual value will stay at 100 as the quantity of Deluxe computers to produce varies from 5 through 25 If cell DS Quantity to Produce is increased to 15 made non adjustable using the Remove Adjustable command via the Adjustable dialog box or the toolbar button and the model is re solved then profit decreases to 13 500 15 000 100 15 as shown in the following Tas Gor i s Microsoft Excel il Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o ER E3 fe constant G XYZ COMPUTER CORPORATION PRODUCTION PLAN Standard Deluxe constant Dual Val PROFIT 20 ish 13 500 Low Rng Upp Rng 300 500 Product Component Requirements Components Quantit
51. s Staff Size equals the five day total For example the formula for the Staff Size on Monday C7 reads G7 G10 G11 G12 G13 The value in C7 must always be greater than or equal to the Staff Needs for Monday To ensure this result a greater than gt constraint was entered in cells D7 D13 with C7 C13 on the left hand side and E7 E13 on the right hand side of the equation What If vs What sBest Try a What If solution to this problem by entering initial estimates of the numbers of employees who will start their five day workweek on each day G7 G13 As you meet Staff Needs for some days you begin to violate the constraints for others Adjust your entries for Number Starting This Day to satisfy all the constraints but be sure to meet all staff requirements After each estimate judge your solutions by minimizing Total Cost G18 When you find a solution you might be satisfied with note your final figure for Total Cost Now that you have arrived at a What If spreadsheet solution you re ready to solve the model The STAFF Worksheet After Optimization DIN g iF STAFFadsx Microsoft Excel aca Home Insert Page Layout Formulas Data Review View Developer Team What sBest VY ai o EN 8 STAFF SCHEDULING Number Staff Staff Starting Day Size Needs This Day Mon 180 Tue 160 Wed 150 Thu 170 Fri 190 Sat 140 Sun 110 180 80 160 30 150 10 160 50 190 20 140 30 110 D y y y non ow
52. sBest can find values to accomplish a desired result commonly called goal seeking or backsolving The sample model Flow Network Modeling is an example of a non optimization model Models with Integer Restrictions Users frequently need to find answers that consist of whole units De variables expressible as integers In personnel scheduling for example the most efficient use of workers may call for 2 37 persons on a shift but it s difficult to find 37 of a person who is capable of meaningful work Therefore What sBest allows you to restrict values to be whole numbers or general integers Binary integer 0 1 restrictions can also be helpful in yes no or on off decisions GETTING STARTED 3 System Requirements To install and run What sBest check that you have the following Software Microsoft Windows 7 8 or Windows XP Vista Microsoft Excel 32 bit version 2002 or higher version 2007 2010 2013 or Microsoft Excel 64 bit version 2010 2013 with latest Service Packs Microsoft NET Framework 4 0 Hardware Pentium class PC e 500 MB of RAM e 50 MB of free disk space An Internet connection is required to download the latest version of What sBest You can also contact LINDO Systems to obtain a copy Add ins library and executable files from LINDO Systems are digitally signed Additional information can be found in the nstallation Overview 4 CHAPTER 1 Installation Ove
53. that the WBA XLA or WBA XLAM file can not be found and prompt you to delete it Thus click Yes and the entry will be removed from the list Similarly to clean up the Excel list of toolbars choose the View Toolbars Customize command or right click on the Ribbon bar If the What sBest toolbar appears in the list of Toolbars select the What sBest toolbar click the Delete button and click the OK button to delete it from the list INSTALLATION DETAILS 463 The What sBest add in can always be reinstalled by launching the installation program again Appendix B Contacting LINDO Systems If you have questions or problems running the software or you have a suggestion regarding the software or documentation you can contact LINDO Systems by e mail phone FAX or mail E mail is often the best means of submitting questions regarding the operation of the software because it allows us to research the questions and provide detailed answers To resolve a problem running a specific model we may require that you attach a copy of the model in your email All models sent to LINDO Systems are treated as strictly confidential Sales and Marketing can be reached at e mail sales lindo com phone 312 988 7422 FAX 312 988 9065 Mail Courier LINDO Systems Inc 1415 North Dayton Street Chicago IL 60642 USA Tech support is available during business hours 9 00 AM to 5 00 PM Central Time e mail tech lindo c
54. v HU r r r r r r r Kb HHH Total Enployees 220 200 TOTAL COST 44 000 M 4 gt M WEBI Status STAFF J Hal m Ready Bam 100 352 CHAPTER 7 The best possible solution to this problem is a Total Cost of 44 000 Note that the constraints in D7 D13 are all tightly satisfied That is there is no overstaffing at all D Dual Values The best solution to this problem recommends starting some people on each day of the week except Sunday If someone on your staff can only work Sunday through Thursday you can analyze the model to find what the cost would be of starting this person on Sunday instead of some other day Do this by using the Advanced Dual command to display in cell H13 the dual value of cell G13 the Number Starting on Sunday Then solve the model again Refer to the section About Dual Values in Chapter 3 Additional Commands for more information on dual values After solving a dual value of 67 0 666 appears in cell H13 This indicates that the total cost would increase by 67 if one person were to start a workweek on Sunday You can confirm this by placing a 1 in cell G13 and using the Remove Adjustable command to lock the value in place Then solve once again The total cost of this solution has increased to 44 067 an increase of 67 from the previous best solution exactly as predicted by the dual value in cell H13 However you get fractional numbers o
55. will only search for any feasible integer solution if it is at least as good as the bound specified in HurdleTolerance 0 None NodeSelectionTolerance 0 Solver Decides NodeSelectionTolerance controls the order in which the branch and bound solver selects branch nodes in the tree 0 Solver Decides 1 Depth First 2 Worst Bound 3 Best Bound StrongBranchTolerance The StrongBranchTolerance option uses a more intensive branching strategy during the first n levels of the branch and bound tree where n is the option s setting During these initial levels the solver picks a subset of the fractional variables as branching candidates performs a tentative branch on each of MACROS THE VBA INTERFACE 185 the variables in the subset and selects as the final candidate the variable that offers the greatest improvement in the bound on the objective KBest No KBest is an integer indicating the number of solutions desired as part of the K Best solutions feature The WBKBEST function is used to specify the trade off cells KBestReport No False KBestReport is a boolean indicating Off the generation of the K Best report The reporting cells may be defined with the function wbIntegerSolverKBestReport BNPBlocks No Oorl BNPBlocks is an integer indicating Off the number of blocks defined with the Branch and Price solver and should be greater or equal than 2
56. x 2 y 2 22 lt 0 z gt 0 Sample Models Introduction This section provides sample models for problems in manufacturing finance engineering scheduling etc They are real world problems that demonstrate the practical use of the elegant concepts of linear and nonlinear programming A major strength and advantage of the spreadsheet environment compared to the more traditional methods of mathematical modeling is the ease with which relationships among data are visualized We ve assembled a wide range of sample spreadsheet models for you to investigate Some of them are very nearly full fledged applications All of them clearly demonstrate the principles of modeling with What sBest We ve organized them in the following groups Blending Models Blending Blending elements with various qualities into the lowest cost product to meet designated quality requirements HOGFEED XLSX Chance constrained Blending As above but quality content in the constituent elements varies at random making the model nonlinear HOGCHANC XLSX Engineering Models Box Design A simple nonlinear model that finds dimensions for a cabinet to meet various design requirements BOX XLSX Flow Network Modeling Calculating flow and pressure across a complex network FLOWNET XLSX Financial Models Bond Portfolio Optimization A multi period model that recommends bond purchases to minimize costs while providing a specified ca
57. 0 0 0 0 0 0000 0 0000 Not Not Not Not Not Not Not Not Not Not Not Not EN A Determine Adjustable Cells The adjustable cells in the model are the percentages of capital invested in each Asset B3 D3 and the differences Over and Under in G4 H15 The Overs are forced to be the amount by which a Return is greater than the Expected Return The Unders similarly are the amount by which a Return is less than the Expected Return These adjustable cells are forced to take these values by the constraints in 14 115 which we explain in detail under C Specify Constraints below B Define Best You can choose one of three best cells in this model We ll show solutions for all three minimization objectives Variance in H18 Semi Variance in H19 and Downside Risk in H20 Sp 100 tll 300 CHAPTER 7 The Variance is calculated in H18 with the formula E4 G4 H4 2 E5 G5 H5 2 E6 G6 H6 2 E7 G7 H7 2 E8 G8 H8 2 E9 G9 H9 2 E10 G10 H10 2 E11 G11 H11 2 12 G12 H12 2 E13 G13 H13 2 E14 G14 H14 2 E15 G15 H15 2 This is equivalent to the sumproduct of the probabilities and the squared values of the difference between Return and Target Return The Downside Risk is calculated as the sumproduct of the probabilities in Column E and the Unders in Column H The Semi variance is formulated as the sumproduct of the probabilities and the squ
58. 000001 goLinearizationDelta is a number indicating the Delta coefficient goLinearizationBigM 100000 goLinearizationBigM Coefficient is a number indicating the Big M coefficient goStatusReport 0 Always Created goStatusReport is an integer indicating when to show the status report 0 Always Created 1 Never Created 2 Only on Error Warning goStatusReportBegEnd 0 Beginning goStatusReportBegEnd is a flag indicating the location of the reports in the workbook 0 Beginning 1 End goSolutionReport 2 Never Created goSolutionReport is an integer indicating whether to show the solution report 0 Always Created 1 Always Created with Details 2 Never Created goWrnNonlinear 1 True Nonlinearity is a True False flag MACROS THE VBA INTERFACE 179 indicating whether to provide warning of nonlinear formulas or not goWrnBest No 1 True goWrnBest is a True False flag indicating whether to provide warning on presence of Best cell goWrnBlank No 0 False goWrnBlank is a True False flag indicating whether to provide warning of blank cells referenced in formulas or not goWrnFunction No 1 True goWrnFunction is a True False flag indicating whether to provide warning of unsupported functions or not goWrnStringArg No 1 True goWrnStringArg is a True False flag indicating whether to provide warnin
59. 13 B Define Best XYZ Corporation s goal is to maximize profit which may be expressed as Total Profit Quantity of Standard Models Produced TIMES Profit per Unit of Standard Models PLUS Quantity of Deluxe Models Produced TIMES Profit per Unit of Deluxe Models 14 CHAPTER 1 This formula appears in cell G6 as C5 C8 D5 D8 This is the sumproduct of C5 D5 and C8 D8 and could also be entered as SUMPRODUCT C5 D5 C8 D8 This function can be especially useful when doing similar operations on larger ranges To make G6 the objective best cell move the cursor to that cell and either 1 choose Best from the WB menu select Maximize and click OK or 2 use the Maximize toolbar button iz V If you use the Best dialog box via the menu you ll notice that the right text box on the Best dialog box indicates G 6 the current selection The Objective Best Cell in XYZ a licrosoft Excel bolak ew View Developer Team What sBest Y e o pp ss D D8 v F H J RODUCTION PLAN PROFIT E ai ints otal Number GETTING STARTED 15 C Specify Constraints The constraints for this problem are that the Total Usage of components E15 E17 must be less than or equal to the number in stock G115 G17 The formula for Total Usage of Standard tower components is C5 C15 D5 D15 Cells E16 and E17 have similar formulas for the Deluxe tower and hard drives To specify the constraints highl
60. 200 o fe 150 D N 250 300 _ 1 1 u o re 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 For a mixed function look back at the graph of X SIN 3 1416 B3 in the preceding section Smooth vs Non smooth Expressions Smooth expressions have a defined first derivative slope or gradient at every point Graphically a smooth function of a single variable can be plotted as a single continuous line with no abrupt bends or breaks Non smooth expressions include nondifferentiable and discontinuous functions Expressions having one or more points for which the first derivative is not defined are called nondifferentiable Graphs of nondifferentiable expressions may have abrupt bends at such points Taking the absolute value of an adjustable cell ABS A1 is an example of a nondifferentiable expression This is illustrated in the following graph Graph of ABS A1 MATHEMATICAL MODELING 219 100 90 80 70 60 50 40 30 20 10 0 100 50 50 100 Here there is an abrupt bend in the graph at the point of zero This can dramatically increase solution times Additional non smooth functions are MAX and MIN Discontinuous functions are even more challenging to a nonlinear solver Discontinuous functions are expressions whose graphs contain breaks The spreadsheet F function with adjustable cells as arguments is commonly used to express a discontinuous expre
61. 4 Objective of Optimization You will use your historical data to estimate values for the beta coefficients 8 D 2 and 2 in formula i You want your estimation function to avoid the case where it might be a poor predictor on one type of home Thus you have decided you want your model s objective to minimize the maximum error in your cost estimations Note that this process of fitting a linear function to a set of data points is referred to as linear regression 314 CHAPTER 7 The Worksheet A picture of the worksheet used to solve this problem is listed below You can find it in your sample models directory under the name LINEARZ sample file The LINEARZ Worksheet Before Optimization kino ce goe LINEARZ xlsx Microsoft Excel kala Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o E ZS Error 78 5 105 8 149 1 173 8 224 4 267 0 302 7 302 0 438 7 490 4 Sq Feet 1500 1600 2200 2600 3000 3500 4000 5200 8200 8700 nla lnoloclerteales nol ual al amp RWEKMNM NM Coefficients Max Error 0 0000 0 0000 0 0000 0 0000 M 4 gt gt LINEARZ 2 al Mm Ready G 10 A Determine Adjustable Cells The adjustable cells in the model are the beta coefficients We need What sBest to pick the values for the coefficients that minimize the maximum prediction error There are four beta Coefficients so we added four adjustable cells to r
62. 51 22 23 S 24 Histogram 25 26 0 6 27 S 28 2 0 2 Kl 29 o T T T mm _ m E T m T d 30 De p Ko op fe amp pod y S d S a i a d a 29 By A N Ne oY aN BS bd D WB Status WB _Stochastic WB Histogram Model SO D lt gt Notice that even though the driving random variable Demand has a Normal distribution the total profit has a highly skewed decidedly non Normal distribution 236 CHAPTER 6 The histogram graph is Histogram TOT_PROF Defining an SP Model in What sBest Multi Stage Example Next we give a slightly more complex example that illustrates how to formulate an SP with more than two stages model SP_INVESTMENTCOLLEGE XLSX This example was originally given by Birge and Louveaux in their book Introduction to Stochastic Programming You want to set aside 55 000 now hoping that it will grow to 80 000 in three periods so as to support your child in college Only two investments are available Stocks and Bonds At the beginning of each period or stage you re allocate you money between these two investments Each year the return on each investment is a random variable given by the table Stocks Bonds Scenario 1 1 25 1 14 Scenario 2 1 06 1 12 Stocks have the higher expected return so if we just wished to maximize expected return we would put all our money in Stocks at the beginning of each stage Stocks however al
63. 6 to a table and repeat Count As Integer TableRow As Integer Initialize the profit of product Z to 45 Sheets PRODMIX Select Range C6 44 Evaluate the effect of changing the profit on product Z by increasing it by one unit and resolving Solve the model save the results in a table and increnent the profit on product Z For Count 1 To 20 Copy a new value to the profit of product Z Range C6 Range C6 1 Solve the current model Application Run macro WBUsers whSolve Set TableRow to Count plus Z since the table will start in row 3 TableRow Count tz Copy the profit per unit for product Z to the table Sheets PRODMIX Select Cells TableRow 12 Range C6 Copy the solution so it can be pasted into the table Range B8 68 Copy Paste the solution to the table We paste in the values only to prevent the cells in the table from being treated as Adjustable Range Cells TableRow 13 Cells TableRow 18 PasteSpecial Paste xlValues Save the Total Profit in the table Cells TableRow 19 Range A3 Next Count Ead Sub Lines beginning with a single quotation mark are comments MACROS THE VBA INTERFACE 151 The macro shown here performs range analysis by incrementing the profit unit of product 2 from 45 to 64 The For Next form of looping in Visual Basic is used here but other looping forms such as Do Loop and For Eac
64. 8 0 WS WE WM E ee ee ee E Ge ee d Goes 9 2 SS Ka 49848 TEE Ue 10 2 64399 847 440 2 7 4 4 Oo eM 11 2 r 8449 2 84 4 79 2997 8 12 0 S894 404144 TST 1 e Oe Cw 13 0 S9o6 14 476 6 110 4 44 amp 14 0 63 4 OG 934 E WS 1428 4A 15 0 1000000000000 0 0 0 16 0 122 000000000000 0 0 0 7 18 Pool Days 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 20 21 E 22 ad gt H WB Status FIXED1 DK C_m EH Ready 22 Bam 100 Q The above screens show the solution when only the cells for full time employees are adjustable The total cost is 14 400 The full time staff needed to cover these requirements is 12 people Note Though we ve illustrated the model without pool employees as part of the solution you can also use it if you have access to part time or pool employees and need not rely only on full timers to meet staffing needs Just make the cells representing pool R18 AE18 adjustable before solving This will result in a 1 760 saving in this case since with pool cells adjustable there s much more flexibility in matching the Scheduled personnel with Recommended levels Sometimes the lowest cost solution results in fractional values for the adjustable cells Although these fractional numbers provide the lowest cost they are not practical for implementation purposes since it s difficult to locate 2 3 of a person who is in any condition to work Fortunately though realistic whole number solutions c
65. 90 0 0 0 25 0 92 9 114 4 116 9 115 0 0 0 0 0 105 6 107 0 96 5 98 4 0 0 16 6 103 8 132 1 113 3 115 0 0 0 0 0 108 9 130 5 173 2 163 6 486 0 0 109 0 119 5 102 1 104 7 0 0 10 3 108 3 139 0 113 1 8 116 0 1 0 0 0 103 5 928 100 6 99 8 0 0 15 2 117 6 171 5 190 8 183 6 68 6 0 0 OO rJO 0 P GAb 2 3 4 5 6 W 8 9 10 11 12 13 14 15 16 17 Expected Return 122 2 18 Target Return 115 0 Variance 0 0745 19 Return gt Target gt Semi Variance 0 0103 Invest Total 100 Downside Risk WB Status PORTSCEN Minimized downside risk comes to 0559 Minimization of the three measures of risk yield the following portfolios Asset 1 Asset 2 Asset 3 Minimize Variance 52 5 33 9 13 6 Minimize Semi Variance 46 8 1 53 1 Minimize Downside Risk 6 6 12 4 81 0 It is interesting to observe that although minimizing all three measures of risk Variance Semi variance and Downside Risk individually produces a similar level of risk it also produces rather different portfolio allocation and expected returns This illustrates why it is important to consider the measure of risk that is most appropriate for your investment goals 304 CHAPTER 7 Seasonal Sales Factoring File name SEASON XLSX TYPE NONLINEAR OPTIMIZATION The Problem in Words You sell a seasonal product and you would like to find out how the seasons affect sales
66. Beet Constraints and Solve which are discussed in ABC s Basic Functions 8 CHAPTER 1 Of these two access methods the What sBest menu provides for full interactive use of the entire range of What sBest commands For faster access the What sBest toolbar offers rapid one click access to the most commonly used operations The What sBest toolbar also makes tool tips available To learn the function of a particular toolbar button just move the cursor over the button for a second and a statement of the button s function will appear as follows When What sBest is first installed the following events should occur 1 the What sBest add in is loaded 2 the What sBest menu is inserted in the Excel menu bar and 3 the toolbar appears in floating undocked mode The user may then reposition the What s Best toolbar to a preferred part of the Excel window To remove the toolbar from view either go to WB Toolbar or to View Toolbars on the main Excel menu bar and uncheck the What sBest toolbar Reverse the process to return the toolbar to view Should you wish to remove the What sBest toolbar you would use View Toolbars Customize command select the What sBest toolbar and press the Delete button You would then have to reinstall What sBest in order to restore the toolbar What seet advises the user as to its progress via the Excel status bar displayed at the bottom of the Excel window This bar norma
67. Chance Constrained We specify that we want more than 80 probability to have the Protein amount constraint satisfied to consider the model feasible by placing the expression WBSP_CC_GT C23 0 G10 into cell A23 All the Expected Value calculation will be turned off in this type of model 248 CHAPTER 6 The Sp FEEDERMIXCCP Worksheet After Optimization BH e e D SP_FeederMixCCP xlsx Excel Al A B E D E F G H 0 0x HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Unde Sys PON Product Feed Mix Problem v J K L 1 Product Fled Mix Problem with Chance Constraints 3 The variables are defined at stage 0 the randoms at stage 1 4 5 1 Core model 6 x1 x2 ES x4 Total 7 0 66874 0 0 30931 0 02195 42913696 8 OR 2455 26 75 29 405 9 FAT 23 56 111 13 57 10 PROTEIN 12 0484 10 8224 50 9056 51 9565 2494327 gt 11 UNITY 1 1 1 1 if 12 13 3 Probability info 14 The protein coefficients are random Normal 15 Means 12 119 418 52 1 16 Std Dev 0 53 0 44 45 0 79 17 WBSP_DIST_NORMAL 18 WBSP_DIST_NORMAL 19 WBSP_DIST_NORMAL 20 WBSP_DIST_NORMAL 21 23 WBSP_CC_GT 0 8 lt lt Prob Protein constraint satisfied 2 Vande Panne and Popp presented a CCP formulation of feed mixer problem Obj 29 89 WB Status WBI _Stochastic WB _Histogram Feeder Mix BD 2 Stage info WBSP_VAR WBSP_RAND 4 Sampling info WBSP_STS
68. Constraint Evaluation checkbox to have What sBest s nonlinear solver evaluate constraints only on an as needed basis Thus not every constraint will be evaluated each iteration This generally leads to faster solution times but can also lead to problems in models that have functions that are undefined in certain regions For example What sBest may not evaluate a constraint for many iterations only to find that the solver has moved to a point in a region where the constraint is no longer defined In this case there may not ADDITIONAL COMMANDS 63 be a valid point for the solver to retreat to and the solution process terminates with an error Turning off Selective Constraint Evaluation eliminates these errors The default setting for Selective Constraint Evaluation is on Steepest Edge When What sBest is not in Steepest Edge mode the nonlinear solver will tend to select variables that offer the highest absolute rate of improvement to the objective regardless of how far other variables may have to move per unit of movement in the newly introduced variable The problem with this strategy is that other variables may quickly hit a bound resulting in little gain to the objective When the steepest edge option is enabled the nonlinear solver spends a little more time in selecting variables by looking at the rate at which the objective will improve relative to movements in the other nonzero variables Therefore on average each iteration
69. Excel will not properly handle the What sBest functions and displays the REF error code Suggestions Close the workbook and then reopen it using the following procedure When Excel opens the workbook and detects formulas with incorrect paths to your What s Best add in it will present you with a message about automatic links and then ask Do you want to update all linked information Answer Yes and use the Browse button to find the WBA XLA or WBA XLAM file in your LIBRARY subdirectory of your main Excel directory If this does not remove the REF error then use the What sBest Update Links button on the General Options dialog box This should correctly update the path If you fail to update the links with the What s Best Update Links button then Excel will place the error code of REF into the cells with the incorrect path to WBA _XLA or WBA XLAM If you frequently exchange models with other What sBest users that have their program files in a different location or you have updated or re installed the What sBest program files in a different location please refer to the discussion of the Update Links button under Options General 402 CHAPTER 8 What are the system requirements to install What sBest To install and run What sBest check that you have the following Software Microsoft Windows 7 8 or Windows XP Vista Microsoft Excel 32 bit version 2002 or higher version 2007 2010 2
70. Hand Side LHS Right Hand Side RHS and Stored in fields respectively Then select lt less than or equal to gt greater than or equal to equal to lt c convex gt c concave c convex in order to specify the direction of the constraint If no type is selected What sBest will default to lt less than or equal to Selecting None will clear the cell Clicking OK will apply the constraints The user can explicitly specify the constraint convexity to the Solver by integrating a c in the direction see the Usage Guidelines for Constraints part for additional information You need be concerned with lt c or gt c only if using the Global solver Note _What sBest uses the loose inequality operators rather than the strict inequality operators of gt greater than and lt less than Left Hand Side LHS Right Hand Side RHS and Stored in Specify the cells or ranges to be constrained in these text boxes What sBest attempts to automatically fill in these boxes based upon what the current selection is The cells just to the left of the currently selected cells are entered as the Left Hand Side of the constraint The cells just to the right of the currently selected cells are entered as the Right Hand Side of the constraint The currently selected cells become the Stored in range displayed When a row is selected it is assumed the cells just above the row are the left hand side and the cells just
71. Markets Dollars Group1 Group Group Group4 Group5 Group6 Allocated Media onone wna 9 Times 10 0 00 10 Mirror 10 0 00 11 Tribune 0 00 12 Herald 0 00 13 Post 0 00 14 15 Exposures 0 0 0 16 Met Not gt Not gt Not gt Mot gt Mot gt Met gt TOTAL COST 17 Requirement 25 0 40 0 60 0 1200 400 11 0 _ 0 00 18 19 20 21 4 gt gt MEDIA 2 A Mm Ready 23 Flog 100 The exposures per dollar are listed for each media source and each media source in B9 G13 Notice that each media source reaches different combinations of target groups per dollar spent Cells B15 G15 show the minimum required exposures for each of the target groups A Determine Adjustable Cells The adjustable cells in this model are the Dollars Allocated to each media source cells H9 through H13 B Define Best The best solution is the one that meets Requirements at the lowest cost The Total Cost cell H17 shows that every change in Dollars Allocated will have a direct bearing on cost C Specify Constraints The constraints are that the minimum Requirements be met The Exposures formulas in B17 G17 are the sumproduct of the number of exposures per dollar for a media source and the amount in dollars being allocated to that source The formulas in the row Met B16 G16 force these amounts to be greater than or equal to the required exposures for each targeted group B15 G15 326 CHAPTER 7
72. Omaha Portland imitation in Tons 8 9 Baltimore 10 Cheyenne 11 3alt Lake City 12 Memphis 13 Wichita 14 15 leetDemand Not gt 16 Demand 10 0 17 18 4 4 gt gt Shipping Costs Amount Shipped Z3 Ready A Determine Adjustable Cells The adjustable cells in PLANTLOC are the quantities shipped from each potential plant to each demand city B9 G13 on the Amount Shipped worksheet and the number of plants open at each location 19 113 of the Shipping Costs worksheet In addition since either a whole plant or none at all must be erected at any location 19 113 of the Shipping Costs worksheet are specified as binary integers What sBest will return only a zero or one as values in these cells B Define Best The best solution consists of minimizing Total Operating Cost in cell J18 of the Shipping Costs worksheet This cell contains the sum of the two subtotals for Operating Costs and Transportation costs in cells J15 and J16 of the Shipping Costs worksheet respectively The Transportation cost subtotal in turn is the sum of the values in cells B16 G16 of the Shipping Costs worksheet The formulas in these cells represent the total shipping costs to the city in question from all plant locations For instance the formula in cell B16 is SUMPRODUCT B9 B13 Amount Shipped B9 B13 C Specify Constraints The two blocks of constraints in the Plant Locating problem ensure that demand is satisfied in the six citie
73. Place the function WBSP_HIST in cell Histogram Chart Create the histogram for any cells displaying the number of bins and the mid points using the function WBSP_HIST Number of bins o Select any cells to report multiple selection holding the Ctrl key wo List of selected cells select and change by i Add or Remove Add Remove Place the function WBSP_HIST in cell Ten A te ADDITIONAL COMMANDS 101 Here s an example of the histogram report for the SP NEWSVENDOR sample model H ca a Q SP_NEWSVENDORxlsx Excel 7 D D xX HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys Al x fe What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A B D E z 13 2201 622357 2201 62236 2201 62236 0 005 14 15 700 973037 587 868656 644 420846 0 01 16 416 188067 61 676896 177 255585 0 025 17 188 07856 634 866908 411 472734 0 045 18 708 652903 1255 516689 982 084796 0 085 19 1279 344153 1838 842378 1559 093266 0 125 20 1848 826299 2414 888163 2131 857231 0 195 21 2431 076291 3002 818791 2716 947541 0 51 22 23 S 24 Histogram 25 26 0 6 27 S D 28 2 0 2 29 Eo e m m N 30 We p amp ob oi e ox gt 31 S Z d SF S 22 A A a D Ba k gt WB Status WB _Stochastic WEB Histogram Model Sa Ka al D Once created the WB Histogram report will stay on the workbook and the solver will just clear the s
74. Shadow Price The dual value of a constraint is the rate of improvement in the best cell as the right hand side of the constraint is increased The dual value of a constraint is often referred to as the shadow price because it foretells the price you should be willing to pay for that item For example in the XYZ sample model referred to earlier in Getting Started dual values can be specified for the constraints in cells F15 F17 These could be put in any convenient place on the spreadsheet We chose H15 H17 below 9 2 E x W o GG XYZ xlsx Microsoft Excel bala Home Insert Page Layout Formulas Data Review View Developer Team What sBest VY ei o ER amp f ll B Cc D E E G XYZ COMPUTER CORPORATION PRODUCTION PLAN p S E 9 Standard Deluxe PROFIT Quantity to Produce 60 30 33 000 Profit per Unit 300 500 Product Component Requirements 1 2 3 4 5 6 T 8 9 10 11 12 Components Quantity Required Total Number 13 Standard Deluxe Usage In Stock 14 Standard Tower 1 0 60 lt 60 Deluxe Tower 0 1 30 lt 50 Hard Drive 1 2 120 lt 120 18 19 20 21 lt gt M WB Status al m Ready 23 G GI 100 gt ADDITIONAL COMMANDS 113 The dual cells are inserted by highlighting the cells H15 H17 clicking on WB Advanced Dual selecting F15 F17 for the For Cell Range box and clicking OK When we re solve the dual values for the stock constraints will ap
75. Solve without Conversion will try to solve as a What sBest spreadsheet without conversion Exit to cancel Help to access the manual Notes You may remove these hidden names or after conversion via the menu What sBest gt Options gt Reset To Default You can alternatively convert these names into What sBest format via the menu What sBest gt Advanced gt Convert Model Format For further information look up HIDSNAME tag in What sBest gt Help gt Index TROUBLESHOOTING 417 IKBREP K Best WBIKB_REP Format Using the K Best feature What sBest can return the trade off solution information Trade off values tell you how sensitive the successive solutions are to various parts of the model The WBIKB_REP function is used to request trade off values If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message ERROR K Best WBIKB_REP Format Help Reference IKBREP A WBIKB_REP cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBIKB_REP cells where cells must refer to variable cells cell address Suggestions There is an incorrectly formatted K Best Report cell in the model A reporting cell must use the format WBIKB_REP cells where cells is a reference to the cells you want to report the trade off
76. Special Ordered Sets Range values tell you over what range a particular set is valid The WBSOS1 WBSOS2 or WBSOS3 functions are used to request SOS ranges If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message KE RROR Special Ordered Sets Cell Format Help Reference WBSOSFORM A SOS cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSOS1 cells where elle must refer to adjustable cells cell address Suggestions There is an incorrectly formatted WBSOSx function in the model A WBSOSx function cell must use the format WBSOS1 cells where cells is a reference to the cells you want the SOS on The cell reference should be to an adjustable cell For more information on range values refer to section Integer Special Ordered WBUPFORM Upper Range Cell Format If requested What sBest can return ranging information Range values tell you over what range a particular dual value is valid The WBUPPER function is used to request upper ranges If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message Upper Range Cell Format Help Reference WBUPFORM An upperr range cell is incorrectly formatted Correct the formula in the cell below The format should
77. Status BOX J Ready The resulting 23 03 x 6 87 x 9 56 inch box is the lowest cost design 50 97 per unit that meets all the requirements of your various departments 270 CHAPTER 7 Flow Network Modeling File name FLOWNET XLSX TYPE NONLINEAR The Problem in Words You are the manager of a network of pipelines and you need to determine a balance of flows along each arc of the network while satisfying demand at the nodes Background In the FLOWNET model you have two supply nodes with connections to a total of six other nodes The pressure at the supply nodes G and H is fixed at 240 lbs square inch PSI There s a known demand at each of the six other nodes in C13 H13 of the Arc Resistance worksheet You need to calculate the pressure at each node and the flow across each arc The following diagram helps visualize this Supply 240 Ibs eren OS Ab es E o E KS wm t rv d A Le sf Ei BCS te ktp Flow Direction amp T E A BR ER zg Arc Resistance d WT RI H ry La Supply 240 Ib lbs SAMPLE MODELS 271 The Worksheet ARC RESISTANCE Destination C D E A B Cc D E F G H 0 240 240 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 A B cC D E F G H Flow Conservation Not Not Not Not Not Not ARC RESISTANCE ARC FLOW SAMPLE MODELS 273 eT ov i RL Le Erm x W 3 e g r
78. The XYZ Worksheet Before Optimization Zj W 3 g l Side Microsoft Excel cay xT Home Insert Page Layout Formulas Data Review View Developer Team What sBest VY ei o E IXYZ COMPUTER CORPORATION PRODUCTION PLAN 2 3 Product Standard Deluxe 4 PROFIT 5 Quantity to Produce 0 0 6 0 T 8 Profit per Unit 300 500 10 Product Component Requirements 11 12 Components Quantity Required Total Number 13 Standard Deluxe Usage In Stock 14 15 Standard Tower 1 0 0 60 16 Deluxe Tower 0 1 0 50 17 Hard Drive 1 0 120 18 19 gt xv Sp 10 CU Examine the layout and logic of the model You might want to experiment with various What If projections For example try to adjust the Quantity to Produce in both cells C5 and DS so as to maximize profit G6 without allowing your Total Usage E15 E17 to exceed the number of components in stock G15 G17 For example a sensible production plan might be to make as many Deluxe models as possible since these yield the highest per unit profit Then with what is left make as many Standard models as possible This production plan would use all 50 Deluxe computer towers E16 20 Standard computer towers E15 and all 120 hard drives E17 currently in stock It would result in a total profit of 31 000 G6 However this solution can be improved by using What sBest 12 CHAPTER 1 The ABC s Now let s apply the ABC s to this spreadsheet
79. This reference to What sBest is made by checking the WBA XLA or WBA XLAM box under Tools References from within the Visual Basic Editor The Visual Basic Editor is called via Tools Macros from the main Excel menu bar If you do not create this reference then when your code attempts to call the What sBest attributes or procedures Excel returns the error message Sub or Function not defined Object Browser Excel s Object Browser is a useful tool for developing macros that run What sBest The Object Browser provides for display of all publicly declared objects within a given unit of code such as a module or the What sBest add in WBA XLA or WBA XLAM Once you ve selected such an object the Object Browser provides a view of all objects procedures and attributes that are available to any macros you write for that object For example by selecting the What sBest add in object WBA XLA within the Object Browser you can view the particular attributes and procedures of What sBest that you can employ in a macro 143 144 CHAPTER 4 The Object Browser is a feature of the Visual Basic Editor and is opened from the Excel menu by Tools Macro Visual Basic Editor Having opened the Visual Basic Editor select View Object Browser to start the Object Browser From the Object Browser you designate What seet as your object by selecting WBA XLA for the Library Workbooks instead of lt All Libraries gt If you do no
80. Total Profit wbBest G6 G6 Maximize Constrain Total Usage E15 Stock G15 G17 wbConstr aint W Solve the model wbSolve lngSol Rare Display the results Select Case IngSolutionStatus Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case End Sele Exit Sub Solution status unknown 1 MsgBox The m 2 MsgBox The m Range WBMAX 3 MsgBox The m 4 MsgBox The m 5 MsgBox The m 6 MsgBox The m 5 MsgBox The m 8 MsgBox The m 9 MsgBox The m 10 MsgBox The m Jr MsgBox The m 12 MsgBox The m 13 MsgBox The m 14 MsgBox The m Else MsgBox CE utionStatus lt G15 G17 the best cell to Maximize E17 to be less than Number in WELD E odel is Globally Optimal odel is Globally Optimal amp odel is Infeasible odel is Unbounded odel is Feasible odel is Infeasible or Unbounded odel is Near Optimal odel is Locally Optimal odel is Locally Infeasible odel is Cutoff odel is Numerical Error odel is Unknown odel is Unloaded odel is Loaded MACROS THE VBA INTERFACE 149 Handler MsgBox The error description is amp whError Err End Sub In the above example any line starting with a single quotation mark is a comment Note If Excel returns the erro
81. What sBest encountered an error during the solution process then it opens the status report worksheet tab entitled WB Status as opposed to the worksheet that was open before the run Based upon the error message returned you can troubleshoot your model The default setting for the General Options dialog box Options General is to produce a status report following each solve command Most of the following errors will be found in the status report worksheet after the model is solved Errors from VBA Code Excel generates these error messages when the WBA XLA file has not been checked off as a reference add in for your calls to the What sBest VBA interface To ensure the What sBest procedures are available to your Visual Basic code choose Tools References from the Visual Basic Editor and make sure WBA XLA is checked Note The first step in running What sBest from VBA is to create a reference to What sBest This reference is made by checking the WBA XLA box under Tools References from within the Visual Basic Editor The Visual Basic Editor is called via Tools Macros from the main Excel menu bar If you do not create this reference then any attempt to use the What sBest attributes or procedures will produce the error message Sub or Function not defined TROUBLESHOOTING 407 Runtime Errors If you did not place error handling into your VBA code then Excel handles a What sBest error by generating a r
82. accepts the numbers 1 for binary and 2 for general Error Codes Description Int_BadIntNameArg Bad ntName argument Int_BadRefers_toArg Bad Refers_to argument Int_BadIntChoiceArg Bad JntChoice argument Int_ProtectedSheetError Unable to set integer cells on a protected sheet Int_CreateError Error setting integer cells Remarks Integer variables can dramatically increase the solution time Example To constrain cell F6 to be a general integer using the range name staff enter wbInteger staff F6 General To constrain cell F7 to be a binary integer using the range name OnOff enter wbhInteger OnOff F7 Binary Note The second of these two examples could be done without the IntChoice argument of Binary which is the default MACROS THE VBA INTERFACE 171 wbintegerCard For additional discussion of the functionality provided see the section entitled Integer Special Ordered Set which refers to the Special Ordered Set Cardinality dialog box that calls this procedure This routine is used to build the Cardinality ranges WBCARD Adjustable cells contained in these ranges will be restricted to integral values by the What sBest solver If you wish to delete a CARD function using VBA instead of deleting it on the spreadsheet you can use Selection Clear This statement clears the selected cell from any of its content Syntax wbIntegerCard CardNumber ArgList Refers_to N
83. all integer restrictions may not be satisfied Best Objective Bound Assuming a best cell is present this shows the theoretical bound on the objective for integer programming models or any model solved with the global solver Steps This shows the number of solver steps required by any extended solver Active This shows the number of pending subproblems to be solved by any extended solver Solution Time This shows the length of time the solver has been running in hours minutes and seconds Additional detailed information about your model can be found by generating a solution report You can enable the solution report option via the Solution Report drop down box on the General Options dialog box 3 Additional Commands What sBest has a number of additional commands to allow you to do such things as perform sensitivity analysis identify integers variables change the type or appearance of a report or locate a particular type of cell Others will wish to tailor the performance of the solvers by manipulating various option settings This chapter discusses these additional commands and options Options and Solvers Some options in What sBest pertain to the overall operating parameters of the What sBest solvers or to the user interface and data display These general options such as teration limit or Runtime Limit are set in the General Options dialog box Other options modulate the performance of a particular solver For exampl
84. also not nest any What sBest functions in a single expression Can I protect my workbook from viewing You can password protect worksheets data and macros from viewing However you may not protect any of the adjustable dual or range cells What sBest will still be able to solve the model but it won t be able to access these protected cells in order to write the results 404 CHAPTER 8 How large can my model be The size model you can solve will depend primarily on the size license you purchased For a list of the various sizes and their specific limitations see section About What sBest Other indirect limitations are memory and time Your model may physically fit within the limits of your version of What sBest but particularly for very large models there may not be enough random access memory available to successfully solve your model Also certain classes of models are very difficult to solve A tough model may take more time to solve than you are willing to wait For more information on what makes a model tough and techniques for making models easier to solve refer to the section Overview of Mathematical Modeling How do I fix the Error Opening File error message This error message results from temporary files that couldn t be closed from the last run of the What sBest Solver Go to the folder where your model file is located and remove any What sBest temporary files These files are named LI
85. and select Dual Value Then specify the cell in which you want the dual information displayed in the Report Information in box Note When taking the dual value of a constraint be sure to specify the cell containing the constraint function not the right hand side of the constraint Upper Range and Lower Range Select Upper Range or Lower Range to cause What sBest to return the upper and lower valid ranges for a dual value That is the upper and lower bounds of the range over which the dual value of a constraint or adjustable cell stays the same Note Calculating upper and lower ranges may significantly increase solution times so it is good to weigh the benefits of the additional information against the amount of extra time it will take to get that information This runtime consideration is particularly relevant for large models Report Information in Specify the host range of cells you would like to see the dual information placed in the Report Information in text box What sBest will automatically fill this box with the current selection of cells 112 CHAPTER 3 Usage Guidelines for Dual Values Dual values can provide valuable sensitivity information They can give you a feel for how sensitive a solution is to a particular constraint cell or adjustable cell What sBest can provide dual information on any adjustable cell constraint cell or any cell that is a function of adjustable cells Dual Value of a Constraint Cell
86. and your sales growth This information would help you in forecasting sales and making future ordering decisions Background This model calculates seasonal factors that measure the effect each season has on sales and fits a straight line to the normalized data by minimizing the squared error The trend or slope of the line is the sales growth per season The base is the sales figure at time zero You have the sales data by season for the last two years 1500 K feg 600 Sprig Summer Fal Whiter Objective of Optimization The objective is to predict sales for the next two years based on the Base Trend and Seasonal Factors while minimizing the error SAMPLE MODELS 305 The Worksheet Let s look at the SEASON sample file The SEASON Worksheet Before Solving x ld ayy G t nis SEASON xlsx Microsoft Excel EE bala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 CA o El Ss fe SEASONAL SALES Sales Season Period 1000 s Predicted Error 10 00 0 00 10 00 14 00 0 00 14 00 12 00 0 00 12 00 19 00 0 00 19 00 14 00 0 00 14 00 21 00 0 00 21 00 19 00 0 00 19 00 26 00 0 00 26 00 Spring Summer Fall Winter Spring Summer Fall Winter 1 2 3 4 5 6 T7 8 Seasonal Factors Trend Spring 0 00 Base Summer 0 00 i Fall 0 00 Sum of Squared Winter 0 00 Error 2475 000 Average 0 00 Not 1 00 M 4 gt H S
87. any existing data or information to set the Adjustable Best cells and Constraint cells from the default selected spreadsheet tab Then just click on Solve to see the What sBest results UI Support of Excel XLSX XLSM XLSB file formats The solver module has been redesigned to support up to date platforms and operating systems Windows XP Vista and 7 8 with Microsoft Excel 2002 or Excel 2007 2010 2013 What sBest can run models saved with the new workbook format XLSX XLSM or XLSB with the maximum size of 16384 columns and 1048576 rows What sBest is also provided as a 64 bit version for Excel 2010 or 2013 64 bit xvi LI Select Display Language to be English Chinese French or Japanese This feature allows the user to select the language of his choice to be either English Chinese French or Japanese without reinstalling the add in The language selection makes easier the project for companies working in a multi cultural environment QO Simulation Support Based on a stochastic model the user can set up the random parameters and their associated distributions and What sBest will calculate the values of the reporting cells This feature is useful for simulating the behavior of some cells along the scenarios and to display their histograms without defining an adjustable constraint or objective cells Q Multithreading Support This includes multi cpu extensions to take advantage of compu
88. argument must be a numeric constant and the fourth argument is an optional TRUE FALSE value cell address Suggestions The VLOOKUP function requires three arguments as follows VLOOKUP lookup_value table_array col_index_num range_lookup What sBest places the following restrictions on these arguments the col_index_num argument must be a value not a formula or a cell reference all arguments must evaluate to being numeric rather than text and range_lookup is an optional TRUE FALSE argument Refer to the What sBest sample file VLOOKUPWBSOLVER XLS for an example of valid VLOOKUP usage MEMORY Insufficient Memory If there is not enough random access memory on your machine the following error message will be displayed on the WB Status tab Error Message Insufficient Memory Help Reference MEMORY There is not enough random access memory on the machine to solve the mode to completion Try closing all other applications or adding memory additional message Suggestions The solver was not able to allocate sufficient memory Try shutting down any other applications that are open to free up memory Memory requirements grow along with your model so reducing the model s size may help too Another option is to try and increase the amount of virtual memory available to your computer Unfortunately relying on virtual memory rather than true RAM memory will slow the solver down substantially 4
89. arguments should be used wbSetIntegerOptions RelativeOptimality 1 wbSetintegerPreSolverOptions This routine is used to set the What sBest integer pre solver options seen in the Integer Pre Solver Options dialog box For additional discussion of the options available through this routine see the section entitled Options Integer Pre Solver All arguments are optional Syntax wbSetIntegerPreSolverOptions HeuristicLevel ProbingLevel MaxCutsPasses RelativeCutsLimit CoefficientReduction Disaggregation FlowCover GCD Gomory GUB KnapsackCover Lattice Lifting PlantLocation ObjIntegrality Basic Cardinality Disjunctive Argument Required Default Description HeuristicLevel No 3 High HeuristicLevel controls the level of integer programming heuristics used by the integer solver These heuristics use the continuous solution at each node in the branch and bound tree to attempt to quickly find a good integer solution 0 None 1 Low 2 Medium 3 High Cutoff Criterion No 0 Solver The Cutoff Criterion is used to control the Decides criterion for terminating heuristics 0 Solver Decides 1 Time 2 Iterations ProbingLevel No 0 Solver ProbingLevel controls the amount of probing Decides that occurs in integer models Probing involves taking a close look at the integer variables in a model and deducing tighter MACROS THE VBA INTER
90. be very time consuming for large models 104 CHAPTER 3 Print Scenarios Horizontally in Report This flag enables to print the scenarios along a row in the WB _ Stochastic report so the reporting cells will be displayed along a column It is useful for models reporting numerous cells for a few scenarios The default setting is off meaning the scenarios will appear vertically in the report Use Preview Window for Scenario Selection Once the solver has completed the stochastic calculation the user can have a preview of the cells to report by selecting the scenario number By default the solution values of the scenario 1 will be written back into the spreadsheet but another scenario solution can be selected This will allow a closer look of a particular scenario when reading the spreadsheet The cells are selected via the same WBSP_REP function for either an Adjustable Variable Number Constraint Random Parameter or any Dual references All the scenarios will be anyway written in the WB _Stochastic sheet is this report was previously requested What sBest Scenario Selection for Stochastic Solver 64 bit axe Select the Scenario Values for the Reporting Cells 11 445663 0 000000 Q 85 794823 TOT_PROF 2201 622357 Display a scenario into the spreadsheet This Selection Take Default ADDITIONAL COMMANDS 105 Page Chance Constrained Stochastic Support a Core Stage Distribution Scenario
91. blend Grain 4 which is not a bargain at 95 per bushel is not purchased D Dual Values Dual values have been included in two locations in this worksheet C18 F18 and J7 J10 The dual value entries in cells J7 through J10 show the reward i e how much money could be saved if each respective constraint H7 H10 were relaxed by one unit In practical terms this means that you could save 4 55 per bushel if the requirement for Nutrient C were reduced to 4 If slightly less sprightly hogs are tolerable in return for such a savings relaxing this nutritional requirement would be a good decision Likewise if the requirement for Nutrient D were reduced to 20 the cost bushel would go down by 17 Note that the dual values are zero for Nutrients A and B Lowering the requirement by one unit offers no savings because there is already an excess of Nutrients A and B in your optimum blend since constraints H7 and H8 are not tightly satisfied 262 CHAPTER 7 The other dual values in the Swine amp Roses model C18 F18 show the amount by which the price of an unused grain would have to be reduced before it would be cost effective to use it in the minimum cost blend For example the dual value for Grain 4 is 57 88 F18 This tells you how much the price of Grain 4 would have to be reduced in order for it to appear in the optimal solution of HOGFEED This is a good number to have handy when negotiating to get a lower price For more information
92. cells on which to apply the Chance Constrained feature You can select multiple ranges in the same function which will be treated as being in the same set Otherwise specifying different functions the solver will treat the Chance Constrained functions as different set The reference ranges are entered into the text box Place function in cell Specify the cell in which to write the WBSP_ function The reference ranges have to be entered into the text box Frame Specifications The Stochastic Solver option allows you to solve models in which some cells are random variables The frame posted by the Options Stochastic Solver command appears as follows Specifications Optimization Method Solver Decides v Seed for Random Generator IR Common Size per Stage Iw Sampling on Continuous Distribution Only ml o ADDITIONAL COMMANDS 107 Optimization Method Indicates the method you would like the stochastic solver in What sBest to employ using the Optimization Method drop down box Possible choices include Solver Decides Free Deterministic Equivalent Nested Benders Decomposition Augmented Lagrangian Decomposition and Simple Benders Decomposition The Solver Decides setting currently defaults to the free method The default setting for Solver Method is Solver Decides Seed for Random Generator This is the Seed to initialize the random number generator Possible values are positive integers and can be
93. command 410 CHAPTER 8 ENTIRERANGE Entire Range Selection In the situation where some of the formulas are selecting an entire column or row the following warning message will be displayed on the WB Status tab Warning Message Entire Range Selection Help Reference ENTIRERANGE A function argument selects an entire column or row in a worksheet for instance showing A A or 1 1 This full selection creates several blank cells that may not be necessary to the model then requesting extensive memory resources for the model depending on the format of the file as XLS or XLSX A correction would be to select the exact range or cells in the formula cell address Suggestions What sBest will create a 0 value number for any blank cell being referenced by a formula thus memory allocation for the system An entire column selected means 1048576 cells and an entire row means 16384 cells ina XLSX format Similarly in a XLS format it means 65536 cells for a column and 255 cells for a row This warning message will not be displayed if the selection is shorter than these numbers EXLVER Excel File Format If your workbook is not saved in a current workbook file format the following warning message will be displayed on the WB Status tab Warning Message WARNING Excel File Format Help Reference EXLVER The file format you have chosen is from an older release of Excel Please resave your file using the lat
94. constraints are enforced by means of the formulas in D7 D9 D11 D13 and D15 In D7 the formula WB C7 gt E7 forces the total Surface Area of the cabinet in C7 calculated by the formula 2 Length Width Length Height Width Height to be at least as great as the lower limit of 888 square inches in E7 In D9 the formula WB C9 lt E9 forces the Footprint in C9 to be no greater than the upper limit of 252 square inches in E9 The Footprint is calculated by the formula Width Length In D11 the formula WB C11 gt E11 forces the Volume in C11 calculated by the formula Length Width Height to be at least as great as the lower limit of 1512 cubic inches required to fit the electronic equipment in the cabinet Finally in D13 and D15 the formulas WB C13 lt E13 and WB C15 gt E15 force the ratio of Height to Width to fall between 718 and 518 where C13 and C15 both calculate Width Height Now you re ready to solve the model and find the optimum design The BOX Worksheet After Optimization S mmm Gleis Boxausx Microsoft Eed elak File Home Insert Page layout Formulas Data Review View Developer Team What sBest e 2 o El X f E FG CABINET DESIGN ACTUAL LIMIT Surface Area 888 000 888 Length Width Height 23 03 6 87 9 56 Footprint 158 123 252 Volume 1512 000 1512 UNIT COST Width Height 0 7187 lt 0 718 weng Width Height 0 718 gt 0 518 4 4 WB
95. disabled For this reason the linearization option is provided with some user adjustable parameters that are set in the General Options dialog box You may wish to try different degrees of linearization to see what works best for your model It is highly recommended that you consider performing linearization on your own If What sBest indicates that your model is nonlinear it can be beneficial to investigate the expressions in the nonlinear cells and determine whether any could be reformulated in a linear manner Note The locations of all nonlinear cells will be displayed in the staus report assuming that the Nonlinearity present warning has been enabled in the General Options dialog box The Solution Process Determining Optima Local Optima vs Global Optima Linear and nonlinear problems are distinguishable by their different kinds of solutions When the What sBest linear solver finds a solution to a linear optimization model that solution is a best solution Such a solution is called a global optimum because there is no better feasible solution By contrast conventional nonlinear solvers are only able to identify local optima i e solutions for which no better feasible solutions can be found nearby What sBest tells you what type of solution you have reached by returning either Globally Optimal or Locally Optimal in the Solution Status field of the status report If a model is nonlinear and the global solver is not used then the statu
96. do not have a license key you can run a Demonstration Trial version of What sBest In addition the box at the bottom of the dialog box supplies the location of the What sBest add in file WBA XLA or WBA XLAM with the necessary accompanying files to run What sBest and the location of the license file LNDWBxxx LIC which has to be in the same location of the add in The capacity and size for the different versions of What sBest are as follows Name Constraints Variables Integers Nonlinear Global Trial Version 150 300 30 30 5 Personal Version 250 500 50 50 5 Commercial Version 1000 2000 200 200 10 Professional Version 4000 8000 800 800 20 Industrial Version 16000 32000 3200 3200 50 Extended Version Unlimited Unlimited Unlimited Unlimited Unlimited ADDITIONAL COMMANDS 135 Toolbar Ribbon Bar In Excel versions 2002 2003 use the ToolBar command to toggle the What sBest toolbar on and off When What sBest is installed the toolbar appears in floating undocked mode as follows The user may then reposition the What sBest toolbar to a preferred part of the Excel window Select the Too Bar command to turn the toolbar off Select it again to turn the toolbar back on A checkmark will appear next to the Too Bar command when the toolbar is on The What sBest toolbar offers rapid one click access to eight of the most commonly used operations The What sBe
97. e it is at the top of the peak or bottom of the valley Algebraically it means that for each variable the partial MATHEMATICAL MODELING 221 derivative is zero Explaining these conditions on models with constraints lies beyond the scope of this help file It suffices to say that the interpretation can be generalized to constrained models There are two primary reasons for the optimality conditions to be reported as uncertain First if the optimum best cell value lies at a discontinuity or a point where the objective function is non smooth the slope is undefined At a point for which the slope is undefined the optimality conditions cannot be said to be satisfied hence they are determined uncertain Second if in the search for a solution What sBest completes several iterations without making any significant improvement in the objective function it will stop even though the optimality conditions are not satisfied This may be a situation in which the objective function is very nearly flat over an unusually large region Whether the optimality conditions are satisfied or uncertain if the solution is locally optimal then another local optimum may exist that improves on the current solution Even though the mathematical conditions to prove optimality may be inconclusive the value returned in the best cell is locally optimal Therefore you should always consider re solving the model with different values for the adjustable cells to
98. five years You ve concluded that to meet these financial obligations he should invest in some very low risk securities such as government bonds You must recommend bonds to buy to minimize his total cost now yet cover his cash flow requirements This is also an example of how to defease debt how to wipe it off the books Background Your client s specific cash flow needs are as follows Year 0 1 2 3 4 Cash Flow Need M 17 0 62 0 23 0 35 0 62 0 In graph form the data look like this 70 00 70 00 GE 60 00 50 00 4 40 00 30 00 20 00 10 00 4 0 00 Year 0 Year 1 Year 2 Year 3 Year 4 SAMPLE MODELS 279 You ve counseled your client to buy government bonds not only because of their low risk but also because a bond owner receives a fixed set of cash payouts For each year until the bond matures your client receives an interest payment and at maturity He also gets back the face value or principal of the bond Generally a broad spectrum of such investments are available on a given day To keep it simple let s assume you come across the following quotations for nine U S Treasury bonds Year to Asking Price Maturit Rate 1000 1 Year 0 996 0 997 2 Year 0 923 0 987 3 Year 0 993 1 061 0 883 4 Year 1 102 0 889 Objective of Optimization Interest Rate 10 5 10 5 10 75 11 2 11 8 12 0 10 0 12 6 10 2 You want to minimize your cl
99. following cell contains an equation with an unsupported reference to SUMIF The first and third arguments to a SUMIF function must be cell ranges with the same shape and size Furthermore all arguments must evaluate to being numeric not text cell address TROUBLESHOOTING 449 Suggestions The SUMIF function requires three arguments as follows SUMIF range criteria sum_range What sBest places the following restrictions on these arguments the range and sum_range arguments must be cell ranges with the same shape and size all arguments must evaluate to being numeric rather than text Refer to the What sBest sample file SUMIFWBSOLVER XLS for an example of valid SUMIF usage TEMPFILE Error Managing Temp Files What sBest makes use of a number of temporary files when solving your model If What sBest encounters a problem managing its temporary files the following error message will be displayed on the WB Status tab Error Message Error Managing Temporary Files Help Reference TEMPFILE An error occurred while attempting to access temporary work files Please delete the following files from the folder containing your workbook LINDOWBS XLS LINDOWBX XLS LINDOWBS XLSB LINDOWBX LINDOWBRC TXT LINDOWBSOLN TXT LINDOWBSTATUS PRN LINDOWBSOLN PRN LINDOWBSTOC PRN LINDOWBSTOH PRN Also verify the access rights on this folder to create files The folder path name should be shorter and may no
100. for solving nonlinear problems are important aids to solving nonlinear problems However if the problem is poorly formulated then the options can only help alleviate the effects of poor formulation The following section provides some suggestions for good formulation of nonlinear problems MATHEMATICAL MODELING 223 Nonlinear Modeling Guideline Nonlinear models can be extremely complex to solve It can pay off in terms of solution speed and reliability to spend a little extra time to make sure the model is formulated in a way that is most efficient to solve This section gives some general guidelines to consider when building and solving nonlinear models Supply Good Initial Values The initial adjustable cell values can affect the path What sBest takes to the solution Starting with initial adjustable cell values near the optimal solution can reduce the solution time In many situations you may not know good initial values However when reasonable values are known they should be used If near optimal values are not known simply starting with values that satisfy all constraints may be helpful Starting from any reasonable answer may be better than starting with zeroes in the adjustable cells Always start with adjustable cell values that avoid undefined values in adjustable dependent equations For example if an equation divides by an adjustable cell then a value of zero for that adjustable cell makes the equation take an undefined
101. guess what the source of the error is then you must resort to unchecking the What sBest add in from the list generated by the Tools Add ins command This forces the removal of the previous unhandled error Now you can return to the add in list and check the What sBest add in to reinstate it You now have another chance to determine the source of the error and insert error handling code 408 CHAPTER 8 Errors from an embedded application In the case of an error running What sBest embedded within a Visual Basic project the Run time error 5 Invalid Procedure Call or Argument message box shown above will be displayed This may be followed by a Run time error 440 Automation Error To correct this problem you will need to terminate the application insert appropriate error handling and run the application again The error handling for an embedded application is distinct from normal error handling for a stand alone Excel application A code sample of this error handling is provided toward the end of the section entitled wbError and Error Codes in chapter VBA Interface Invalid Outside Procedure This is often the result of using parenthesis without the CALL keyword in Visual Basic code Either put the keyword CALL in front of the procedure calls where you use parenthesis or remove the parenthesis ADDINLINK Multiple Add in Links In the case of multiple installations of What sBest the solver may be confused on th
102. in link may be remaining under the name wba that should be deleted INSTALLATION DETAILS 459 Add ins If you wish to disable remove the What sBest add in and menu you may do so by going to the Excel menu s Tools Add ins dialog You can then uncheck the What sBest add in from the list which disables the add in while you are still in Excel When you reopen Excel the WB menu item will not be present The What sBest add in and its menu are reenabled by checking the What sBest add in from the list posted by the Tools Add Jus dialog If What sBest does not appear in the current list of add ins the browse button can be used to locate it The add in file WBA XLA or WBA XLAM can be found in the Library subdirectory or the WB subdirectory on your C drive or elsewhere if you so requested Details are described in Location of the Add in Files and Update Links Please note that it is not possible to disable the What sBest menu if the add in is installed to the XLSTART subdirectory The What sBest functions are only available when the What sBest add in is loaded If you disable remove the What sBest add in from Excel then you must manually re enable it the next time you wish to build or solve a model Note 1 Starting with What sBest release 6 0 1 the add in name is now WBA XLA instead of the former WB XLA name Starting What sBest release 10 0 0 0 the add in name can be either WBA XLA for Excel 2002 or WBA XLA
103. is also a column labeled Trade off Cells which lists the value in each solution of a designated trade off variable Any scalar variable in a model can be selected as the tradeoff variable In this example there are 9 variables and the objective cell WBMAX is automatically selected as a tradeoff variable The idea behind the trade off variable is that it allows you to weigh the trade offs in a model s objective value with a secondary goal In this case our secondary goal is the number of our favorite items in the picnic basket In particular we see that there are three solutions with slightly worse objective values 23 vs 25 that include one of our favorite items For example if we selected the solution Run 2 and pressed the This Selection button we d see the following solution containing one of our favorite items Brownies cell F4 The Take Default button selects the Run 1 which is the solution of the objective cell These buttons allow you to display selected solutions returned by the K Best solver Once a final solution is selected all subsequent status and solution reports will be based on that particular solution Here s an example of the K Best report for the KNAPSACK_KBEST sample model when the option was selected before solving ADDITIONAL COMMANDS 87 H e e e D i Knapsack_KBest xlsx Excel 0 A xX HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys A1 sl fe What s
104. j Well1 Well2 Ref 1 Ref 2 Ref 3 Ref 4 Through PumpA 1 50 3 15 5 00 7 00 0 00 0 00 Well Pumping Costs Refinery Pumping Costs Total Pumping Costs 0 00 SAMPLE MODELS 371 A Determine Adjustable Cells The adjustable cells are the amounts sent from the two Wells to the three Pumps B7 B8 and C7 C9 and the amounts sent from the three Pumps to the Refineries E7 E8 F7 F9 G8 G9 H8 H9 Cells B9 E9 G7 and H7 are fixed cells with a value of zero representing pipelines that are not open B Define Best The best solution to this problem is the one that minimizes Total Pumping Cost in cell E37 The formula in E37 is the sum of the two subtotals for Well and Refinery pumping costs Each subtotal in turn is the sumproduct of pumping costs along each open pipeline from the Wells to the Pumps in the first instance and from the Pumps to Refineries in the second and amounts carried on that pipeline C Specify Constraints The constraints in the PIPELINE model must perform several functions First supply capacity at the Wells must not be exceeded In cells B12 and C12 constraint formulas require that the sum of amounts pumped from each Well is less than or equal to the Capacities B11 and C11 Second the amount received at each Pump must equal the amount pumped out Such constraints are known as conservation constraints To achieve this cells D7 D9 contain constraint formulas forcing the sum of amounts pu
105. link into Excel to execute the functions e Make sure to run Excel version 2002 or later e Make sure Excel is not already busy with another process e Turn off the virus scan for macro applications In the mean time select Retry from the Server Busy window TROUBLESHOOTING 415 HIDSNAME Hidden Solvers Names If the What sBest solver was able to detect hidden names coming from other solvers and belonging to the workbook the following message will be displayed on the pop up window Message Convert Model Format What sBest has found hidden names in this workbook related to non What sBest model format Convert and Solve Try to Solve without Conversion Exit Help Where Convert and Solve will convert these names into a What sBest format for the current selected worksheet and try to solve This will create What sBest style Adjustable Best and Constraint cells in the workbook Try to Solve without Conversion will try to solve as a What sBest spreadsheet without conversion Exit to cancel Help to access the manual Notes You may remove these hidden names or after conversion via the menu What sBest gt Options gt Reset To Default You can alternatively convert these names into What sBest format via the menu What sBest gt Advanced gt Convert Model Format For further information look up HIDSNAME tag in What sBest gt Help gt Index 416 CHAPTER 8
106. lt C1 Or in Excel 2007 C PROGRAM FILES MICROSOFT OFFICE OFFICE12 LIBRARY LINDOWB wba xlam WB A1 lt C1 In the case of the sample model files the prepended path may not coincide with the path to your What sBest add in file For this reason Excel prompts you to update links and after declining this you should use the What sBest Update Links button in the General Options dialog box The Update Links command in What sBest finds the path to your What sBest add in file and then returns the equations to the previous form without a prepended path If you leave the paths in their incorrect form then Excel fails to find your What sBest add in file and it inserts an error code of REF into each of the cells having an incorrect path After updating is completed the workbook sheet should be saved Delete Reports Click on the Delete Reports button to remove the WB Status the WB Solution WB _ Stochastic and the WB Histogram reports from the workbook you have open The next time you solve the model new reports will be generated according to your specifications in the Status Report and the Solution Report drop down boxes You might want to use the Delete Reports button if you have already solved the model and want to save it without the What sBest reports especially when the reports are at the end of many worksheets Options Linear Solver The dialog box posted by the Options Linear Solver command appears as f
107. menu Tools add ins reset the add in by browsing to the right location save the model and restart Excel In some situations you may need to remove the add in from your system to clean up any remaining link in the Excel Add ins list Also you can carefully correct the link by accessing the registry editor from the Windows Start menu then run REGEDIT Usually the links are displayed in the registry folder HKEY CURRENT_USER Software Microsoft Office 10 0 Excel Options In Excel 2007 adjust the security setting from the Excel Options then click on Advanced TrustCenter TrustCenterSettings Enable macros and grant the same access in the Macro Settings tab In case your add in has been digitally signed you will need to enable this add in to run your model In some situations a time delay may occur after enabling the add in Refer to the What sBest sample file Shipping MacroFunctions xls for an example of valid user defined function usage FUNCMACRO Failed to Access the Macro If the What sBest solver is unable to execute a macro that is needed to calculate a user defined function the following error message will be displayed on the pop up window Error Message Failed to Access the Macro Help Reference FUNCMACRO The solver needs to access the VBA code to run the users defined function from Excel Select Trust Access to Visual Basic Project via the Tools Macro Sec
108. model A random cell must use the format WBSP_RAND arg cells where arg is a numeric value or a cell reference to a numeric value and cells is a reference to the cells you want to apply this timing information The cell reference should be to a random cell Also make sure of the staging consistency in the model For more information on using the stochastic feature refer to section Options Stochastic Solver SPREP Stochastic WBSP_REP Format Using the stochastic feature What sBest can return the solution information on any cells These values tell you how sensitive the solutions are to various stages of the model The WBSP_REP function is used to request solution values on variables and outcomes on random cells If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message KE RPROR Stochastic WBSP_REP Format Help Reference SPREP A WBSP_REP cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_REP cells where elle must refer to random or variable cells cell address Suggestions There is an incorrectly formatted Stochastic Report cell in the model A reporting cell must use the format WBSP_REP cells where cells is a reference to the cells you want to report the solutions The cell reference should be to a random or a variable cell For more inf
109. much of each grain S amp R should buy at today s prices to meet their nutritional requirements at lowest cost This always has a chance of being wrong if price fluctuates unexpectedly 260 CHAPTER 7 The Worksheet Let s open the HOGFEED sample file and look over the ABC s f The HOGFEED Worksheet Before Optimization 8 Gleis HOG FEED Microsoft Excel bala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V o Eil ZS Nutrients Per Unit Weight of Grain Nutrients Minimum Dual 1 2 3 4 Supplied Reqd Value 7 Nutrient A 22 3 4 7 2 0 0 Not gt 24 1 00 8 Nutrient B 14 1 1 0 0 0 0 Not gt 0 7 1 00 9 Nutrient C 2 3 5 6 11 1 0 0 Not gt 5 0 1 00 Nutrient D 12 0 11 9 41 8 0 0 Not gt 210 1 00 Cost Bushel 35 00 50 00 80 00 Percentage Unity of Blend 0 0 00 00 00 Not Dual Value 1 00 1 00 1 00 1 00 M 4r HOGFEED 23 D I SI GB 100 gt A Determine Adjustable Cells The cells What sBest is free to change in this model are the Percentage of Blend contributed by each grain C16 F16 B Define Best The best solution to this problem meets nutritional needs at the lowest cost Total Cost J16 contains the formula SUMPRODUCT C16 F16 C13 F13 That s the Percentage of Blend times the Cost Per Bushel for each grain C Specify Constraints There are two limitations on the solution to this problem First the final mix must contain
110. of tab Suggestions A cell is considered nonlinear if it applies nonlinear mathematical operations to quantities that depend on the adjustable cells As an example suppose that cells Al and B1 are both adjustable cells Furthermore suppose that we have the following formula somewhere in the workbook A1 B1 Dividing by an adjustable cell is a nonlinear operation so this term causes the formula containing it to be considered nonlinear For more information on identifying and solving linear and nonlinear expressions see Overview of Mathematical Modeling When possible formulate your models using linear expressions Problems composed entirely of linear relationships solve faster and with a higher degree of confidence Evaluate the formulas in the nonlinear cells to determine if these formulas can be rewritten as linear expressions In many cases a nonlinear expression can be rewritten in an equivalent but linear manner Unfortunately the 434 CHAPTER 8 techniques for doing this are not particularly intuitive Referring to a good text on mathematical programming may be of help In some cases the Linearization capability in What sBest can automatically reformulate your model under the hood to make it entirely linear However linearizing a model by hand is always more efficient Plus if the Linearization feature does not linearize the model completely you may end up with a more difficult model to solve In many cases linear
111. over quadratic cones 252 CHAPTER 6 Quadratic Cone 2 sox y z gt 0 More generally in n dimensions a simple quadratic cone ice cream cone constraint is of the form x0 2 x142 x2 2 xn 2 lt 0 x0 gt 0 Second order cone constraints are more general than they might at first appear For another conic form consider the constraints uv x42 lt 0 u v gt 0 The first constraint by itself describes a nonconvex feasible region colored blue and green illustrated in Figure 2 The three constraints together however describe a convex feasible region colored green only called the rotated quadratic cone MATHEMATICAL MODELING 253 Rotsted Quadratic Cone uv gt x u v gt 0 Te Gaee Figure 2 Rotated Quadratic Cone More generally in n dimensions the rotated quadratic cone constraint in standard form is 2x0 x1 x2 2 x3 2 xn 2 lt 0 x0 x1 gt 0 In both simple and rotated quadratic cones a variable can appear in at most one cone constraint If naturally you would like to have a variable say x2 appear in two cone constraints then you must introduce an extra copy of the variable say y2 for the second cone constraint and then connect the two with the linear constraint x2 y2 0 Notice using a standard transformation rotated quadratic cone constraints can be shown to be equivalent to quadratic cone constraints y u v 2 z u v 2
112. per square inch Objective of Optimization The objective is to determine the specifications of the box with the smallest production cost 268 CHAPTER 7 The Worksheet Let s open the BOX sample file Let s look at how the requirements are translated to the spreadsheet format The BOX Worksheet Before Optimization x Mgr ES is MMM Microsoft Excel kalak File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o El 3 FIG CABINET DESIGN ACTUAL LIMIT Surface Area 6 000 Not gt 888 Length Width Height 1 00 1 00 1 00 Footprint 1 000 lt 252 Volume 1 000 Not gt 1512 Width Height 1 000 Not lt 0 718 Width Height 1 000 gt 0 518 44 gt BOX 2 al il EES A Determine Adjustable Cells The adjustable cells in the BOX model are the Length Width and Height in H8 J8 These cells are further identified as ranges L W and H respectively B Define Best The best solution is the minimum cost cabinet that satisfies all the constraints This objective is calculated in cell 113 by means of the following formula 2 0 05 Length Width Length Height 0 1 Height Width The interpretation of which is The cost of the side top bottom panels the sum of the areas of one side and one top bottom panel the cost of front back panels the area of a front back panel all multiplied by 2 SAMPLE MODELS 269 C Specify Constraints The
113. problem with equations expressing an interest rate of 8 5 085 and budget constraints of 12 850 000 The difference in magnitude between these numbers is on the order of 10 to the 9 1 100th compared to 10 000 000 A difference of 10 to the Ah or less between the largest and smallest units would be preferable In this case the budget could be expressed in units of millions of dollars That is 12 85 to represent 12 850 000 This lowers the difference in magnitude of the units of these numbers to 10 to the 4 1 100th compared to 10 Simplify Relationships Whenever possible use linear rather than nonlinear relationships Some nonlinear expressions can be reformulated in a linear manner A simple example is a constraint on the ratio of two adjustable cells Consider the constraint WB A1 B1 lt 25 where Al and B1 are adjustable cells that each must be greater than zero The relationship A1 B1 is nonlinear If you multiply both sides of the constraint by B1 the constraint becomes WB A1 lt 25 B1 This is mathematically equivalent to the original constraint but it is now a linear rather than nonlinear constraint As much as possible avoid non smooth expressions notably spreadsheet functions like ZF MAX MIN ABS and table lookup functions Models with non smooth relationships are generally more difficult to solve If you can approximate the non smooth relationship with a smooth expression Reduce Integer Restrictions Mi
114. require some of the random variables to be dependent on each other There are several ways of doing this in What sBest You can specify an explicit arbitrary discrete joint distribution table form any of WBSP_DIST_DISCRETE SV table rand_vars Equi probable sequenced vertically WBSP_DIST_ DISCRETE SH table rand_vars Equi probable sequenced horizontally WBSP_DIST_DISCRETE_ SV_W table prob rand_vars Weighted prob sequenced vertically WBSP_DIST_DISCRETE_SH_W table prob rand_vars Weighted prob sequenced horizontally Another common way to characterize dependencies among variables drawn from standard univariate distributions such as the Normal or Poisson is by standard correlation measures What sBest supports three correlation types WBSP_CORR_PEARSON matrix rand_vars Pearson s linear correlation WBSP_CORR_SPEARMAN matrix rand_vars Spearman s rank correlation WBSP_CORR_KENDALL matrix rand_vars Kendall s rank correlation Sampling a Scenario Tree For stochastic programs with infinite event space What sBest offers an easy to use function to create finite scenario trees implicitly with user specified dimensions This is especially handy when there are several stochastic parameters and the task of explicit sampling becomes tedious In this context the user can specify the dimensions of a scenario tree by either of the following methods Specify the number of nodes per stage In this method the user should provid
115. runs is a concern then the Iterations option should be selected Under the Solver Decides setting What s Best chooses the most appropriate strategy What sBest defaults to Solver Decides Probing Level Specify the level to which you would like probing applied to your model with the Probing Level drop down box Level 1 is the lowest level of probing while Level 9 is the highest Setting the Probing Level to None will turn probing off The Probing Level option is applicable to mixed integer linear models Probing examines the integer variables to deduce tighter variable bounds and right hand side values This process is referred to as tightening the formulation and can result in the integer variables taking on values that are closer to being integral when the continuous relaxation of the model is solved Probing can often tighten an integer model enough to dramatically speed solution times In other cases probing cannot adequately tighten a model and the expense of the probing step simply slows down the overall solution time 70 CHAPTER 3 Settings are None no probing Level 1 minimum simple presolving Level 2 probing Level 3 coefficient reduction Level 4 elimination Level 5 dual reductions Level 6 use dual information Level 7 binary row presolving Level 8 row aggregation Level 9 maximum pass ff OHHH Ki The default setting for Probing Levels is Solver decides which results in the s
116. sch sch E EH h sch E sch E sch sch sch sch sch EH CH h sch sch EH sch EH sch sch sch sch COON hh zb ch EA E E EH OO OO OO OO A ch sch zk E OO CEO EH EN ER wh wh EI ER wh wb wh sch sch seh CH CH CH CH CH CH o CH CH CH CH CH Pool Days MAP FXEDI I DER Ready 2 Bam 100 Screen 2 depicts 10 work patterns that incorporate the assumptions and work rules outlined earlier Each work pattern represents an employee working 5 days a week 10 days per two week time period Employees get one out of two weekends off and nobody works more than 4 days at a stretch Cell L16 contains the average daily cost per full time employee and cell L17 contains the average daily cost per pool employee These estimates should be based on accounting and payroll data and can be updated on an as needed basis A Determine Adjustable Cells The adjustable cells are the number of people scheduled according to each work pattern P5 P16 Pool employees can be added to the model by making cells R18 AE18 adjustable and re solving B Define Best The best solution is the one that results in the minimum total cost in cell L19 Cell L6 contains the aggregate requirement level L8 and L9 contain the minimum cost staffing levels with breakdown between full time and pool employees Cell L11 contains the total employees scheduled and cell L19 is the objective of optimization the total cost figure SAMPLE MODELS _ 363 C S
117. see whether another local optimum improves the solution No Feasible Solution Found The message Solution Status INFEASIBLE is displayed in the status report if What sBest was unable to find a solution that satisfied all the constraints If the model is linear then there is no answer that satisfies all constraints If the model is nonlinear then either no feasible answer exists or a feasible answer exists but What sBest was unable to find it For details please see the topic Solution Status No Feasible Solution Unbounded The message Solution Status UNBOUNDED is returned if without violating any constraints the value of the cell to be minimized can be decreased without limit or the value of the cell to be maximized can be increased without limit For details please see the topic Solution Status UNBOUNDED Numerical Error The message Solution Status NUMERICAL ERROR is returned if there was a serious error For details please see the topic Solution Status NUMERICAL ERROR Case 2 Non optimization Models If no best cell has been specified i e there is no objective function there are only two possible outcomes of an attempt to solve the model What sBest either finds a feasible solution or reports that a feasible solution was not found As with nonlinear optimization models if the model is nonlinear there may be a feasible solution that What sBest was unable to find You may want to consider re solving with different initi
118. sharing a directory for Excel data files If What sBest users share a common data directory over the network the data files of one user could be inadvertently overwritten by the data files of another user If this installation is for multiple users it is recommended that the example files XLS be copied to a private data directory for each user Setup Type When prompted for setup type of Default or Specified choosing Specified installation will ensure that you are prompted to confirm the location of the version of Excel you are installing with It also prompts you for the location of the What sBest program files which can be on a local drive or any drive on the network in which you have write privileges Users who wish to accomplish the following Installing What sBest on a network Installing on systems with multiple versions of Excel or Operating a non English version of Windows will need to select a Specified installation 455 456 APPENDIX A If Excel is installed on a network server the What sBest add ins files should be installed and run locally If you have a network license or site license then you can follow the instructions in this section to install What sBest to the server and set up directories for each node If you have questions regarding installation of What sBest the type of license you have or the number of copies licensed to you please call LINDO Systems It is important that
119. should be to a random cell For more information on using the stochastic feature refer to section Options Stochastic Solver SPDIST2 Stochastic WBSP_DIST 2 Format Using the stochastic feature the user has to associate a distribution to a random cell either discrete or continuous The WBSP_DIST function is used to request a two argument distribution If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message KE RROR Stochastic WBSP_DIST 2 Format Help Reference SPDIST2 A WBSP_DIST cell with 2 arguments are incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_DIST arg1 arg2 cells where argl and arg2 are references and cells must refer to random cells cell address Suggestions There is an incorrectly formatted distribution function cell in the model A distribution function cell must use the format WBSP_DIST arg1 arg2 cells where arg and arg2 are cell references and cells is a reference to the cells you want to apply this two argument distribution The cell reference should be to a random cell For more information on using the stochastic feature refer to section Options Stochastic Solver SPDIST3 Stochastic WBSP_DIST 3 Format Using the stochastic feature the user has to associate a distribution to a random cell eith
120. specify the location of the VWBA XLA or WBA XLAM add in file in the WB directory 462 APPENDIX A Uninstall Files There are two ways to uninstall What sBest First you can rerun the executable file used for the initial installation Alternatively you can open the Control Panel of your Windows operating system select the Add Remove Programs icon click on What sBest in the list of programs and click the Add Remove button Both of these ways will redirect you to a common What sBest maintenance window that resembles the following Welcome to the What sBest 64 bit Maintenance Window Please select one of the following Sr Install a Remove Remove will keep the existing license key HINT Control Panel of Windows shows all What sBest to remove nstallShield Cancel Simply click on the Remove Only button Then a dialog box will appear to confirm your choice By clicking Yes your What sBest add in files will be completely removed Selecting No and then Cancel will close the uninstall program After uninstalling the software you might want to verify that Excel has cleaned up its own lists e g Toolbar and Add ins available To do this simply open Excel and choose the Tools Add ins command or the Office Button then Options Add ins If the What sBest add in appears in the list of Add Ins available click on the check box before it An error message should appear informing you
121. status report The warnings are Nonlinearity Present warning that nonlinear functions or formulas are present in the model Nonlinear functions can adversely affect the speed and performance of the What sBest solver When possible nonlinearities should be avoided See Overview of Mathematical Modeling for a discussion of nonlinear relationships No Best Cell warning that no objective best cell is specified for the model The omission of a best cell may be intentional e g in a goal seeking model or unintentional e g in an optimization model Reference to Blank Cell warning that blank cells are referenced in formulas The reference of a blank cell in a formula may be intentional e g summing across a large range that contains a few bank cells or unintentional e g accidentally referencing A21 instead of A12 Unsupported Function warning that an unsupported function appears in the model The value of a cell containing an unsupported function will not be recalculated during the solution process String Argument Present warning that a text argument appears in a function that is expecting a numeric argument Unexpected text arguments are treated as if they have a numeric value of zero Irreconcilable Constraint warning that a violated constraint does not depend upon adjustable cells and therefore cannot be reconciled Infeasible Constraint warning that the debugger feature will list the infeasibl
122. string argument usage STRRES String Result of Formula What sBest supports string cells and arguments under certain conditions but the formula should return a numeric value instead of a string The following warning message will be displayed on the WB Status tab Warning Message String Result of Formula Help Reference STRRES What sBest encountered formulas displaying results in a text form You can use the String Support feature which allows you to use strings as arguments but the formula should return a numeric value instead of a string so their results have been taken to be zero Otherwise you may want to set omitted areas to discard these cells cell addresses listed at bottom of tab Suggestions What sBest may have encountered the following situations on the string support The return value of a formula cell should be numeric rather than text A numeric result displayed in a text form An illegal string operation An omitted string cells or sheets that are not relevant to the model Refer to the What sBest sample file VehicleRouting xls for an example of valid string argument usage SUMIF Unsupported Sumif Usage What sBest supports the SUMIF Excel function only under certain conditions If you use an unsupported variant of SUMIF the following error message will be displayed on the WB Status tab Error Message Unsupported Sumif Usage Help Reference SUMIF The solver has been halted because the
123. successive iterations made without a significant improvement in the objective function in the Iteration Limit for Slow Progress text box In other words if the value has not improved by the Nth iteration N having been set as the Iteration Limit for Slow Progress then the solver terminates the solution process In cases when the model has a flat objective function around the optimal solution a large iteration limit may be required to allow for sufficient iterations to move to the optimal solution The default setting for the Iteration Limit for Slow Progress is 100 Derivatives Use the drop down menu to control the derivative method in the nonlinear solver There are two different methods to use Numerical or Analytical derivatives Numerical derivatives are computed using finite differences There are two choices available Central Differences and Forward Differences Analytical derivatives are computed directly by symbolically analyzing the arithmetic operations in a constraint Again the two choices are Backward Analytical and Forward Analytical By default What sBest uses backward analytical derivatives However different derivatives can improve speed and precision on many nonlinear models Experimenting with the various derivative options may be required to determine which method works the best for a particular model The default setting for the Derivatives is 0 or Solver Decides ADDITIONAL COMMANDS 65 Options Global
124. textbox If this limit is encountered before a solution has been found then the solution search is terminated and if the model contains integer variables the best integer solution found up to that point is returned If this limit is encountered and the model does not contain integer variables the returned solution is meaningless Please note that returning to any previously established best solution may take some time The default value is None signifying that no iteration limit is imposed Runtime Limit You can specify the maximum amount of time in seconds the solver should spend searching for a solution with the Runtime Limit seconds text box If this runtime limit is encountered before a solution has been found then the solution search is terminated and if the model contains integer variables the best integer solution found up to that point is returned If this limit is encountered and the model does not contain integer variables the returned solution is meaningless Please note that returning to any previously established best solution might take some time The default value is None signifying that no runtime limit imposed Constraint Display Select Slack or Indicator to prompt What Beet to return the slack value or indicator display for the constraint cells ADDITIONAL COMMANDS 53 Indicator mode places the sign of the equation gt lt in the constraint cell If an indicator is tightly satisfied De the const
125. the minimum required levels of nutrients This is enforced by a constraint for each nutrient H7 H10 Each constraint will return the Not gt indicator until the minimum requirement 17 110 for that nutrient is met in the Nutrients Supplied column G7 G10 Second the constraint in G16 forces the percentages in C16 F16 to sum to 100 SAMPLE MODELS 261 The Nutrients Supplied cell for Nutrient A G7 contains SUMPRODUCT C7 F7 C 16 F 16 which sums the product of the Percentage of Blend and the amount of Nutrient A for each grain Each grain contains different combinations of each nutrient C7 F10 Now let s solve the model with What sBest to find the optimal solution The HOGFEED Worksheet After Optimization xH 2 e g rf HOGFEED xlsx Microsoft Excel kalak Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o Ss Nutrients Per Unit Weight of Grain Nutrients Minimum Dual 1 2 3 4 Supplied Regd Value Nutrient A 22 3 4 L k 3 77 gt 24 0 00 Nutrient B 14 1 1 0 0 107 gt 0 7 0 00 Nutrient C 2 3 5 6 11 1 p 5 0 gt 5 0 4 55 Nutrient D 12 0 11 9 41 6 21 0 gt 21 0 0 17 Cost Bushel 35 00 50 00 80 00 95 00 Percentage Unity Total of Blend 66 5 1 3 302 00 Cost 48 78 Dual Value 0 00 0 00 0 00 57 88 HOGFEED 7 Mal wv Ti oO D 100 y The What sBest solution has a total cost of 48 78 per bushel of the optimal
126. the Default option only with respect to placement of the add in files It first check if a Library subdirectory already exists but then the setup program lets you choose the most convenient place for locating the What sBest add in files As a reminder you might consider the following folders for What sBest add in files INSTALLATION DETAILS 461 LIBRARY the Library subdirectory of your main Excel directory usually a path ending in Program Files Microsoft Office Office14 Library LINDOWB This LINDOWB subdirectory is the recommended location for installing the What sBest program files XLSTART the XLSTART subdirectory of your main Excel directory Unlike using other location options if installed to the XLSTART directory the What sBest menu cannot be disabled through the dialog box posted by the Excel menu command Tools Add ins WB the What Beet directory where the sample files are installed Note Ifyou are running Excel from a server verify if you have write access to Excel s Library or XLSTART subdirectories In the Windows Registry What sBest creates two keys in the following locations HKEY CURRENT_USER Software LINDO Systems Inc for CheckUpdate Language and Registration Note When you re enable What sBest it appears on the list given by Tools Add ins if the add in is installed to the Library directory If it is not on the list you may use the Browse button on the Add ins dialog box to
127. the demonstration version of What sBest R The Demo version is fully functional but has limited capacity with respect to model size Use this command to input your What sBest license key If you have already purchased a larger version of What sBest you will find your What sBest license key enclosed with your CD Please enter the license key in the text box exactly as it appears including all hyphens and press the OK button If you have requested and received a license key via e mail even a trial key you may copy and paste it directly into the space provided Ctrl C to copy Ctrl V to paste This command can also be used to upgrade What sBest to handle larger problems greater number of constraints variables and integers or to add options to solve other types of problems To upgrade simply obtain a new license key from LINDO Systems and enter it here then select OK If you would like to run the downloaded demonstration version of What sBest 150 constraints 300 variables 30 integers 30 nonlinear variables and 5 global variables just click the Demo button This is a fully functional license but is limited in capacity and will replace any already existing license ADDITIONAL COMMANDS 137 Select OK to erase your previous key and create a trial key otherwise select Cancel Trial Key Capacity Constraints 150 Adjustables 300 Integers Binaries 30 Nonlinears 30 Globals 5 The User I
128. the random variables and of course is not possible in practice For a minimization it s true that EVWS lt EV with the converse holding for a maximization Technically speaking EVWS is a relaxation of the true Stochastic Programming model obtained by dropping the nonanticipativity constraints Possible flag values are Disable False or Enable True The default setting is off the EVWS is not calculated Calculation for Expected Value of Policy Based On Mean Outcome This Expected Value of Policy Based On Mean Outcome EVEM is the expected true objective value if we mistakenly assume that all random variables will always take on exactly their mean values EVEM is computed using a two step process First the values of all random variables are fixed at their means and the resulting deterministic model is solved to yield the optimal values for the stage 0 decision variables Next a the stage 0 variables are fixed at their optimal values from the previous step b the random variables are freed up c the nonanticipativity constraints are dropped and d this wait and see model is solved EVEM is the objective value from this EVWS model Possible flag values are Disable False or Enable True The default setting is off the EVEM is not calculated Calculation for Expected Value of Perfect Information This Expected Value of Perfect Information EVPI is the absolute value of the difference between EV and EVWS This corresponds to th
129. the reduced cost because it is the amount by which the cost of producing that adjustable item would have to be reduced in order to make it profitable The dual values for the adjustable cells can be placed in the model by clicking on the cells to put the information in choosing Advanced Dual entering the adjustable cells in the For Cell Range edit box and clicking OK The dual values can be placed in any convenient location in the spreadsheet ADDITIONAL COMMANDS 115 For illustration we continue with the XYZ model changing the available number of hard drives G17 to 50 and re solving causing the number of Deluxes adjustable cell D5 to drop to 0 and the total profit to be reduced to 15 000 We also requested dual values on our two adjustable cells placing the dual values in cells C6 D6 After re solving we get the following results amas lt gO Zs Microsoft Excel bala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest YV ei o ER X WBDUAL SCS5 0 D WE E F G XYZ COMPUTER CORPORATION PRODUCTION PLAN Standard Deluxe PROFIT 50 0 Co o sam 8 Profit per Unit 300 500 9 10 Product Component Requirements 11 12 Components Quantity Required Total Number Standard Deluxe Usage In Stock 15 Standard Tower 1 0 50 lt 60 16 Deluxe Tower 0 1 0 lt 50 17 Hard Drive 1 2 50 lt 50 18 19 20 21 v 4 gt gt WB Status wi 2 7 gt t
130. the three requirements In B12 F12 yearly production at each plant the sum of car models produced at a given plant is required to be no greater than that plant s capacity For instance the constraint for Plant D B12 is WB SUM B8 B10 lt B11 322 CHAPTER 7 In D15 D17 the total quantity Produced of each auto C15 C17 is forced to be no greater than the quantity required according to that model s demand curve formula E15 E17 The estimates for these demand curves have been supplied by your econometrics department For example the demand curve formula for the Mercurial E16 is 495 13 B16 3 B15 B17 Note that the demand curves for the three makes of auto are interdependent the sales of one influence demand for the other two Finally cell C20 contains the constraint WB B20 gt D20 which forces the average Miles Gallon across the produced quantity of all three makes B20 to be at least 24 The formula in B20 is SUMPRODUCT G4 G6 C15 C17 SUM C15 C17 Note The federal guideline is expressed in miles per gallon The constraint could more properly be expressed as gallons per mile as if each car sold were driven one mile a measure taken of total gallons used and the total cars sold divided by total gallons used This is because using miles per gallon assumes each car running until the fuel tank is empty Obviously the higher MPG car would go further on a tank of fuel skewing the overall production in its f
131. to improve numerical stability The What sBest status tab displays the value of these coefficients and the cells in which they appear Often simply changing units of measure e g dollars to thousands of dollars will be enough to bring this ratio into line Experimenting with some of the solver parameters via the WB Options command may help solve the problem However should this not solve the problem be sure to restore all options back to their default settings You may be able to choose an alternate solver For example with linear models you can choose the primal dual or barrier solver For nonlinear models there are two versions of the standard nonlinear solver a quadratic solver and a global solver to choose from 440 CHAPTER 8 SPCONFLICT Stochastic Conflicting Declarations Using the stochastic feature the user has to associate a stage information to a variable cell The WBSP_RAND and WBSP_VAR functions are used to specify the timing information If the arguments to these functions are duplicated or found to have cross references the following error message will be displayed on the WB Status tab Error Message Stochastic Conflicting Declarations Help Reference SPCONFLICT A Stochastic function cell is incorrectly formatted It appears the argument cell below refers to a cell being specified by other Stochastic functions leading to contradictory declarations Correct the formula and the validity of t
132. to compute new search directions This technique uses a linear approximation in search computations in order to speed iteration times In general the number of total iterations will tend to rise when this method is used However runtimes will tend to be shorter The default setting for SLP Direction is on SLP Solver The nonlinear solver is provided with a SLP Solver The user is advised to try this solver which may offer better performance for some models This option should not be used with the Multistart feature of the Global Solver The default setting for the SLP Solver is off Quadratic Recognition Check the Quadratic Recognition checkbox to have What sBest s nonlinear solver use algebraic preprocessing to determine if an arbitrary nonlinear model is actually a quadratic programming QP model If a model is found to be a QP model then it can be passed to the faster barrier or conic solver Note that the QP solver is not included with the standard version of What sBest but comes as part of the barrier option The default setting for Quadratic Recognition is on Presolve Check the Presolve checkbox to have What sBest s nonlinear solver identifiy and remove extraneous variables and constraints from the formulation before solving In some cases this greatly reduces the size of the model thus reducing the solving time The default setting for Presolve is on Selective Constraint Evaluation Check the Selective
133. to execute it TROUBLESHOOTING 405 If your add in has been digitally signed you will need to enable this add in to run your model then retry the call In some situations a time delay may occur after enabling the add in Also make sure Excel is calling the add in in the right folder In Excel 2002 there is an additional security setting that the user needs to set for accessing and executing a macro from the Solver Select Trust Access to Visual Basic Project via the Tools Options Security MacroSecurity TrustedSources menu Then save the model and restart Excel In Excel 2007 this feature can be set via the OfficeButton ExcelOptions TrustCenter TrustCenterSettings What Excel file format should be used In Excel 97 2003 the file format is XLS with a maximum size of 256 columns and 65536 rows per sheet Staring Excel version 2007 the new format is either XLSX XLSB for workbook or XLSM for macro enabled workbook with a maximum size of 16384 columns and 1048576 rows per sheet You can save your file with any of these formats What 32 bit or 64 bit format should be installed What sBest depends on the bit format of Excel not Windows The bit format is clearly indicated via the File Help menu of Excel For instance you may have installed a 32 bit format of Excel on a 64 bit version of Windows In this case you should install a 32 bit What sBest What sBest 64 bit should be in
134. to which you ve become accustomed Call that 11 your threshold return The return on Asset 2 is below your threshold return of 11 in a couple of scenarios and under Scenario 7 you actually lose money on your portfolio perhaps forcing you to sell the entire baseball card collection While the 19 9 return is very appealing the thought of parting with even some of your baseball cards is frightening You ve decided you would like an average or expected return of at least 13 call this your desired return but you want to minimize the likelihood that you ll have to sell off some of those valuable cards Objective of Optimization The objective is to invest for a profit while minimizing the risk of diminishing your baseball card collection 296 CHAPTER 7 The Worksheet Let s look at the DNRISK sample file The DNRISK Worksheet Before Solving DIN 2 e g rf DNRISK xlsx Microsoft Excel elle File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 CA o El Ss fe Downside Risk Portfolio Model E G H Stock 3 0 0 0 0 Scenario Downside Forcing Return Risk Constraints 14 4 16 9 0 0 0 0 Not gt 10 7 3 5 0 0 0 0 Not gt 32 1 13 3 0 0 0 0 Not gt 30 5 73 2 0 0 0 0 Not gt 19 5 2 1 0 0 0 0 Not gt 39 0 13 1 0 0 0 0 Not gt 7 2 0 6 0 0 0 0 Not gt Average Desired Threshold Budget Investment Return Return Return Equals 100 Percent 0 0 Not gt
135. to zero However you may override this default lower bound of zero on an adjustable cell by making it free Adjustable cells that may assume negative as well as positive values are referred to as free variables To create an adjustable and free cell s specify the cell or cell range you wish to change in the Refers to field Then enter a name in the FREE Names in Workbook field You can choose any combination of letters for your range name Once this is done pressing the Add button causes What sBest to assign a WBFREE range name to the selected cells which will appear in the list on the Free dialog box For instance if you used the name BuySell in the FREE Names in Workbook text box a range name WBFREEBuySell would be assigned to the selected cells If the cells are already adjustable you can make them adjustable and free by following the steps above Alternately if you are removing a free variable designation for a given cell range simply select the name of the range to remove and press the Delete button A negative adjustable cell representing the number of televisions to produce would not be meaningful However there are scenarios in which allowing an adjustable cell to assume negative values would be appropriate For example if you have the ability to either buy or sell a stock you could create a single adjustable cell representing your decision to buy sell shares A positive value would represent the amount to buy and a nega
136. unbounded In an actual production situation there may be constraints other than raw material or component availability such as limited plant capacity or labor supply Excluding any of these could lead to an unbounded solution Also What sBest might give you an unbounded error message if you maximize the wrong cell or maximize the objective cell when in fact you really wanted to minimize it Anytime What sBest finds the objective heading toward infinity you ll receive the Solution Status UNBOUNDED error message For details see the topic UNBOUNDED in Troubleshooting No Feasible Solution Found Linear What if you add a constraint that contradicts one or more of the existing constraints In the XYZ problem if you add a requirement that the number of Deluxe computers to be produced is greater than 60 What sBest will return the Solution Status INFEASIBLE message in the WB Status worksheet The original constraint requires that no more than 50 Deluxe computer towers be used However this new constraint requires production of at least 60 Deluxe computers exceeding the limitation of the first constraint Anytime What sBest can t find a solution to a linear problem that satisfies all constraints you ll see the INFEASIBLE error message By examining the state of the constraints in the returned infeasible solution you may be able to determine how to reformulate and eliminate the source of infeasibility No Feasible Solution Found N
137. uncertainty e Revenue management in the hospitality and transport industries Multistage Decision Making Under Uncertainty Stochastic programs fall into two major categories a Multistage Stochastic Programs with Recourse and b Chance Constrained Programs What sBest capabilities are extended to solve models in the first category namely multistage stochastic recourse models Chance constrained models will be supported in future versions In this chapter the term stochastic program refers to a multistage stochastic model with recourse The term stage time and period are used interchangeably unless otherwise is stated The terms random parameter and stochastic parameter are also used interchangeably Multistage decision making under uncertainty involves making optimal decisions for a 7 stage horizon before uncertain events random parameters are revealed while trying to protect against unfavorable outcomes that could be observed in the future In its most general form a multistage decision process with T 1 stages follows an alternating sequence of decisions and random events decisions events decisions events decisions 226 CHAPTER 6 0 1 in stage 0 we make a decision x0 taking into account that 1 0 at the beginning of stage 1 Nature takes a set of random decisions ol leading to realizations of all random events in stage 1 and 1 1 at the end of stage 1 having se
138. value Start the solve attempt with a nonzero value for that adjustable cell Consider changing the initial values and re solving the model if 1 you suspect there is an answer better than the answer returned by What sBest 2 you know a feasible solution exists even though What sBest returns the message No Feasible Solution Found Use Reasonable Bounding Constraints Adding constraints that bound the upper and or lower values of adjustable cells to fall within a reasonable range of values may help shorten the solution time For example assume you know that reasonable values for an adjustable cell Al are between 500 and 1000 Values outside of this range are not mathematically impossible they just don t make sense Add the constraints WB A1 gt 500 and WB A1 lt 1000 This ensures that What sBest won t waste computation time investigating solutions you would view as meaningless Similarly adding bounds to restrict expressions from investigating values at or very near undefined regions i e division by zero may reduce computation time and increase the reliability of the solution Scale the Model to a Reasonable Range of Units Try to model your problem so that the units involved are of similar orders of magnitude Mathematically manipulating numbers that differ in size by a large amount can increase the computation time and may introduce problems due to round off error 224 CHAPTER 6 For example consider a financial
139. will lead to larger gains in the objective In general the Steepest Edge option will result in fewer iterations However each iteration will take longer The default setting for Steepest Edge is off Starting Point The Gather Information for Starting Point option may be useful when solving nonlinear models This option computes the slack values for the constraint cells and uses these values internally to compute an improved starting point After solving the spreadsheet goes back to the original Slack Indicator display The default value for Gather Information for Starting Point is off Optimality Tolerance Specify the Optimality Tolerance in this text box The nonlinear solver operates by taking each variable and making small changes to assess the rate of improvement in the objective function The nonlinear solver s Optimality Tolerance is a tolerance placed upon that rate of improvement calculation for the objective function If for a given variable the computed value proves to be less than or equal to the Optimality Tolerance then the solver does not attempt further adjustments to that variable s value Decreasing the Optimality Tolerance toward zero will tend to make the solver run longer but may lead to better solutions to poorly formulated or poorly scaled models The default setting for Optimality Tolerance is 0 0000001 64 CHAPTER 3 Iteration Limit for Slow Progress Specify an integer limit upon the number of
140. with a Looping Macro 150 VBA Interface Procedures o oecicaciaiienadi a aea A iia aeaa 151 WbAddAdjustable Give 152 whAddBestStyles Aessen a Seed Eet ender gente 152 Ve tele VUE UE 152 Ve E EE 153 WOBBES EE 154 WIBBIN EE 155 WOCONSTa EE 156 wbDelete een EE 158 wbieleteuWDMenu reira naea daaa a ea areare ta adera 158 Ve BIEN 159 WDError and Error Ee 160 le Ee EE 162 WBEREE EE 168 WBINT fae soa coo et tees hae ane ate E 169 elle 170 whintegerCald EE 171 elle Ee EE 172 Kell Ee EE 173 wblntegerSolverKBestReport sssseessrsesssrrssssrnesrrnnesrennestennastnanentnnnatennestennadnennestnaneanan 174 WIBOMI geen 175 wbResetOptionsToDefaull ccccccceceeseceeceeeeeeeeeeeneeeeeeeeeseseeaeceeeeeeesecsacaeeeeeeeseeennaees 176 wett unchonfZupport nnne st ennn nnmnnn eent 176 wbSetGeneralOptions ecccccccececeeeeeeeceeeceeeeeeeeeeeaeaeceeeeeegcecaaeaeeeeeeeseesnneeeeeeeeteneeeees 177 wbSetGlobalOptions eee 181 whSetlntegerOptions NENNEN ENEE EENS 183 whSetlintegerPreSolverOptions eee ceeeeeeceeeeeeeeeeeaeeeeeeaeeeeeeaeeeseeaeeeseeneeeseeneeeeeeaas 186 whbsetLinearOptions mamerne REENEN cise eae EEN r E a 189 wbSetNonlinearOptions s sessssesseeeeeennrensteetttnrttsttertrtntttsstettttnnn test tnrnnn nnter tnnn nennen tnnt 190 wbSetStochasticOptions ccccccceceeeeeeeeceeceeeeeeeeeceaeceeeeeeesecenaeceeeeeeesecsacaeeeeeeesenennaees 193 wbettochasteGupport nenten nnnn nenet en
141. 0 200 Not lt 950 1 900 250 Not lt 1200 2 400 300 Not lt 1500 3 000 260 Not lt 1760 3 520 250 Not lt 2010 4 020 240 Not lt 2250 4 500 210 Not lt 2460 4 920 140 Not lt 2600 5 200 Time Period Sern an ewhr el ES DS DES WS 1 2 3 4 5 6 H 8 9 d d d d ech On Om P GAb DES DES D OR DR KK Cl KKK ooooocooocceoceo 1 2 3 4 30 M 4 gt gt INVENT 271 Wal Mm Ready 23 fag 100 A Determine Adjustable Cells The adjustable cells D6 F18 are the amounts purchased for each time period from each of the three supply sources B Define Best The best solution to this inventory problem consists of the combination of purchases from each source in each time period that results in the minimum Total Cost H21 The formula in this cell SUM H6 H18 is the sum of period costs Each period cost is composed of the sum of the purchasing and inventory holding costs for that period C Specify Constraints The constraints are that there must be sufficient supply for each time period to satisfy your demand and the capacity of the three suppliers must not be exceeded SAMPLE MODELS 329 The first constraints are found in C6 C18 Look at the formula in C6 WB B6 lt G5 SUM D6 F6 The amount held over from the period before G5 is added to the sum of purchases from the three sources and required to be greater
142. 0 0 3 PlantB 0 4 Not gt 800 D 5 PlantC S6 P Not gt 800 Output Capacity Capacity 0 lt 1200 1800 Costs so S0 Shipping Costs 0 00 PROFIT From ALL PLANTS less SHIPPING COSTS M 4 gt gt Shipping PlantA PlantB PlantC Si Wal Ready w The remaining three worksheets Plant A Plant B and Plant C are the manufacturing plant screens They were built by placing the PRODMIX model into each of the three tabbed worksheets Each sheet represents one of the three manufacturing plants 336 CHAPTER 7 With the exception of steel the starting inventories of all the raw materials are the same as in the original problem The starting inventory of steel for each plant now becomes the amounts shipped from the steel mills to that plant For example the formula in cell J13 of Plant A worksheet Starting Steel Inventory for steel at Plant A is Shipping B6 Shipping F6 Each plant s sheet tells the quantity of each item produced inventory total usage amounts and the profit contribution from that plant The Plant A Worksheet Before Optimization Xlid 9 e g S BLOCK xlsx Microsoft Excel bala Home Insert Page Layout Formulas Data Review View Developer Team What sBest V e o EN es Minimum Steel Requirement Product Resource Requirements Steel Wood Plastic Rubber Glass Paint RA gt Shipping PlantAPlantB lt Pente ta Hal mi Ready amp Bam s
143. 0 Disable 1 Enable Lattice 1 True Lattice is used to enable or disable lattice cuts 0 Disable 1 Enable Lifting 1 True Lifting is used to enable or disable lifting cuts 0 Disable 1 Enable PlantLocation 1 True PlantLocation is used to enable or disable plant location cuts 0 Disable 1 Enable Objlntegrality 0 False Objintegrality is used to enable or disable the 188 CHAPTER 4 objective integrality cuts 0 Disable 1 Enable Basic No 1 True Basic is used to enable or disable the basic cuts 0 Disable 1 Enable Cardinality No 0 False Cardinality is used to enable or disable the objective cardinality cuts 0 Disable 1 Enable Disjunctive No 1 True Disjunctive is used to enable or disable the objective disjunctive cuts 0 Disable 1 Enable Error Codes Description IntPreSolvOpt_BadHeuristicLevelArg Bad Heuristic Level argument IntPreSolvOpt_BadCutoffCriterionArg Bad Cutoff Criterion argument IntPreSolvOpt_BadProbingLevelArg Bad Probing Level argument IntPreSolvOpt_BadMaxCutsPassesArg Bad Max Cuts Passes argument IntPreSolvOpt_BadRelativeCutsLimitArg Bad Relative Cuts Limit argument IntPreSolvOpt_BadCoefficientReductionCutsArg Bad Coefficient Reduction Cuts argument IntPreSolvOpt_BadDisaggregationCutsArg Bad Disaggregation Cuts argumen
144. 0 967 3000 1020 Not gt Not gt Not gt Not gt End Waste In Stock Width Inches 1450 967 3000 1020 Inches 100 16 313 13 055 56 250 26 775 End Waste Cost Per Inch Ft 0 75 Total End Waste Cost 112 392 Total Edge Waste Cost 0 Edge Waste Cost Total Waste Cost 112 392 Per Inch Ft 1 50 HAH CUTSTOCK 27 i al Ready 2 EG 10 In B4 B7 the number of cuts of the 15 inch width is entered for each pattern e g pattern A has no 15 inch cuts and pattern B has two as shown in the schematic on the previous page The total Cut cells B9 E9 display the footage cut to each width In G4 G7 Edge Waste in inches is shown Edge waste is the total of inches cut per pattern subtracted from the stock width of 100 inches End Waste in inches B13 E13 is the amount cut less the amount needed A Determine Adjustable Cells The adjustable cells in this model are the Feet Cut Pattern F4 F7 They contain the number of feet to be cut into each of the four available patterns B Define Best The best solution to this worksheet is the combination of cut patterns that minimizes total Waste Costs while meeting the required footage for each width The value of Total Waste Costs is located in cell E19 and is the sum of the edge waste costs resulting from each cut pattern and the end waste costs of excess footage of any width produced 342 CHAPTER7 C Specify Constraints The constrain
145. 00 00 EXPOSURES REQUIREMENT 1 2 3 4 5 el oof lt 100 7 8 30 CHAPTER 2 In your What sBest model if an adjustable cell representing the advertising expenditure was in cell B3 and D3 was a fixed cell with a value of 10 000 you could enter the constraint formula WB B3 lt D3 anywhere in the spreadsheet to enforce the first constraint We ve entered it in cell C3 where it makes visual sense Likewise in cell C6 the formula WB B6 gt D6 enforces the second constraint What sBest would then optimize so as to satisfy these constraints With B3 selected as the objective to minimize the program will select at least 100 exposures that add up to the lowest possible expenditure With B6 selected as the objective to maximize the program will select the highest number of exposures over 100 whose summed cost is less than 10 000 Alternatively you could do away with cell D3 and use the formula WB B3 lt 10000 The Constraints command lets you enter single cell references in the left hand side and single cell references single cell range names or values in the right hand side of your formula When entering a constraint formula manually you have the additional option of entering an expression which evaluates to a number not an array on either side of the Indicator such as WB B3 B11 lt D3 D11 Constraint Display Using the Constraint option in the Display box under the Options General command you c
146. 013 or Microsoft Excel 64 bit version 2010 2013 with latest Service Packs Microsoft NET Framework 4 0 Hardware Pentium class PC 500 MB of RAM 50 MB of free disk space Make sure you have administrative privileges to install files on your default drive System and Program Files folders An Internet connection is required to download the latest version of What sBest You can also contact LINDO Systems to obtain a copy Additional information can be found via the Help command on the What sBest menu How do I install What sBest add in on my computer If you are installing What sBest from the original CD open the What sBest folder click on setup exe If you downloaded the demonstration version from the website simply run the executable or unzip the zip file and then run the executable Excel should be closed during the install process An installation program will then commence and will verify if What sBest has already been installed If it has you will be asked you if you would like to remove the previous version or to write over it In the next step you will be presented with the standard license agreement for What sBest which you must agree to What sBest will then confirm that your system requirements are adequate If so you will then choose a destination directory for the What sBest sample files Next you will be given a choice between a Default and a Specified setup for the ad
147. 02 7562 637 9 31 Warehouse 3 25946 10534 6750 6274 32 33 Epsilon 0 01 Total Cost 102049 34 M 4 gt WB Status TRAFFIC lt 43 al m SA 10 SAMPLE MODELS 379 Truck Loading File name TRUCK XLSX TYPE LINEAR OPTIMIZATION Application Profile This is an example of the Knapsack class of problems in which a number of things boxes books or Bradley Fighting Vehicles must be efficiently or profitably packed in a container trucks crates or C130 aircraft The objective can be to minimize wasted space in the container to maximize or minimize total load weight or as in this case to maximize the value of the load The Problem in Words You have to decide which items to load on a truck Each item must be shipped in its entirety or not at all 1 e 25 of an item cannot be shipped The Truck Loading problem illustrates a situation in which non integer fractional answers are not acceptable To demonstrate potential problems involved in rounding fractional answers well solve the problem using two different methods In the first case well use What sBest to optimize by the conventional method The solution may suggest fractional answers but we ll just round the fractions to the nearest whole number that does not violate any constraints In the second case well find an integer solution using the binary Integer command Background Items are to be loaded onto a truck with a 10 000
148. 05 B Backsolving 221 Backward analytical 64 Barrier 59 75 Base 304 Best bound 78 Best Button 25 Best cell 9 13 25 none 26 Best command 25 Best dialog box 25 Best Objective Bound 39 Beyond VBA 145 Binary integer variables 2 44 Blending Models 258 BLKCELL 409 BLOCK XLSX 334 Bond portfolio optimization 278 BONDS XLSX 278 Bounding constraints 223 Box Design 267 Box Selection 67 BOX XLSX 267 Branching Direction 67 74 Budget 324 C CALL 408 Capacity 320 344 369 Car pricing 320 Cardinality constraint 46 Cash flow 278 467 468 INDEX Cell best command 26 dual value range 111 Central Differences 64 Chance Constrained Modeling 244 CheckUpdate 139 Classification Data 37 Coefficient Reduction 72 Cold Start 75 Commercial Version 134 concave 27 32 Concavity 218 conic programming 62 251 430 Constraint cells 9 automatic generation of 15 creating 27 Constraint Cuts 71 Constraint Ranges 118 Constraint Related Problems 31 Constraints 134 Button 27 command 27 dialog box 27 Constraints 27 Contacting Lindo Systems 465 Container 379 convert model format 128 convex 27 32 convex 217 Convexity 217 Copyright 2 COS 205 COSH 205 Cost 258 263 267 284 292 313 317 339 344 349 360 369 376 Covariance matrix 288 Crop Allocation 383 CROPALLOC XLSX 383 CUTSTOCK XLSX 339 D Default 4 Define Best 16 Delta 66 Demand 327
149. 0o0o00c0 0c CC CCC E T eeeeeeeeeeee a Oce ceo oo 62626 Kc E e E a E a a e E E o UI Il za c STAFF NEEDS MET Not gt PREFERENCE TOTAL el HAH FIXED2 2 WEI ri Ready 23 B w OVO A total of 10 people need to be scheduled 4 each for Schedules 2 and 8 and 2 each for schedules 3 and 5 Each person s preference score is multiplied by his or her seniority index to get a weighted preference score Employees are assigned to work patterns according to these weighted scores with the highest score employees assigned first The only exception to this rule occurs when assigning an employee with a high score to a first choice It may be necessary to assign employees with low weighted scores to their lowest preferences In such instances the program would assign the senior employee to the second or third choice so as to benefit the junior staff members This is in keeping with the objective of maximizing group preference rather than individual preferences To follow strict seniority in staff assignment just use a different scale for seniority performance scores For example vary the scores between zero and 100 rather than 10 and 20 The first scoring scheme would place a much higher emphasis on senior employees than the latter one You can tailor the model to meet specific needs with only slight modifications in the structure of input data The same is true for the stage 1 model SAMPLE MODELS _ 367 A D
150. 109 5 of the original portfolio value 294 CHAPTER 7 The cash required to buy any asset must come from selling some asset The Proceeds From Sales is calculated in E17 by the formula E7 1 C 7 E8 1 C 8 E9 1 C 9 The constraint in cell F17 WB E17 gt G17 requires the Proceeds from Sales to be at least as great as the Cost of Buys in G17 calculated by the formula F7 1 C 7 F8 1 C 8 F9 1 C 9 Now let s solve the model After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning This warning can be shut off from the General Options dialog box Your solved model now appears as follows i The PORTCOST Model After Solving Cii I es i PORTCOST xisx Microsoft Excel kala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o El ZS fe PORTFOLIO WITH TRANSACTION COSTS c D D WITH TRANSACTION COSTS Transaction Cost Return Rate Begin Sold Bought End Asset1 9 0 1 0 50 0 0 0 28 1 78 1 Asset2 135 1 5 30 0 17 6 0 0 124 Asset3 18 0 20 20 0 11 3 00 87 Covariance Matrix End Value Desired Asset 1 Asset 2 Asset3 Port Return End Value 109 5 gt 109 5 Asset 1 25 0 25 0 0 Asset 2 25 150 0 40 0 Proceeds Cost of Asset 3 0 0 40 0 256 0 From Sales Buys 28 4 28 4 Variance PORTCOST lt J Nal il Sen we O In the optimal solution you are holding 78 1 of Asset 1
151. 12 4 of Asset 2 and 8 7 of Asset 3 These amounts are percentages of the value of your original portfolio You may notice that the percentages add to only 99 2 rather than 100 This is because 8 of the value of the original portfolio has gone to the transaction costs required to shift your investment levels Note also that the variance has been lowered to 20 85 from 35 54 SAMPLE MODELS 295 Portfolio Minimizing Downside Risk File name DNRISK XLSX TYPE NONLINEAR OPTIMIZATION Application Profile An obvious objective and common strategy in investing is to minimize the risk of losing ground This model demonstrates how to accomplish this The Problem in Words You re considering investing in three different assets You need to determine how much to invest in each of three assets to minimize the risk of having to sell your baseball cards Background You have forecasts for the expected return of each asset under seven equally likely scenarios there is a transportation strike interest rates rise or fall crops fail Cubs win the World Series Bulls win NBA finals etc You know that if you invest 100 of your capital in Asset 2 the average return under all possible scenarios your expected return is 19 9 You plan to live on the return from your portfolio After figuring your living expenses you find that a return below 11 will force you to start selling off your beloved baseball card collection to live in the manner
152. 15 0 Target Return 115 0 Variance 19 Return gt Target gt Semi Variance 0 0105 20 Invest Total 100 Downside Risk 0 0572 21 22 4 4 gt gt WB Status PORTSCEN J al i Sp 100 Oy Variance minimizes to 0211 302 CHAPTER 7 Solutions for downside risk and semi variance appear below The PORTSCEN Worksheet After Minimizing Semi Variance Al El PORTFOLIO SCENARIO MODEL M Prob Return Difference Forcing Over Under Constraints 8 3 122 0 7 0 0 0 8 3 118 7 3 7 0 0 8 3 132 4 174 0 0 8 3 93 7 0 0 21 3 8 3 105 7 0 0 9 3 8 3 100 8 0 0 142 8 3 108 9 0 0 6 1 8 3 143 0 28 0 0 0 8 3 105 4 0 0 9 6 8 3 110 9 0 0 41 8 3 101 9 0 0 13 1 8 3 156 5 415 0 0 116 6 115 0 Variance 0 0328 gt Semi Variance Downside Risk 0 0649 After solving the semi variance is minimized to 0089 SAMPLE MODELS _ 303 The PORTSCEN Worksheet After Minimizing Downside Risk GIE KSC PORTSCEN xlsx Microsoft Excel kalak Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o ER S amp S WBMIN e SUMPRODUCT E4 E15 H4 H15 LS E 2 eee F e Wy 1 PORTFOLIO SCENARIO MODEL Asset 1 Asset 2 Asset 3 Return Difference Forcing Scenario 66 124 81 0 Over Under Constraints 130 0 122 5 114 9 116 8 1 8 00 110 3 129 0 126 0 125 3 10 3 0 0 121 6 121 6 141 9 138 0 23 0 0 0 954 72 8 92 2
153. 2 SONE EN 33 Getting the Best Results anaia a a a A e a aS A 36 3 ADDITIONAL COMMANDS ccccceseeececeseeeeeeeeeeeeeeeeneeseseseeeseeeeneeseseeneeseseenenseseeneesnseenaees 41 Options and Solvers a ae ee aee a aaa a aaa ee 41 integers llnteger BiNa ennyien a a a a a e A 43 Integer Names in Workbook cccceeseeeeeee cence ee ceeeeeeeeeneeeeeseneaeeeeeeeaeeeseeeeeeeseneaeeeseenaees 44 R fers UO EG 44 IN El EE 44 GeneraleW BIN E EE scat test ol Deets ete int oa the a nes EE Ee 44 Runtime Concerns in Integer Probleme 44 Integers Special Ordered St nesreci iier A ARAE AE ETERA AI 45 Special Ordered EE 45 Eat elen ee hee ee inten ee ee e ie ee ee dea 46 select Any e EE 47 Listot sel cted CellS watson ieee dese ia ele ee EE 47 Place the Function in Cells cccccccecceeeeeeeeceeeceeeee sees ceaeeeeeeeeeseseaaaeeeeeeeeesanencieeeeeeeeeees 47 Integers S MIACONTINUOUS Siaa EATE S AAA 48 select Any CellS sees AA A A A Ee de 49 List of Selected Be EE 49 Place the Function in Cells ccccccceceeeceeeencceeceeeeeceeeaaaeeeeeeeeeceeeaeaeeeceeeeesancneeeeeeeeeeees 49 ele EE 50 Options G en rals c ce1i 3 cae eege eed ade la ad etd eed dee 51 Feasibility Tolerance deed eect eid de eid ected ee in dd adda nen 52 Iteration BL 52 Runtime LEE 52 Constraint Dis play esinaine heed de end eed andes aisle aint idee ad ele 52 Auto Select Free Int Omit Ranges aesseesssicessneessrre
154. 32 CHAPTER 8 If all else fails you should consider adding more memory to your machine This assumes that you haven t already added the maximum amount of memory possible to your machine In the case where you have already maxed out your machine you will need to reduce the size of the model MODERR Parsing Cell Formula If What sBest can t parse a particular cell formula the following error message will be displayed on the WB Status tab Error Message Parsing Cell Formula Help Reference MODERR What sBest was not able to parse the formula in the following cell cell address additional message Suggestions If a formula contains an unexpected inappropriate or unrecognized operation where a comma is expected instead of the multiplication operator What sBest may not know how to proceed Here is a list of possible causes The formula contains an unsupported combination of cells and areas e g multiplying a range of cells by a numeric value The formula may reference a cell in an error state e g VUM The cell s formula may exploit some feature unsupported by What sBest Some Excel functions need to meet a particular format to be supported by What sBest If the formula still results in this message and the cell is used only for reporting purposes you may wish to place it ina WBOMIT range to force What sBest to ignore the cell TROUBLESHOOTING 433 NAME Unsupported Nam
155. 66 Multistart Attemptsia 2 c21 4 Geesse geess dene Ee needa aaa 66 OPIA Scheele ees cee ea hae eee ene ne ee die a a ie 66 Delta toe ca nea eter aera ee eee ee ee Rete te ee 66 MahiablesBOun eebe eeh ee ek ENT 67 leese as a ee ie een 67 Branching Directions fuss citiedet ee E A de eee i 67 Box Ee NEE 67 Algebraic Reformulation sce esi ege eeschte E 67 Options Integer Pre Solver ariei iaire REEE A IAE EAA AA 68 He ristics Levels nicnn ieir EENEG doch 69 Heuristics Cutoff Criterion assieibeii nsii riein reedride i 69 Probing Level ic ccs0 toni oat er ec end a a al 69 Constraint Cuts 2sc0ic cence teed edit eee SNE EES it ee peed deed eed 71 Options Integer Soler mecusi eie r ae i 73 Branching Utecton deed er iaei ee ind iid e e Cer 74 le El EE 74 e TEE 75 pelt ge edd dae indeed adage aan ie Aa ae ant 76 Re e 77 Usage Guidelines for K Best Solutions 2 00 eceeceeeee cette eee e titres ee teeeeeteeeeeteeeeenneeeeee 82 Options Stochastic SONE A8 E aged EE E reget 88 Stochastic Modeling SUPPO si E e e are eataa E 88 Page Stop 1 Coremodel cette er E EE EE dee 89 Page Step Re UE e e EE 90 Page Step 3 distributions or Correlations ccceeecceeeeneeeeeeecneeeeeeeeeeeeenaeeeeeenaeeeeseeaaes 92 Page Step 4 scenario SAMpling cccccesceeeeesseeceeseseeceenseeeceeteneeseeeedeesenseceeenenseeeeeneanes 95 le NEE 97 Use Preview Window for Scenario Gelechon 104 Page Chance Constrained ccccccscscescces
156. 90 In this problem if the original lower bound is exceeded by one 6 the dual value is reduced to zero Ifthe original upper bound is exceeded 26 or more the number of hard drives in stock is insufficient and the model is infeasible Either way the dual value changes when the range is exceeded In some problems the range of a dual value may be very small or zero When this occurs you may find that different starting solutions result in different dual values This may also indicate that more than one combination of the adjustable cells will result in the optimal value of the best cell In this case your model is said to have multiple optima In any event before making use of dual values in decisions of economic importance you should investigate the range over which they re valid 124 CHAPTER 3 To retrieve dual values for all adjustable and constraint cells without entering dual value formulas in the worksheet you may request a solution report with the Options General command Advanced Omit The dialog box posted by the Advanced Omit command appears as follows l Omit 25 The Omit command allows you to specify a range of cells on the workbook to be ignored by the What sBest solver while it is seeking a solution These omitted areas do not contribute toward any limits What sBest imposes in restricted size versions If used properly omit ranges can decrease the solution time However ca
157. AL COMMANDS 95 Refers To Specify the random cell on which to apply the distribution Alternately you can accept the currently selected cells which What sBest has automatically placed in this box You can also type the correct cell range directly into the text box Place function in cell Specify the cell in which to write the WBSP_ function Alternately you can accept the currently selected cells which What sBest has automatically placed in this box You can also type the correct cell range directly into the text box Page Step 4 scenario sampling Stochastic Support S V Use Stochastic Modeling IT Use Simulation Format Core Stage Distribution Scenario Reports Chance Constrained 4 Enter the scenario sampling information by using the function WBSP_STSC Select range with Column1 for Stages Column2 for Scenarios SAS1 Place function in cell SAS sl Insert Specifications Optimization Method Seed for Random Generator Common Size per Stage J Sampling on Continuous Distribution Only ml o 96 CHAPTER 3 This command allows you to specify the Scenario Sampling information for the stochastic part The general format is WBSP_STSC stages_and_sample_sizes e g WBSP_STC B1 C3 means range B1 B3 lists the Stages and range C1 C3 lists sample size for each stage Sampling with WBSP_STSC has to be specified if the model contains a continuous distribution With a discrete distribu
158. AMPLEWB XLSX Car Pricing A nonlinear pricing model illustrating a case in which sales of products are interdependent PRICING XLSX Media Buying Purchasing advertising media space to meet an exposure target at minimum cost MEDIA XLSX Production Models Multi Period Inventory Management Managing inventory across multiple periods to minimize holding costs while maintaining sufficient stock INVENT XLSX Product Mix Using available resources to manufacture a mix of products that yield the highest profit PRODMIX XLSX PMIXMAC XLSM The Building Block Method Combining production and shipping models into one large model a common approach to problem solving BLOCK XLSX Waste Minimization in Stock Cutting Cutting sheet or coil materials to varying lengths while minimizing waste CUTSTOCK XLSX Plant Locating Demonstrating how to locate plants or warehouse facilities to minimize shipping expenses while meeting demand PLANTLOC XLSX SAMPLE MODELS 257 Staff Scheduling Models Staff Scheduling Meeting personnel needs at minimum cost STAFF XLSX Staff Sched Preferred Assignment Covering staff needs while meeting employee preferences for job or shift assignments ASSIGN XLSX Staff Sched Two Stage Fixed Shift Meeting two objectives in this case minimizing cost and maximizing employee satisfaction in scheduling FIXED1 XLSX FIXED2 XLSX Transportation Models Pipeline Optimiz
159. Attempts 66 N NAME 433 Network installation 4 errors 373 Network models 270 Newsvendor 233 No best cell warning 221 No Feasible Solution Found 221 NOADJ 416 NOBEST 435 NOCONST 435 Node 270 Node Selection 78 None Best 25 Nonlinear 134 Expressions 214 Initial Values 223 Magnitude of Model 223 Modeling Guidelines 223 Models 63 220 223 Models Starting Point 63 Optimization 215 Scaling the model 223 Solver Options Dialog Box 61 Undefined Regions 223 Non optimization Models 2 221 NORMINV 205 NORMSDIST 205 NOT function 207 472 INDEX NPV 205 NUMERICAL ERROR 221 O Objective 14 25 Objective Value 39 Omit Cells 175 Omit command what not to omit 125 what to omit 125 OMIT names in workbook 124 OMITTED 436 Operators 205 12 Optimality 66 76 Optimality conditions 220 Optimality Tolerance 63 Optimization 2 Models 2 Nonlinear 215 optima 220 Optimum Global 215 Local 215 Locally 220 Options and Solvers 41 Options command 50 Options General 51 Options Global Solver 65 Options Integer Pre Solver 68 Options Integer Solver 73 Options Linear Solver 58 Options Nonlinear Solver 61 Options Reset to Default 109 Options Stochastic Solver 88 OR function 207 P Parameters Dialog Box 130 Partial 60 Personal Version 134 PI 205 Pipeline Optimization 369 PIPELINE XLSX 369 Plant Location 72 344 PLANTLOC XLSX
160. BNPHeuristic No 1 BNPHeuristic is an integer indicating GP1 the type of heuristic to use as part of the Branch and Price solver where 1 is GP1 and 2 for GP2 Error Codes Description IntOpt_BadBranchingDirectionArg Bad BranchingDirection argument IntOpt_BadAbsolutelntegralityArg Bad Absolutelntegrality argument IntOpt_BadRelativelntegralityArg Bad Relativelntegrality argument IntOpt_BadWarmStartArg Bad WarmStart argument IntOpt_BadColdStartArg Bad ColdStart argument IntOpt_BadAbsoluteOptimalityArg Bad AbsoluteOptimality argument IntOpt_BadRelativeOptimalityArg Bad RelativeOptimality argument IntOpt_BadTimeToRelative Bad TimeToRelative argument IntOpt_BadHurdleArg Bad Hurdle argument IntOpt_BadNodeSelectionArg Bad NodeSelection argument IntOpt_BadStrongBranchArg Bad StrongBranch argument 186 CHAPTER 4 IntOpt_BadKBestArg Bad IntOpt_BadKBestArg argument IntOpt_BadKBestReportArg Bad IntOpt_BadKBestReportArg argument IntOpt_BadBNPBlocksArg Bad IntOpt_BadBNPBlocksArg argument IntOpt_BadBNPHeuristicArg Bad IntOpt_BadBNPHeuristicArg argument Example If one wished to set all the options the following would work wbSetIntegerOptions 1 000001 00001 3 1 00008 DI 120 0 1 20 1 False 0 1 To set individual options here setting the RelativeOptimality tolerance to 10 named
161. Best 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A B i C D E F fa 1 What sBest 13 0 d 0 Sep 30 2014 Lib 9 0 1889 103 64 bit K Best Re 2 3 DATE GENERATED Oct 14 2014 09 34 AM 4 5 6 REPORTING CELLS 7 Run 8 Knapsack E13 Knapsack F3 Knapsack F4 Knapsack F5 Knapsac De ee 10 1 25 0 0 0 11 2 23 0 1 0 12 3 23 1 0 0 ENN 4 23 0 0 1 SS 14 5 22 0 0 0 15 16 ex WB Status WB Solution WB _KBest Knapsack Ka fa gt 88 CHAPTER 3 Options Stochastic Solver The Options Stochastic Solver command allows you to support Stochastic Modeling via the series of dialog boxes Note The user can directly enter or modify the stochastic functions in the spreadsheet without reopening the dialog box Stochastic Modeling Support By checking this option the model will be processed as a stochastic model Otherwise What s Best will treat the core model even if some stochastic functions are set in the spreadsheet The default setting is False unchecked ADDITIONAL COMMANDS 89 Page Step 1 core model Stochastic Support kd Use Simulation Format Core Stage Distribution Scenario Reports Chance Constrained 1 Design the model with its Adjustable Best Constraint and Random cells Specifications Optimization Method Seed for Random Generator Common Size per Stage IV Sampling on Continuous Distribution Only _ tee x
162. Best the following error message will be displayed on the WB Status tab Error Message Invalid Model Help Reference INVMOD Your model must have at least one adjustable cell and one formula that is dependent upon an adjustable cell Refer to the Getting Started section of the online help to learn how to format a model for What sBest Suggestions The model you are attempting to solve does not have the appropriate formatting for What sBest You will need to identify the adjustable cells identify the best cell and input your constraint cells Refer to section ABC s Basic Functions for details on how to format a model IRRECONST Irreconcilable Constraints If a constraint is violated and it does not depend upon any adjustable cells What sBest will not be able to satisfy the constraint and it is considered irreconcilable In which case the following error message will be displayed on the WB Status tab Error Message Irreconcilable Constraints Help Reference IRRECONST The cells listed below contain violated constraints that do not depend upon adjustable cells and therefore cannot be reconciled These constraints were ignored during the solution process An example of an irreconcilable constraint would be WB 1 lt 0 Please check to see that these constraints have been entered correctly and that all adjustable cells have been specified cell addresses listed at bottom of tab Suggestions A simple e
163. C 1 32 5 Reporting cells WEE Sr WBSP_HIST MATHEMATICAL MODELING 249 The scenario by scenario report is generated on the WB _ Stochastic tab A portion of it appears below H S E ei Q0 SP_FeederMixCCP xlsx Excel 7 P x HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys Al al fx What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w ESS _ B C D E F G a 59 CHANCE CONSTRAINED 1 SI renee 61 SCENARIO SET TYPE TARGET WEIGHT STATUS REFERENCE 62 1 Feeder Mix G10 G 0 8 D Satisfied 63 Feeder Mix G10 64 2 Feeder Mix G10 G 08 D Not satisfied 65 Feeder Mix G10 66 3 Feeder Mix G10 G D D Satisfied 67 Feeder Mix G10 68 4 Feeder Mix G10 G 0 8 D Satisfied 69 Feeder Mix G10 70 5 Feeder Mix G10 G D D Satisfied 71 Feeder Mix G10 72 6 Feeder Mix G10 G 08 D Satisfied 73 Feeder Mix G10 74 7 Feeder Mix G10 G D D Satisfied 75 Feeder Mix G10 76 8 Feeder Mix G10 G 08 0 Not satisfied 7 Feeder Mix G10 78 3 Feeder Mix G10 G 08 D Satisfied 79 Feeder Mix G10 v WB Status WB Stochastic WB _Histogram Feeder Mix Ill D 7 Any of the standard statistical tools in Excel can by used to analyze the scenario data 250 CHAPTER 6 The histogram generated on the WB Histogram tab is H S e m Dis SP_FeederMixCCP xlsx Excel D
164. Decides of bound limit 182 CHAPTER 4 0 Solver Decides 1 None 2 All Variables 3 Selected Variables GlBranchingDirection 0 Solver Decides GlBranchingDirection indicates the branching direction 0 Solver Decides 1 Absolute Width 2 Local Width 3 Global Width 4 Global Distance 5 Absolute Violation 6 Relative Violation GIBoxSelection 0 Solver Decides GlBoxSelection indicates the box selection 0 Solver Decides 1 Depth First 2 Worst Bound 3 Best Bound GlAlgebraicReformulation 0 Solver Decides GlAlgebraocReformulation indicates the algebraic reformulation 0 Solver Decides 1 None 2 Minimum 3 Medium 4 Maximum Error Codes Description GlobalOpt_BadGlStratGlobalArg Bad Global Solver argument GlobalOpt_BadGIMultistartA ttemptsArg Bad Multistart Attempts argument GlobalOpt_BadGlOptimalityToleranceArg Bad Optimality Tolerance argument GlobalOpt_BadGIDeltaToleranceArg Bad Delta Tolerance argument GlobalOpt_BadGlVariableBoundLimitArg Bad Variable Bound Limit argument GlobalOpt_BadGlUseBoundLimitArg Bad Use of Bound Limit argument GlobalOpt_BadGIBranchingDirectionArg Bad Branching Direction argument GlobalOpt_BadGIBoxSelectionArg Bad Box Selection argument GlobalOpt_BadGIAlgebraicReformulationArg Bad Algebraic Reformulat
165. DualLoc No DualLoc is the range or cell where the information is to be displayed If omitted the default is the current selection DualChoice No DualChoice is a string indicating the type of information desired Dual or Dual Value for dual value Upper or Upper Range for upper range and Lower or Lower Range for lower range If omitted the default is Dual For backwards compatibility with earlier versions of What sBest DualChoice also accepts the numbers 1 for Dual 2 for Lower and 3 for Upper Error Codes Description Dual_BadDualsCellArg Bad DualCells argument Dual_BadDualLocArg Bad DualLoc argument Dual_BadDualChoice Bad DualChoice argument Dual_ProtectedSheetError Unable to enter dual formulas on a protected sheet Remarks On integer models dual value information is only of limited use Example To create the dual value for cell E5 in cell F5 enter woDualValue E5 F5 Dual Value To create the upper and lower ranges for cell E5 displayed in cells F6 and F7 respectively enter wbDualValue E5 F6 Upper Range woDualValue E5 F7 Lower Range 160 CHAPTER 4 wbError and Error Codes It is very important to handle any possible What sBest errors using some form of the On Error statement as shown in the code example below when error handling code is in place If a What sBest VBA procedure encounters an error then your code handles the particular error For
166. EASON 21 al D Sp 100 X On A Determine Adjustable Cells The adjustable cells in the model are the Trend in B15 the Base in B16 and the four Seasonal Factors in E15 E18 B Define Best The best cell is the Sum of Squared Error in B19 The formula there is SUMPRODUCT ES E12 ES5 E12 This is the sum of the range of Errors in E5 E12 squared C Specify Constraints The only constraint F19 is the requirement that the Seasonal Factors average to 1 This is enforced by the formula WB E19 G19 where E19 contains AVERAGE E15 E18 306 CHAPTER 7 The equations to calculate the predicted points D5 D12 are of the form Predicted Seasonal Factor Base Point Period Trend The Error terms are the Predicted points minus the Sales data points For example the Error for Spring of Period 1 in E5 is found with D5 CS Now let s solve the model After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning This warning can be disabled from the General Options dialog box Your solved model now appears as follows The SEASON Worksheet After Solving Fal Wdo e us SEASON xlsx Microsoft Excel 777 S ez File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ai o El 3 fe SEASONAL SALES Season Spring Summer Fall Winter Spring Summer Fall Winter Trend Base Sum of Squared Error Period ANON WN
167. EE EN Runtime Limit Reached Help Reference RUNTIME The limit for the maximum runtime was reached before the final solution could be found Check the solution carefully it may be sub optimal or infeasible The runtime limit is set via the WB Options General menu Suggestions The runtime limit is set through the WB Options General menu In some cases the solver may be able to return the best solution found so far after hitting a runtime limit However the same precautions regarding the returned solution apply as when interactively interrupting the solver For more details refer to section Solver Interrupt above The Global Solver for nonlinear model may have limitations when combined with other features such as the Function Support for Excel or User s Defined Functions In such a situation What sBest will display the following warning message and eventually an additional error message on the WB Status tab SOLVERGOP Global Solver Use Error Message Global Solver Use Help Reference SOLVERGOP The Global Solver does not proceed when a User Defined Function or an Unsupported built in function is found in the instruction list You may turn off the Function Support via the Advanced menu cell address TROUBLESHOOTING 439 Suggestions The Global Solver needs a complete understanding of the function in the search of a global optima Functions that are not supported by default cannot provide any valuable detail
168. EMATICAL MODELING 227 Recourse Models The decision taken in stage 0 is called the initial decision whereas decisions taken in succeeding stages are called recourse decisions Recourse decisions are interpreted as corrective actions that are based on the actual values the random parameters realized so far as well as the past decisions taken thus far Recourse decisions provide latitude for obtaining improved overall solutions by realigning the initial decision with possible realizations of uncertainties in the best possible way Restricting ourselves to linear multistage stochastic programs for illustration we have the following form for a multistage stochastic program with 7 1 stages Minimize or maximize c0x0 Fl clxl ET c2x2 ET cTxT Such that A00x0 b0 A 1 10x0 A l 11x1 ball A l 42 20x0 A l 2 21x1 A l 2 22x2 b ul u2 2 A ul uT T0x0 Al UT Tixl A ul uT TT xT b l T T LO lt x0 lt U0 Loi lt xl U l l L i Af lt xT lt U wl u7 T where 1 2 f represents random outcomes from event space 1 Uf up to stage t A ul u tp is the coefficient matrix generated by outcomes up to stage t for all p 1 t 1 7 c ul ut t is the objective coefficients generated by outcomes up to stage t for all t 1 7 bot art is the right hand side values generated by outcomes up to stage t for all t 1 T Lo
169. FACE 187 variable bounds and right hand side values In many cases probing can tighten an integer model sufficiently to speed overall solution times 0 Solver Decides 1 None 2 10 increasing levels of probing MaxCutsPasses 200 MaxCutsPasses sets the maximum number of iterative passes through a model determining appropriate constraint cuts to append to the formulation RelativeCutsLimit 0 5 RelativeCutsLimit is a fractional value imposing a relative limit on the number of constraint cuts that are generated The default limit is set to 0 5 times the number of true constraints in the original formulation CoefficientReduction No 1 True CoefficientReduction is used to enable or disable coefficient reduction cuts False Disable True Enable Disaggregation 1 True Disaggregation used to enable or disable disaggregation cuts False Disable True Enable FlowCover 1 True FlowCover is used to enable or disable flow cover cuts 0 Disable 1 Enable GCD 1 True GCD is used to enable or disable greatest common denominator cuts 0 Disable 1 Enable Gomory 1 True Gomory is used to enable or disable Gomory cuts 0 Disable 1 Enable GUB 1 True GUB is used to enable or disable generalized upper bound cuts 0 Disable 1 Enable KnapsackCover 1 True KnapsackCover is used to enable or disable knapsack cover cuts
170. FEED solution in the previous example because you have compensated here for the variability in the amount of Nutrient D in the various component grains It s now necessary to use the relatively more expensive Grain 4 rich in Nutrient D to reach a 95 confidence in fulfilling all your nutritional requirements D Dual Values Dual values are included in two locations in this worksheet C20 F20 and J7 J9 J11 The dual values in cells J7 J9 J11 show the shadow prices or reward how much money you would save if each respective requirement 17 19 I11 is relaxed by one unit This means for example that you would save 97 per bushel if the requirement for Nutrient C is reduced to 4 A reduction to 4 9 saves you 0 97 If slightly less sprightly hogs are tolerable in return for such a saving relaxing this nutritional requirement would be a good decision Note that the dual values are zero for Nutrients A and B Lowering the requirement by one unit offers no savings because there is already an excess of Nutrients A and B in your optimum blend since constraints H7 and H8 are not tightly satisfied The other dual values in the Swine amp Roses model C20 F20 show the amount by which the price of an unused grain would have to be reduced before it would be cost effective to use it in the minimum cost blend For example the dual value for Grain 2 is 11 62 D20 This tells you how much the price 266 CHAPTER 7 of Grain 2 would have to be reduc
171. GUCHION osida d ie abd etch cee i ehaatulemeandes ebb dat e a E E devs cae 373 eelere Mei e UE 373 Traffic Congestion Cost Minimization 0 ec eeceeceeneeeeeeeeneeeeeeaeeeeeenaeeeeeeaeeeeeeaeeeeeenas 376 eelere Neie UE 376 PUCK Loading WEE 379 eelere Neie UE TE 379 Crop Allocation Under Uncertainty 00 0 0 eccceceeeeeeeeeeeeneeeeeeaeeeeeeaeeeeeeaeeeseenaeeeeeeneeeeneaas 383 eelere Nie UE 383 Put ee EE 390 Application Be UE 390 8 TROUBLESHOOTING ir cccisccceevstecacessetteeesstitecessictenevetetaeesstueitecvstetacestbeteeeveetieesstusenessiee 399 FAQ Frequently Asked Questions sssssseesesiresetrrssttrrstttrrstttntssttnrattenttstennastennnattnnnneen 399 Error Messages A Waminge 406 Errors trom VBA GOde ebe Ee ege ee een 406 R ntime Etage see ad fate cate e a EES alte 407 Errors from an embedded application 408 Invalid Outside Procedure ececcceceeceeceeeeeeeeeeeeeeeeeeeeeeeseeeeeeeseeeeeeeeeneaeeeseeeaeeetenaeeeeeeaeeees 408 ADDINLINK Multiple Add in Links 0 00 2 cece enneee ee eeneee ee enneeeeeteeeeetaeeeeeteeeeeeneeeeee 408 ARITHERR Arithmetic Error 409 BLKCELL Blank Cell Warnie A Ga a aea 409 ENTIRERANGE Entire Range Gelechon 410 EXLVER Excel File Format 410 FORMULA Formula Parsing 0 c ccceceeececeeeeeeeeeeeeeeeeeseneeeeeseeaeeeseneaeeeseneaeeesenaeeeeeeeaees 411 FORMULA2 Unsupported Functions cccceceeeeeeecceeeeeeeeeceeeaeceeeeeeeseceeeaeeeeeeeeeeensaees 411
172. HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys Al S fe Investment Planning for Going to College After y G H J K L M N 0 Q fa 4 vealth under goal Step 2 Time stage specifications for 5 unit over goal Random variables Decision variables 6 7 Investin 8 Stocks Bonds 9 0 0000 0 0000 10 0 0000 0 0000 11 0 0000 0 0000 Step 3 Distribution specifications 12 Growth factor distribution 13 equally likely 14 Scenario _ Stocks Bonds 15 A 1 25 1 14 16 B 1 06 1 12 17 18 Step 4 Sampling specifications by stage 19 Stage Scenarios 20 1 2 22 22 3 2 23 24 Step 5 Reporting specifications 25 26 v Model 4 gt READY 5 Stepping through the five steps again for this multistage example Step 1 The core model is described in the range A3 H16 The growth factors for Stocks and Bonds are in columns B and C They will be declared random in step 2 below The beginning wealth before each allocation decision is given in column D At the beginning it is a constant 55 In subsequent periods the wealth available comes previous period investments and is given by the formulae D10 SUMPRODUCT G9 H9 B10 C10 D11 SUMPRODUCT G10 H10 B11 C11 D12 SUMPRODUCT G11 H11 B12 C12 The decision variables of how much to invest in Stocks and Bonds each period is in columns G and H The total amount invested is computed in column F and is given by F9 SUM G9 H9 F10 SUM G10 H10 F11 SU
173. I D x HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys 25 26 5 ba 5 02 01s 27 0 05 28 o T T T T E 1 Al v f What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A B c D E F 14 20 430957 2155974 20 995348 0 25 15 21 724971 22 654016 22 189493 0 3125 16 22 753934 23 795286 23 27461 0 25 17 24 943247 25 05928 25 001263 0 0625 18 19 20 Histogram 21 0 35 22 23 o 24 29 19 82393 20 995348 22 189493 23 27461 25 001263 30 PROTEIN_AMT 31 WB Status WB _Stochastic WB Histogram Feeder Mix H m 30 Notice that even though the driving random variable Protein amount has a Normal distribution The solver writes a series of solution in the created tab WB Stochastic and WB Histogram with the expected value and displays the first default scenario or a selected scenario on the spreadsheet MATHEMATICAL MODELING 251 Solving Second Order Cone Programs The optimization capabilities of What sBest extend to the solution of second order cone problems SOCP of the following form Optimize AO x bO c0 x subject to Aix bi cix di 0 for i 0 1 m 1 Lj lt xj lt Uj forj 0 1 n 1 xj is integer for j in a specified J C 0 n 1 where Optimize is either minimize or maximize Ai are mat
174. If Alpha is set to 1 the forecast for the next period is based entirely on the actual value from the last period If Alpha is set to 0 the actual value from the last period is completely ignored Since neither of these cases will provide much insight into future data wel constrain Alpha to be between 01 and 99 The Problem in Words In order to minimize costly overstocking and inventory holding your retail outlet needs useful predictions of future sales Background For this simple exponential smoothing problem you have sales data in 1 000 s for eight months You need to find Alpha the smoothing constant that minimizes the sum of the error which in this case is the difference between the actual and predicted sales for each period Objective of Optimization The objective is to determine projected sales and the Alpha smoothing constant while minimizing the squared error SAMPLE MODELS 309 The Worksheet Let s look at the supplied sample file called SIMXPO The SIMXPO Worksheet Before Solving EI ld a Anil LS nis SEO ale Microsoft Excel aaa File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 CA o El Ss fe Simple Exponential Smoothing E E G H Squared Sales Predicted Error 10 10 000 0 000 14 0 000 196 000 12 0 000 144 000 19 0 000 361 000 14 0 000 196 000 21 0 000 441 000 19 0 000 361 000 26 0 000 676 000 nng 2 3 Alpha 0 000 Lower bound No
175. L Register 1 Adjustable Best Constraints Solve ge Equal To gt Advanced W About Check Update Model Definition Settings _Solvers Information Services Al e f b 3 J a FA OD OL Ee 2 SWINE amp ROSES Hog Farm 3 ES Nutrients Per Unit Weight of Grain Nutrients Minimum Dual 5 Item 1 2 3 4 Supplied Regd Value 6 PC Nutrient A 22 34 7 2 15 0 0 Not gt 24 1 00 8 Nutrient B 14 11 0 0 0 8 0 0 Not gt 07 1 00 9 Nutrient C 23 56 11 41 1 3 0 0 Not gt 5 0 1 00 E 10 Hutgent D 12 0 n3 41 8 52 1 0 0 Not gt 21 0 1 00 11 12 13 Cost Bushel 35 00 50 00 80 00 95 00 14 15 Percentage Unity 16 of Blend 0 0 0 0 00 0 0 Not 17 18 Dual Value 1 00 1 00 1 00 1 00 v M 4 gt M HOGFEED 2 Wal D EERI Rean LEI DIR we V O 6 CHAPTER 1 In Excel version 2002 the menu and toolbar show as follow Ed Microsoft Excel HOGFEED XLS SI File Edit view Insert Format Tools Data Window WB Help LG Geneva 10 KX KX I 7 lt s aere B Z U 7 fe SUMPRODUCT C16 F16 C13 SWINE amp ROSES Hog Farm Nutrients Per Unit Weight of Grain ltem 1 Nutrient A Nutrient B Nutrient C Nutrient D Cost Bushel 35 00 50 00 80 00 95 00 Percentage of Blend 0 0 00 00 00 Dual Value 1 00 1 00 1 00 1 00 Nutri Adjustable Best Constraints Solve Integers Options Advanced Locate Help About What sBest ToolBar Upgrade Register
176. LESHOOTING 435 NOBEST No Best Cell Most What sBest models will have an optimization objective i e a best cell It could be profit maximization cost minimization or some other criterion that is a function of the adjustable cells So when a model does not contain a best cell the following warning will be displayed on the WB Status tab Warning Message No Best Cell Help Reference NOBEST Either no cell has been specified to be maximized or minimized or the cell that is marked is not a function of any adjustable cells If this is an optimization model use the Best command or the Minimize or Maximize toolbar button to specify a best cell as the objective of the optimization This warning can be turned off via the WB Options General menu Suggestions If you failed to indicate a best cell before solving specify a cell to be maximized or minimized and re solve Refer to section The ABC s Three Steps to What sBest for information on how to identify a best cell Occasionally you may have models that don t require a best cell where all you want to do is find a set of values for the adjustable cells that satisfy all the constraints In this case you should disable this warning by clearing the No Best Cell checkbox on the General Options dialog box NOCONST No Constraint Cells Most What sBest models will have at least one and most likely many constraints on the adjustable cells Constraints place limitations on t
177. LINEAR OPTIMIZATION Application Profile This example demonstrates how one might develop a model for estimating construction costs as well as performance gains resulting from What sBest s exclusive linearization option Note we classify this model as both nonlinear and linear As you will see the model as formulated is nonlinear However after invoking the linearization option in What sBest the solver automatically converts this nonlinear model to an equivalent linear model The Problem in Words You are a contractor specializing in home construction You have the opportunity to bid on a job that involves building a number of homes in a new housing development In order to place an intelligent bid you need to calculate your expected cost on a per home basis Based on past experience you know the following three factors primarily determine the construction cost of a house total square footage number of bedrooms and number of baths You believe there is a linear relationship between these three factors and total cost Specifically you have come up with the following equation Total Cost B B Sq Feet B Bedrooms B Bathrooms i You pull up the following historical data from projects your company has completed in the past Sq Feet Beds Baths _ Cost 000 1500 1 1 78 5 1600 1 1 105 8 2200 2 1 149 1 2600 3 2 173 8 3000 3 2 224 4 3500 5 2 267 0 4000 4 4 302 7 5200 2 3 302 0 8200 4 4 438 7 8700 6 4 490
178. M G11 H11 We require the amount invested each period to equal the amount available This is enforced by the constraints in column E E9 WB D9 F9 E10 WB D10 F10 MATHEMATICAL MODELING 239 E11 WB D11 F11 The amount over goal at the end is computed with D15 D12 D3 D14 The constraint in E15 constrains this to be nonnegative E15 WB D15 gt F15 The amount under goal is in D15 The net utility to be maximized is given by D16 D5 D15 D4 D14 Step 2 We specify cells G9 H9 as a stage 0 half stage decision variable by inserting the expression WBSP_VAR 0 G9 H9 into cell L6 We specify cells B10 C10 as stage 1 random variables that are observed at the beginning of stage 1 by inserting in cell J7 the expression WBSP_RAND 1 B10 C10 Similar expressions are in cells L7 L8 L9 J8 and J9 for the remaining stages 1 to 3 The cell D14 is the recourse decision adjustable at stage 3 WBSP_VAR 3 D14 Step 3 We tell What sBest that the growth factors have a joint discrete distribution as listed in the scenario table 13 T 14 by inserting the expressions WBSP_DIST_ DISCRETE _SV M15 N16 B10 C10 WBSP_DIST DISCRETE _SV M15 N16 B11 C11 WBSP_DIST DISCRETE _SV M15 N16 B12 C12 into cells J12 J13 and J14 Step 4 We tell What sBest how many scenarios to use in each stage 1 e the sample size by inserting the expression WBSP_STSC L20 M22 into cell J19 Step 5 We specify that we want a scena
179. M for Excel 2007 Note 2 Add ins library and executable files from LINDO Systems are digitally signed 460 APPENDIX A Location of the Add In Files and Update Links If you have already installed What sBest then you can check the location of the add in files WBA XLA or WBA XLAM at the bottom of the About What sBest dialog box The installation program will detect if a previous release of What sBest has been installed Thus it will ask if you wish to remove it first or want to write over it Location of the Add in Files and Update Links Your choice of the Default installation option during the setup program will automatically transfer the program files to the Library subdirectory of your main Excel directory usually C Program Files Microsoft Office Office10 Library LINDOWB for Excel 2002 or in C Program Files Microsoft Office Office14 Library LINDOWB for Excel 2010 You will find the following files CONOPTx DLL LIBIOMPS5MD DLL LINDOx_0 DLL LINDOCU_xx DLL LINDOPRx DLL LINDOWBEF DLL LINDOWBIL DLL LNDWBxxx LIC MOSEKx _0 DLL MXST32 LIB README WRI VCREDIST_x86 EXE WBA XLA Excel 2003 or WBA XLAM Excel 2007 and later WBINTR XLS WBOPT DLL WBOPTLINK EXE WBUNCHADD EXE The Help file will be stored in the same directory LINDOWBHELP CHM Finally sample workbooks will be installed in C WB The 64 bit files are identified with the 64 inside the file name The Specified installation differs from
180. MAL WBSP_HIST 21 a 22 Chance Constrained section 23 WBSP_CC_GT 0 8 lt lt Prob Protein constraint satisfied e FeederMix fl ID MATHEMATICAL MODELING 247 For this specific problem the five steps mentioned earlier are Step 1 The core model is described numerically in the area B7 toH11 Step 2 We specify cell B7 E7 as a stage 0 decision variable by inserting the expression WBSP_VAR 0 B7 E7 into cell J7 We can enter this expression directly or using the Stochastic Support dialog box We specify cell B10 E10 as a stage random variable by inserting the expression WBSP_RAND 1 B10 E10 into cell J10 Step 3 We tell What sBest that the protein coefficient has a Normal distribution with different Means and Standard Deviation by inserting the 4 separated expressions WBSP_DIST_ NORMAL B15 B16 B10 into cell B17 WBSP_DIST NORMAL C15 C16 C10 into cell C18 WBSP_DIST_ NORMAL D15 D16 D10 into cell D19 WBSP_DIST NORMAL E15 E16 E10 into cell E20 Step 4 We tell What sBest how many scenarios to use in each stage ce the sample size by inserting the expression WBSP_STSC J15 K15 into cell J14 Step 5 We specify that we want a scenario by scenario report on the Protein amount against its cosntraint by placing the expression WBSP_REP F7 F10 H10 into cell J19 We request a histogram of Protein Amount by placing the expression WBSP_HIST 0 Feeder Mix F10 into cell J20
181. MATHEMATICAL MODELING 229 The SP_ NEWSVENDOR Worksheet before Optimization part 1 H ce Lei TN SP_NEWSVENDOR xlsx Excel 2 P D x HOM INSER PAGE FORM DATA REVIE VIEW DEVEL Team What Lindo Sys D Al H fe Stochastic Scenario Optimization Y A B c D E F G a Stochastic Scenario Optimization cif Newsvendor Normal Demand Given all costs and prices in Stage 0 we must decide how many newspapers to stock Stage 1 in the beginning unknown demand is revealed to us Stage 1 atthe end we compute our sales and the resulting profit Step 1 Core model Co JO mb UNa 10 11 lt Stage 0 decision 12 lt lt Stage 1 random demand 13 lt Stage 1 recourse decision 14 lt lt Stage 1 constraint 15 lt Stage 1 decision and constraint 16 lt Stage 1 non negativity constraint 17 Stage 0 cost computation 18 lt lt Stage 1 holding cost computation 19 Stage 1 shortage cost computation 20 lt lt Stage 1 revenue computation 21 22 lt Stage 1 expected value maximize Model Scenario Tree CH fT ID 230 CHAPTER 6 The SP NEWSVENDOR Worksheet before Optimization part 2 D H e I Al DCK d to us ulting profit Core model SOON none w 11 lt lt Stage 0 decision 12 Stage 1 random demand 13 lt lt Stage 1 recourse decision 14 lt lt Stage 1 constra
182. ML m Sm 10 O Q A Set Adjustable cells This lets What sBest know that the spreadsheet cells denoting Quantity to Produce C5 D5 are the variables and can therefore be adjusted as What sBest seeks an optimal answer B Define Best As XYZ s goal is to maximize profit the total profit G6 was specified as the objective of optimization This calls for maximizing the value of the formula in cell G6 through manipulation of the values in the adjustable cells C5 D5 C Specify Constraints XYZ s limitations are simply that Total Usage of inventory parts E15 E17 be less than or equal to the total Number in Stock G15 G17 These constraints are specified by means of the formulas in F15 F17 GETTING STARTED 17 Now you are ready to solve the XYZ model with What sBest When you choose Solve from the WB menu or press on the toolbar the What sBest solver is started and the solver status window appears like the one shown below LINDO Systems Inc zi a Copyright 2014 64 bit What sBest 13 0 0 2 Oct 24 2014 Lib 9 0 1905 120 Extended License m Solver Status Model Type State Tries Infeasibility Objective Classification Statistic Category Current Maximum Numerics Adjustables Integers Bin Formulas Constraints Nonlinears Coefficients Obj Direction m Extended Solver Solver Type Best
183. N function is a nonlinear function so this formula causes A1 to be considered a nonlinear adjustable cell On the other hand multiplying an adjustable cell by a constant is a linear operation so this formula alone would not make B a nonlinear adjustable cell For more information on identifying and solving linear and nonlinear expressions see Overview of Mathematical Modeling Evaluate the formulas in which the nonlinear adjustable cells appear to determine if these formulas can be rewritten as linear expressions If this is not possible you will need to either reduce the size of your model or upgrade to a larger version of What sBest When possible formulate your problem using linear expressions Problems composed entirely of linear relationships solve faster and more reliably However in many cases linear reformulation may not be possible If your model contains inherently nonlinear expressions you may choose to turn off this nonlinear warning with the Nonlinearity present checkbox in the General Options dialog box All versions of What sBest are supplied with a linear solver The downloadable and Solver Suite versions of What sBest provide a nonlinear solver with capacity for a few nonlinear adjustable cells For the Commercial and more powerful versions of What sBest the nonlinear option may be purchased from LINDO Systems LICCAPS Global Adjustable Cell Limit If your model has more nonlinear cells than is allowed for your li
184. NDOWBS XLS LINDOWBX XLS LINDOWBS XLSB LINDOWBX LINDOWBRC TXT LINDOWBSOLN TXT LINDOWBSTATUS PRN LINDOWBSOLN PRN LINDOWBSTOC PRN LINDOWBSTOH PRN LINDOWBKBST PRN How do I fix the Error in Auto_add 5 Invalid procedure or call argument error message This error will appear when an Excel function or VBA statement cannot be executed properly In the case of What sBest this is typically due to missing program components Attempting to attach the What sBest add ins over a network can lead to this problem in that not all of the What sBest add in files will get copied to the local machine For this reason we recommend installing What sBest on every platform you intend to use it on Running a complete install on each machine will guarantee that all the correct add in files are copied to the correct folder How do I fix the Error in returning solution in cell error message Usually this error appears when What sBest could not access the worksheet in order to copy the solution back to the adjustable cells or the temporary solution file could not be read First verify that your worksheet is not protected or locked Also make sure Excel is calling the right add in in the Library folder When using Function Support the system seems to hang with the message Server Busy Usually this Windows message appears when a Microsoft Office component could not access the add in in order to read it and
185. Obj Obj Bound Steps Activity Extracting Data Reading File r Elapsed Runtime 00 00 01 I Active The solver status window contains useful information about the properties of your model and the Hold Interrupt Help progress of What sBest toward a solution The information about model properties will also appear on the WB Status worksheet tab added to your workbook after the model is solved so don t worry if the window doesn t remain long enough for you to read the information it contains See the Solve section for detailed information about the solver status window 18 CHAPTER 1 The worksheet soon reappears indicating the highest possible profit The XYZ Worksheet After Optimization XW 3 50l E xyzxlsx Microsoft Excel bala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o Eil Za ag COMPUTER CORPORATION PRODUCTION PLAN Product Standard Deluxe Quantity to Produce 60 30 Profit per Unit 300 500 10 Product Component Requirements 11 12 Components Quantity Required Total Number 13 Standard Deluxe Usage In Stock 14 15 Standard Tower 1 0 60 lt 60 16 Deluxe Tower 0 1 30 lt 50 17 Hard Drive 1 2 120 lt 120 18 19 H 4 gt m WB Status WB Solution XYZ 3 pal e EEE ECTS The What sBest solution yields the best possible profit attainable given your resources an
186. Open No ExcelOpen is a True False flag to indicate whether Excel should remain in the open state or be minimized True to leave Excel open False to minimize Excel If this argument is omitted it defaults to the value of the Minimize Excel on Solve setting in the General Options dialog box NoErrDialog No Any argument e g an integer passed causes all What sBest error dialog boxes from the wbSolve routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number This is useful in an embedded application of What sBest MACROS THE VBA INTERFACE 197 Error Codes Description Solve_UnmappedDrive Error on drive Solve_NoDLL Error on DLL to access Solve_BadSolutionStatusArg Bad SolutionStatus argument Solve_BadExcelOpenArg Bad ExcelOpen argument Solve_MultipleMaxMinError More than one cell is specified as the objective cell Solve_ProtectedWorkbookError Protection can not be on the workbook only on worksheets Solve_ReadLINDOWBRCError Error reading temporary file LLINDOWBRC TXT Solve_SaveTempFileError Error saving a copy of the active workbook Solve_SymbolinSheetNameError Error on sheet name Solve_MinimumFileFormatError The active workbook must be an Excel 8 0 BIFF8 or Excel 97 format or higher Solve_UnableToLoadSolverError There was a probl
187. PTION XLSX TYPE NONLINEAR OPTIMIZATION STOCHASTIC Application Profile The holder of an American put option has the right to sell a specified stock at any time the American feature between now and a specified expiration date at a specified strike price The holder makes a profit in the period of exercise if the strike price exceeds the market price of the stock at the time of sale Wealth is invested at the risk free rate and the stock return for a specific period is the uncertain parameter This is a multi period stochastic problem under the uncertainty of a stock return The Problem in Words A trader of an American style option has the right to sell a stock There is an initial price of the stock of 100 a strike price of 99 a risk free rate of 4 The trader can sell this stock over a 5 time period Given all prices at the beginning of stage n the market makes a random outcome At the end of stage n having seen all of market s n previous outcomes as well as all the previous decisions the trader makes the next decision The trader has to decide when to decide to sell it once so to generate a profit The Worksheet The worksheet has two sections 1 A section where we enter the data the adjustables the randoms the constraint and the objective function for the problem This is similar to the section for solving a deterministic optimization problem 2 A section where we enter the stochastic information I
188. RANTIES OF MERCHANTABILITY FITNESS FOR A PARTICULAR PURPOSE OR OTHERWISE Further LINDO Systems Inc reserves the right to revise this software and related documentation and make changes to the content hereof without obligation to notify any person of such revisions or changes ACKNOWLEDGEMENTS We gratefully acknowledge Professor Sam Savage for his contributions to early releases of What sBest Copyright 2014 LINDO Systems Inc Published by 1415 North Dayton Street Chicago Illinois 60642 USA Sales amp Information 312 988 7422 info lindo com Technical Support 312 988 9421 tech lindo com www lindo com Contents GON TENTS A E geegede eg Seet ddeg cacevvasutevee E E E A E IW PREFACE ges ugeegee geesde AER EE ANESEC NEES CEO AEN Aer EE XIII Other Valuable Features ccccccecccceceeeeeeeeeaeeeceeeeeceeeaaaeaeceeeeesesaaaeceeeeeeesessenaeeeeeeeenes XV 1 GETTING STARTED WITH WHAT SBEST cccccssseeeeeesseeeeeseeeeeeessseeeeesseneeeeseeensesseeeeeees 1 What is What sBest VAN 1 Optimization Models a2cc soet hte nee aa a a T ea da eee eae aaa ea toa 2 Non Optimization Models nn aesttnnnnn annen nn nenen 2 Models with Integer Restrictions sssseessssecesnneesrnnsssrnesnnnandinnnaatannantnnnesnnnadatnaneanannaniananna 2 System RequireMentS indriani ir di da r iaraa 3 installation e EE A The What sBest Interactive Environment 7 Developing a Model in What seet 9 The ABC s Thr
189. RMSL X is the expected amount that demand exceeds a level X if demand has a normal distribution The syntax is WBNORMSL Value Value must be a real number 10 Inverse Triangular Cumulative Distribution WBTRIAINV This function returns the inverse of a triangular cumulative distribution for supplied low mode and high values The syntax is WBTRIAINV Low High Mode Prob The lower limit of the triangular distribution The upper limit of the distribution High must be greater than or equal to Mode Mode The mode peak value of the distribution Mode must be between the Low and High values Prob The probability corresponding to the triangular distribution The probability must be greater than or equal to 0 and less than or equal to 1 212 CHAPTER 5 Probability Low Mode High For example WBTRIAINV 1 3 2 0 7 returns 2 2254 This means that for a triangular distribution over the range 1 3 with mode 2 70 percent of the outcomes are less than or equal to 2 2254 11 Inverse Uniform Cumulative Distribution WBUNIFINV This function returns the inverse of a uniform cumulative distribution for supplied low and high values The syntax is WBUNIFINV Prob Low High The probability corresponding to the uniform distribution The probability must be greater than or equal to 0 and less than or equal to 1 The lower limit of the uniform distribution The upper limit of the uniform distribution High m
190. SP_DIST CAUCHY WBSP_DIST_CHISQUARE WBSP_DIST DISCRETE An WBSP_DIST DISCRETE SH WBSP_DIST DISCRETE_SH W BSP_DIST_ DISCRETE SH IW WBSP_DIST EXPONENTIAL WBSP_DIST F DISTRIBUTION WBSP_DIST GAMMA WBSP_DIST_GUMBEL WBSP_DIST GEOMETRIC WBSP_DIST HYPERGEOMETRIC WBSP_DIST LAPLACE WBSP_DIST LOGARITHMIC WBSP_DIST LOGISTIC WBSP_DIST LOGNORMAL WBSP_DIST_ NEGATIVEBINOMIAL WBSP_DIST NORMAL WBSP_DIST PARETO WBSP_DIST_POISSON WBSP_DIST STUDENTS TI WBSP_DIST SYMMETRICSTABLE WBSP_DIST TRIANGULAR WBSP_DIST UNIFORM WBSP_DIST WEIBULL Correlations WBSP_CORR_KENDALL WBSP_CORR_PEARSON WBSP_CORR_SPEARMAN FUNCTIONS AND OPERATORS 207 Linearization Many of the non smooth functions and operators supported by What sBest may be automatically smoothed by the solver through a process referred to as linearization Linearization replaces a non smooth function or operator with a collection of additional linear variables and constraints such that the modified model is mathematically equivalent to the original with the non smooth functions or operators eliminated Non smooth functions and operators that may be eliminated through linearization are FUNCTIONS OPERATORS ABS lt AND lt HLOOKUP lt gt IF INT lt MAX gt NOT OR SIGN SUMIF VLOOKUP In addition to the above What sBest can also linearize products of 0 1 and continuous variables For more information on the linearization process refer to the section entitled Option
191. ST Model Before Solving X W 2 e g OS PORTCOST xlsx Microsoft Excel kalak File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o El Ss PORTFOLID WITH TRANSACTION COSTS Transaction Cost Return Rate Begin Sold Bought End Asset1 90 10 50 0 0 0 0 0 50 0 Asset2 135 15 30 0 0 0 0 0 30 0 9 Asset3 18 0 20 20 0 0 0 0 0 20 0 10 11 Covariance Matrix End Value Desired 12 Asset 1 Asset 2 Asset3 Port Return End Value 13 112 2 109 5 14 Asset 1 25 0 25 0 0 15 Asset 2 25 150 0 40 0 Proceeds Cost of 16 Asset3 0 0 40 0 256 0 From Sales Buys 17 0 0 0 0 18 Variance 19 20 21 22 HAH PORTCOST 27 al m E o O Wi 2 3 4 5 6 7 8 A Determine Adjustable Cells The adjustable cells are the percentages of each asset to be Bought or Sold in cells E7 F9 B Define Best The best solution minimizes the variance of the portfolio This is accomplished in cell B18 by means of the following formula explained in the previous sample model G742 B14 G7 G8 B15 G7 G9 B 16 G8 G7 C14 G84 2 C15 G8 G9 C16 G9 G7 D14 G9 G8 D15 G9 2 D 16 C Specify Constraints Cell E13 calculates the value of the ending portfolio plus the return over the period with the formula 1 B7 G7 1 B8 G8 1 B9 G9 The constraint in cell F13 WB E13 gt G13 ensures that the End Value Port Return E13 is greater than or equal to the Desired End Value G13 of
192. Solver The dialog box posted by the Options Global Solver command appears as follows Global Solver Options asm Strategy be Global Solver Multistart Attempts Solver Decides geckeg m Tolerance 0 000001 0 0000001 Variable Bound 10000000000 Use of Bound Solver Decides DI Branching Direction Solver Decides DI Box Selection Solver Decides DI Algebraic Reformulation Solver Decides DI ee This command allows you to set a number of options controlling the function of the global solver 66 CHAPTER 3 Global Solver Check the Global Solver checkbox to have the global solver partition the original nonconvex nonlinear problem into several convex linear subproblems The global solver will then use a branch and bound technique to exhaustively search over these subproblems for the globally optimal solution The global solver will rigorously find a global optimum if allowed to run to completion But be aware that runtimes may increase dramatically particularly on large models when selecting the global option For more information on the concept of global versus local optimality refer to section Local Optima vs Global Optima The default setting for Global Solver is off Multistart Attempts Use the Multistart Attempts text box to have the What sBest s nonlinear solver invoke a heuristic for generating multiple good starting points The multistart capability is useful for quickly
193. StochasticOptions StochasticE VPI False Note The AdvStochasticSupport argument should be set to TRUE via the wbSetStochasticSupport function in order to use these options MACROS THE VBA INTERFACE 195 wbSetStochasticSupport This routine can be used to set the What sBest stochastic support option seen in the Stochastic Support dialog box There is only one argument For additional discussion of the options available through this routine see the section entitled Options Stochastic Solver Syntax wbSetStochasticSupport AdvStochasticSupport AdvStochasticSupport AdvStochasticSupport is a True False flag indicating whether or not to use this support Default 0 False Sto_BadAdvStochasticSupportArg Bad AdvStochasticSupport argument Example If one wished to set all the function support options the simplest syntax would be wbSetStochasticSupport True or by the named argument wbSetStochasticSupport AdvStochasticSupport True wbSetStringSupport This routine can be used to set the What sBest string support option seen in the String Support dialog box The first argument is required the others are optional For additional discussion of the options available through this routine see the section entitled Advanced String Support Syntax wbSetStringSupport AdvStringSupport AdvStringLength Argument Required Default Description AdvStringSupport Yes 0 False AdvStringSupport is a True Fa
194. The WBCARD function is used to request Cardinality ranges If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message Cardinality Cell Format Help Reference WBCARDFORM A Cardinality cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBCARD number cells where number is numeric and cells must refer to adjustable cells cell address Suggestions There is an incorrectly formatted WBCARD function in the model A WBCARD function cell must use the format WBCARD number cells where number is an integer and cells is a reference to the cells you want the CARD on The cell reference should be to an adjustable cell For more information on range values refer to section Integer Special Ordered Sets WBDUFORM Dual Cell Format If requested What sBest can return dual solution information Dual values tell you how how sensitive the final solution is to various parts of the model The WBDUAL function is used to request dual values If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message Dual Cell Format Help Reference WBDUFORM A dual cell is incorrectly formatted Correct the formula in the cell below The format should be WBDUAL cell value cell addr
195. This step simply reminds you to first formulate a standard deterministic core model Adjustable Best Constraint A cell that represents a Random quantity is simply filled with an arbitrary number Cells containing equations or strings are inappropriate as random cells What sBest cannot rewrite an equation although the value returned by an equation will change if the equation depends upon any adjustable cells Therefore be sure to enter a numeric value in each of your random cells Note The Random cells will be identified during the Step 2 below 90 CHAPTER 3 Page Step 2 sequencing Stochastic Support Xn V Use Stochastic Modeling J Use Simulation Format Core Stage Distribution Scenario Reports Chance Constrained 2 Specify the stage information for the Variables Adjustables Formulas Constraints cells and the Random cells using the set of WBSP_ Stage Refers to wee ue x fo Tas Place function in cell SAS sl Insert Specifications Optimization Method Seed for Random Generator Common Size per Stage V Sampling on Continuous Distribution Only ml eet This step provides the related pieces of the sequencing of decision and random events or staging The general sequence of events is as follows Stage 0 We make initial decisions Stage 1 beginning First set of random variables are observed Stage 1 end We make additional decision or calculations base
196. U CheckUpdate No H 4 gt gt HOGFEED Ready O Language GETTING STARTED 7 The What sBest Interactive Environment What sBest offers two interactive methods to access commands the What sBest menu and toolbar This section describes how to effectively use this interface In Excel versions 2007 2013 both the menubar and the toolbar are integrated in the Ribbon layout wm wm _ emm DI Ma g Ul Book Microsoft Excel eco a Home Inset PageLayout Formulas Data Review View Developer Team What fest o E gi ES K Make Adjustable if Minimize lt Less Than so Integers Locate AP License Language English H O guem i S Remove Adjustable Z Maximize gt Greater Than Options Help Register KZ Adjustable Best Constraints Solve Equal To a Advanced W About Check Update Model Definition Settings Solvers Information Services In Excel version 2002 2003 1 The What sBest menu WB is embedded in the main Excel menu bar and appears as follows File Edit View Insert Format Tools Data Window Help The WB menu contains all the commands discussed in ABC e Basic Functions and Additional Commands 2 The What sBest toolbar can float on your screen or be repositioned to a preferred part of the Excel window and appears as follows What sBest vx KS BF IA lt The buttons on the toolbar correspond to the menu commands Adjustable
197. UCTION D Eee H Total Units From From Demand Demand Shipped Steel Mill 4 Cost Steel Mill 2 Cost Constraint Plant To Plant A 0 200 0 500 Not gt 50 Plant B 0 300 0 400 Not gt 90 Plant C 0 500 0 600 Not gt Output Capacity Output Capacity 0 lt 100 0 lt 150 a Costs 0 0 Total Cost H HA gt gt SHIPPING 2 IER Mm Ready 7 G D 100 A Determine Adjustable Cells The adjustable cells in this model are the quantities to be shipped from each steel mill to each plant B6 B8 and E6 E8 B Define Best The best solution minimizes Total Cost in cell 112 The Total Cost formula is the sum of the two Cost per Mill cells in B12 and E12 Each of these is the sumproduct of the Units Shipped from each Mill to each Plant B6 B8 and E6 E8 and the cost associated with each shipping arc D6 D8 and G6 G8 C Specify Constraints There are two sets of constraints First each plant location requires certain levels of shipments Second the production of each steel mill must not exceed its capacity The constraints in H6 H8 force the total shipped to each plant to be greater than or equal to that plant s demand 16 18 To guard against exceeding the capacity of a Steel Mill the capacity constraints in C11 and F11 require that a Steel Mill s output the sum of amounts shipped from it be less than or equal to that Mill s capacity SAMPLE MODELS 375 Now let s solve th
198. Visual Studio and 146 CHAPTER 4 choose File Open Project to select the WB_VB sIn project There are WB Module vb WB _Forml vb WB_Form1 vb Design and the WB_VB project properties This sample project will demonstrate a basic dialog box with a button A function WB_VBBuildXYZ will actually open Microsoft Excel initialize the link to the What sBest add in and open the file C WB XYZ XLSX It will then complete the model by setting the Adjustable Best and Constraint cells then solves it The solution will be displayed back onto the worksheet with a message box for the returned status The user can then close the messages The code clarify the basics for opening building and solving a model The user can look at this project as a template for further developments eventually adjusting on the platform NET either 32 or 64 bit Concealing and Protecting a Model from the User What sBest allows model developers to hide aspects of a model that might be proprietary and protect sections of a model from inadvertent or unauthorized modification while allowing the user to access and modify input data While this does not require the use of Visual Basic these techniques can easily be used in conjunction with VBA Information in a What sBest model that is to be hidden from the user must reside on one or more worksheets that are separate from the worksheet s to which the user has access Similarly information that is to be
199. WBNORMSL 211 10 Inverse Triangular Cumulative Distribution WBTRIAINV se 211 11 Inverse Uniform Cumulative Distribution WBUNIFINV 0 eccceeeeeeeeeeeeeneees 212 6 OVERVIEW OF MATHEMATICAL MODELING 00 cccc sececeeeeeeeeeeeeeceeeeeseeeeeeneeeeeees 213 ut vele Eeer EE 213 viii Linear vs Nonlinear Expressions and Linearization ccceceececceceeeeeeeeeeaeeeeeeeeeeennaees 213 Linear ExpreSsionss 5 2 3 2coac ees fea aire a eon aad Eech 213 Nonlinear Expressions ccccccceccecceceeeeeeececeaeceeeeeeeseceaaaeeeeeeeeeseecacaeceeeeeeesensuceeseneneess 214 Lin aniZatlon ai ee eerie a EEN 214 The Solution Process Determining Optima eee eeeeeeeeeeneeeeeeeneeeeeeaeeeeeeaeeeeeenaeeeeeeas 215 Local Optima vs Global Optima 2 2 0 0 ccecececcececeeeeeeecencaeee seer eesecaaeaeeeeeeeeeesenieaeeeeeenees 215 CONWEXILY 2s fis see EE eg ane ig dee se chee Ge 217 Smooth vs Non smooth Exvpressions nn nnstrnnn nnmnnn 218 SOON QUICOMES kaon hs eldest ad is oe a a Metis ethos ee aaa eae 220 Case 1 Optimization Models sssseeseenenensseeettnr tt nssrettrrntnnsstttttnnnnnnnttnrrnn nnns rennen nn nent 220 Case 2 Non optimization Models cccccccceececceceeeeeeeeeeneeeeeeeeeesecceaeceeeeeeeeecsecaeeeeees 221 Guidelines for Modeling with What sBestl ec cccceeeeeeeeeeneeeeeeneeeeeeaeeeeeenaeeeseenaeeeeeeaas 222 General Modeling Gudelmes 222 Nonlinear Modeling Gu
200. What sBest model You can plug regular numbers in a random cell to check results Step 2 Specify staging information about the sequence of decisions and random events This information is stored directly on the spreadsheet using special What sBest functions These functions and formats are Decision variable and their stages are identified by WBSP_VAR stage cell_list and Random variables and their stage are identified by WBSP_RAND stage cell_list Step 3 Distribution information about random cells is stored in WBSP _DIST_distribution table cell_list where distribution specifies the distribution e g NORMAL Step 4 Sample size for each stage is stored in WBSP_STSC table Step 5 Cells to be reported are listed in WBSP_REP cell list or WBSP_HIST bins cell_list You may type these functions in directly or you may use the Options Stochastic Solver drop down menu in What sBest to guide you through the steps We illustrate the formulation of an SP model in What sBest with perhaps the simplest SP model possible the one product newsvendor problem model SP_NEWSVENDOR XLSX This model has just two stages In stage 0 half stage we must decide how much to stock Q of a single product At the beginning of stage 1 demand D is revealed At the end of stage 1 we sell the minimum D Q enjoy our sales revenue and pay a penalty if any for unsatisfied demand or pay a holding cost for leftover inventory
201. What Lindo Sys D Stochastic Scenario Optimization D Newsvendor Normal Demand Stage 0 we must decide how many newspapers to stock Stage 1 in the beginning unknown demand is revealed to us we compute our sales and the resulting profit m x fe Stochastic Scenario Optimization Y B c D E F G a Core model lt lt Stage 0 decision lt lt Stage 1 random demand lt Stage 1 recourse decision lt lt Stage 1 constraint lt Stage 1 decision and constraint lt Stage 1 non negativity constraint Stage 0 cost computation lt lt Stage 1 holding cost computation lt Stage 1 shortage cost computation lt lt Stage 1 revenue computation lt lt Stage 1 expected value maximize S WB _Stochastic WB _Histogram Model Scer a gt 234 CHAPTER 6 The solver writes a series of solution in the created tab WB Stochastic and WB _ Histogram with the expected value and displays the first default scenario or a selected scenario on the spreadsheet The scenario by scenario report is generated on the WB _ Stochastic tab A portion of it appears below H 6 E amp Di SP_NEWSVENDORxIsx Excel a mm P x HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys v Al sl fe What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A B C D E F a
202. What sBest users avoid sharing a directory for spreadsheet data files When solving a model What sBest saves a copy of the model and creates a copy of the solved model under the same file names each time If What sBest users share a common data directory over the network the data files of one user could be inadvertently overwritten by the data files of another user What sBest Add in Files The setup program will attempt to locate Excel and find a Library folder in the dialog box but it is possible it may fail or will find a version of Excel different from the desired one Therefore it is important that you confirm that the supplied path is correct and otherwise correct it Location of the Add In Files This provides you with the choice of where the add in files are to be located The recommended choice of the Library subdirectory is already selected See the section entitled Location of the Add in Files and Update Links for details Final Instructions This gives some important instructions to complete the installation of What sBest When What sBest setup is almost complete click Finish and Excel will open You may receive a message that WBINTR XLS contains macros You must then select the ENABLE MACROS button in order to finish installation Also you can choose to view the README file Add ins library and executable files from LINDO Systems are digitally signed Installation Related Problems Most errors during installatio
203. Your firm has a choice of five locations in which to operate a manufacturing facility Six markets exist with a demand for your product Each potential plant has an associated monthly operating cost and shipping routes to the demand cities have varying costs In addition each potential plant will have a production capacity that must not be exceeded Objective of Optimization The objective is to locate plants in such a way that demand is satisfied in each target city potential plant capacity is not exceeded and overall operating costs are minimized SAMPLE MODELS 345 The Worksheet Let s open the PLANTLOC sample and examine its layout and formulas B The Shipping Costs Worksheet Before Optimization aas ce ie AN oa Microsoft Bed cmc File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 CA o ER Za PLANT LOCATION MODEL Shipping Costs Per Ton Month Proposed Demand City Boston Chicago Denver Omaha Portland 0 15 Operating Cost Trans Cost 0 Trans Costs 0 0 0 0 0 0 TOTAL OPERATING COST SON Wal gt aii 346 CHAPTER 7 The Amount Shipped Worksheet Before Optimization ZW 2 e g rf PLANTLOC xlsx Microsoft Excel bala Home Insert Page Layout Formulas Data Review View Developer Team What sBest V 2 o Ss Amount Shipped 2 3 4 Monthly 5 Proposed Demand City Supply 6 Supply Supply Capacity 7 City Boston Chicago Denver
204. ad the cells in the range as constant values and ignoring any formulas in these cells This name can be useful to bypass the reading of an external link to the model contained in a cell or an unsupported function but may also break any dependencies to other parts of the model when What sBest reads and parses the model from the spreadsheet All the What sBest names can be defined modified or deleted via the Name Manager of Excel Users accessing What sBest via VBA macros can set customer parameters by using the standard VBA code for instance ActiveWorkbook Names Add Name WBLS_DPARAM ANYPARAM RefersToR1IC1 1 23 132 CHAPTER 3 Locate The dialog box posted by the Locate command appears as follows Locate Adjustable DI cells Using Method Identify One by One DI me es Je Specify the type of cell you would like to find in the Locate drop down box to search the worksheet or workbook for Adjustable Best Constraint Violated Dual WBCALC or WBOMIT cells If you choose to locate the best cell then What sBest searches the entire workbook for the maximized or minimized cell and selects that cell If you choose to locate Adjustable Constraint Violated Dual WBCALC or WBOMIT cells then specify whether you wish to simultaneously Select AU Such Cells or Identify One by One with the Using Method drop down box The search can focus either across the Worksheet or the Workbook To Identify One b
205. age No Feasible Solution Found Help Reference INFEASIBLE There is no solution that satisfies all of the constraints and any integrality conditions in the model Check to make sure all the constraints are properly formulated Consider easing constraints in the returned model that are either not satisfied or tight NOTE The answer returned is not feasible therefore the value of the objective function is NOT optimal The solution returned is only for the purpose of illustrating a scenario with violated constraints so the model can be corrected See the list of cells below that may be contributing to the infeasibilities Suggestions A linear optimization model containing constraints that cannot be satisfied simultaneously by What sBest is said to be infeasible With nonlinear models it s possible that a feasible solution exists but What sBest was unable to identify that solution from the starting adjustable cell values you specified In either case the solver tries to find a solution to the problem that satisfies as many constraints as possible and returns the appropriate solution status in the status report worksheet entitled WB Status If a linear or nonlinear problem is truly infeasible correcting the model can be a very complicated task The first step is to investigate those constraints contributing to the infeasibility These cells have been identified for you by What sBest at the end of the WB Status tab If you have selected the
206. aints work properly In C19 the constraint formula WB C17 gt C18 forces the Expected Return in C17 to be at least as great as the Target Return in C18 In C20 a constraint requires that 100 percent of the funds are invested That is that B3 D3 sum to 1 Now you re ready to solve the model After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning This warning can be disabled from the General Options dialog box The solutions for all three objectives follow The PORTSCEN Worksheet After Minimizing Variance ld a e g S PORTSCEN xlsx Microsoft Excel coll File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o El 3 WBMIN aC E4 G4 H4 2 E5 G5 H5 2 E6 G6 H6 2 E7 e RE ER ES BS ES EE e RI Ju 1 PORTFOLIO SCENARIO MODEL Asset 1 Asset 2 Asset 3 Return Difference Forcing Scenario 525 33 9 13 6 Over Under Constraints 130 0 122 5 114 9 1254 104 0 0 110 3 129 0 126 0 118 8 3 8 0 0 121 6 121 6 141 9 R 124 4 9 4 0 0 954 72 8 92 2 87 3 0 0 27 7 92 9 114 4 116 9 103 4 0 0 11 6 105 6 107 0 96 5 104 8 0 0 10 2 103 8 132 1 113 3 114 7 0 0 0 3 108 9 130 5 173 2 125 0 10 0 0 0 109 0 119 5 102 1 111 6 0 0 3 4 108 3 139 0 113 1 119 3 4 3 0 0 103 5 92 8 100 6 f 99 5 0 0 15 5 117 6 171 5 190 8 H 145 8 30 8 1 2 3 4 5 6 7 8 9 17 Expected Return 1
207. al values in the adjustable cells 222 CHAPTER 6 Guidelines for Modeling with What sBest General Modeling Guidelines An example showing how to build a simple linear model is provided in the Tutorial in Getting Started In addition the Sample Models demonstrate how linear and nonlinear models can be constructed for a variety of applications As you construct your own model it may be useful to periodically solve the model and check the status report to determine the type of model you have linear nonlinear and its characteristics In general linear models are the fastest group of models to solve and nonlinear models are the most difficult to solve It is not unusual that a nonlinear model will take many times longer to solve than a linear model with the same number of variables Ifa linear or nonlinear model is close to a solution i e constraints are only slightly violated then increasing one of the feasibility tolerances may allow you to reach a solution Tolerances are set in both the Linear Solver Options and Nonlinear Solver Options dialog boxes For a difficult linear model the options provided in the Linear Solver Options dialog box may help you to reach a solution or shorten the solution time One of the first options you might try is turning on or off Model Reduction Some linear problems will solve faster by a different Solver Method The Barrier method may be considerably faster on big models while the two simplex meth
208. an be obtained by rounding the fractional answers without sacrificing much in total cost If the program returns non integer values in cells P5 P16 or in R18 AE18 when the Pool is used you can manually round these values to whole numbers You could also use the nteger command to force whole number answers but this can significantly increase the solution time The objective in rounding these cells should be to make sure that the Scheduled gt Recommended constraints in D5 D11 and D13 D19 aren t violated and to have a final cost as close as possible to the one before you started rounding SAMPLE MODELS _ 365 Now that the lowest cost schedule has been found the next step is to assign individual employees to the work patterns selected in this stage by preference Stage 2 Preference Maximization The Problem in Words The second stage model assigns existing staff members to the work patterns selected in stage 1 You know the preferences of each staff member from the ranks of all work patterns selected in stage 1 and the model assigns individuals to work patterns so as to maximize cumulative preference of the group This model has provisions for specifying employee preference scores for work patterns and individual seniority levels performance indices or a composite of the two Objective of Optimization The objective of this model is to maximize the cumulative preference of the group while assigning staff members to the minimum cost wo
209. an set the method of constraint display to either Indicator or Slack If you set constraint display Indicator mode the default then the constraint is shown in the cell by one of the following eight visual indicators lt gt lt gt Not lt Not gt Not or If you set What sBest to display the constraint in Slack mode then a numeric value known as the s ack is returned The slack is the amount by which a constraint is not violated For example What sBest would display constraint values based upon the following table Constraint Slack Mode Indicator Mode Tightly satisfied 0 lt Satisfied positive number lt Not satisfied negative number Not lt ABCs 31 Constraint related Problems Constraints must be properly formulated or they can be a source of problems Some of the problems are discussed below Too Few Constraints Unbounded Solutions Let s return for a moment to the XYZ Production model presented in the Tutorial of Getting Started Had you forgotten to include constraints in the model and tried to solve What sBest would have given an error message indicating Solution Status UNBOUNDED in the WB Status worksheet An unbounded solution error occurs when a model is not properly constrained Profit could be increased without limit by producing an infinite number of computers What sBest knows you ve left out one or more constraints and indicates that the problem is
210. ances are computed in B18 and B19 For instance the variance computed for Question 1 in B18 is found by means of the formula SAMPLE MODELS 319 B 10 2 B122 B 5 C 10 2 C 122 C 5 D 10 2 D122 D 5 SE 10 2 E12 2 E 5 B 10 B12 2 B 8 C 10 C12 2 C 8 D 10 D12 2 D 8 E 10 E12 2 E 8 That is for each Stratum its Weight times Variance is divided by its sample size The resulting figures are summed For each stratum from that result is subtracted the Weight times Variance divided by Population size This formulation is from Sampling Techniques W G Cochran 2nd Ed Wiley New York 1963 to which interested readers may refer Now you are ready to solve the model After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning This warning can be shut off from the General Options dialog box Your solved model now appears as follows The SAMPLEWB Worksheet After Solving D E Max LS nis SAMPLEWB xlsx Microsoft Excel 7 7 balba File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o El X fe Stratified Sampling Plan Design Stratum 2 4 Sample Size y i 101 23 Lower Bound gt Upper Bound lt Population 400000 300000 200000 100000 Cost 1 00 1 00 1 00 1 00 Weight 40 0 30 0 20 0 10 0 Stratum Variance Question 1 5 5 Question 2 2 4 5 8 Fixed Cost Total Cost Maximum Variance Question 1 0 043 Qu
211. anta and Denver Note This model is an example of a class of models that returns naturally integer answers even though the adjustable cells have not been specified as integer Since the use of 0 1 integer adjustable cells can cause dramatic increases in computation time it is best to use naturally integer models whenever possible Space here prohibits a detailed explanation of this phenomenon Interested readers may refer to Chapter 8 Introductions to Operations Research by Hillier amp Lieberman 7th ed from McGraw Hill and to Chapter 14 Optimization Modeling with LINGO by Linus Schrage from Duxbury Press The latter text is available from LINDO Systems Call 312 988 7422 for more information 288 CHAPTER 7 Markowitz Portfolio Problem File name MARKOWIT XLSX TYPE NONLINEAR OPTIMIZATION Application Profile In the March 1952 issue of Journal of Finance Harry M Markowitz published an article called Portfolio Selection In it he demonstrated how to reduce the standard deviation of returns on asset portfolios by selecting assets with prices that don t fluctuate in exactly the same ways At the same time he laid down some basic principles for establishing an advantageous relationship between risk and return and his work is still in use forty years later The Problem in Words You re considering investing in three assets and historical data reveal that the return from each asset has fluctuated over time You wan
212. ares of the Unders C Specify Constraints There are three types of constraints in the PORTSCEN model The first requires a bit of thought The Forcing Constraints in 14 115 force the difference between Over G4 G15 and Under H4 H15 to be equal to the difference between the Expected Return F17 and Return F4 F15 For instance in 14 the formula is WB G4 H4 F4 C 17 To find the semi variance and downside risk we need to calculate the amount by which each Scenario Risk SR is below the Target Return TR A shrewd spreadsheet builder will recognize that this calculation can be done using an F function of the form IF SR lt TR TR SR 0 This function returns the difference between the target return and the scenario return if the scenario return is less than the target return Otherwise it returns zero The bend at the origin of this ZF statement makes it a non smooth function A smooth function has no breaks or sharp bends Most ZF functions that depend directly or indirectly on adjustable cells are non smooth and it s wise to avoid non smooth functions since they can be difficult to solve reliably see Chapter 7 Overview of Mathematical Modeling for a discussion of non smooth relationships By adding adjustable cells and carefully formulated constraints it turns out you can avoid the need for most non smooth ZF functions You can choose to use ZF functions instead of finding ways around them but you run the risk of sub
213. as Data Review View Developer Team What sBest 9 ei o El X Number Staff Starting Needs This Da gt 180 gt 160 gt 150 gt 160 gt gt gt 190 140 110 Total Enployees TOTAL COST 4 gt bl STAFF AFI ia Mm Ready 3 flog 100 A Determine Adjustable Cells The adjustable cells in this model contain the number of people whose five day workweeks begin on each day of the week These are shown in the Number Starting This Day column G7 G13 B Define Best The best solution is the one that minimizes total payroll costs In this problem cost is equal to the number of employees times their weekly salary This is shown in cell G18 The formula for Total Employees G15 is the sum of employees starting each day The weekly salary per employee has been entered in cell G16 This means that the formula for Total Cost in cell G18 is G15 G16 C Specify Constraints The requirement of any solution to this problem is that Staff Size is constrained to be greater than or equal to Staff Needs Without such a constraint the job for What sBest would be easy The least expensive solution would always be to hire nobody SAMPLE MODELS _ 351 Take a look at the Staff Size column C7 C13 The formula for Staff Size equals the Number Starting This Day plus the total of the number starting for the preceding four days Remember each employee has shifts on five consecutive days so any given day
214. ast thing to do is to hide and protect the Model sheet To do this select the entire worksheet and choose Format Cells On the Protection tab select Hidden Then with the entire spreadsheet still selected choose Format Row Hide and Format Column Hide Next protect the sheet by giving the MACROS THE VBA INTERFACE 147 command TJools Protection Protect Sheet and enter a password The final step is to hide the Model sheet with the command Format Sheet Hide Now the user will only see the Jnputs and Outputs sheets A clever user would be able to determine that there is a Model sheet but he or she would not be able to view or modify it In the WB subdirectory there is a file called PRODMIX2 XLS which has the changes described above Note It is not possible to use Excel s Tools Protection Protect Structure command with What sBest This command does not allow the WB Status or WB Solution worksheets to be added to the workbook Tutorial on the VBA Interface This section provides a tutorial on the basics of running What sBest commands using VBA Visual Basic for Applications It includes detailed discussion and step by step examples of a variety of different common applications combining Visual Basic and What sBest Note The first step in running any What sBest from VBA is to create a reference to What sBest This reference is made by checking the WBA XLA box under Tools References from within the Visual Basic Editor T
215. astic Support or contact LINDO Systems regarding a license upgrade that includes the stochastic option LICOPT6 Conic Solver Not Licensed If you attempt to use the conic solver option without a license the following error message will be displayed on the WB Status tab Error Message Conic Solver Not Licensed Help Reference LICOPT6 The license for your installation does not allow for use of the conic solver option Suggestions The Conic Solver or Second Order Cone Programming SOCP is invoked when the model is Convex with Global option set and checked the Quadratic Recognition on and the Conic option set The conic programming solver is an optional feature You have attempted to set up a conic model with a copy of What sBest that does not have an appropriate license You will need to contact LINDO Systems regarding a license upgrade that includes the conic option TROUBLESHOOTING 431 LOOKUP Unsupported Lookup Usage What sBest supports the VLOOKUP and HLOOKUP Excel functions only under certain conditions If you use an unsupported variant of either of these lookup functions the following error message will be displayed on the WB Status tab Error Message Unsupported Lookup Usage Help Reference LOOKUP The solver has been halted because the following cell contains an equation with an unsupported reference to either VLOOKUP or HLOOKUP All arguments must evaluate to being numeric the third
216. at does not have one yet Syntax wbAddBestStyle The wbAddBestStyle procedure has no arguments Error Codes Description Best_CreateStyleError Error Creating a Best style Remarks Only one cell the objective cell should use this style wbAddWBMenu This routine is used to add the WB menu item to the Excel menu Syntax woAddWBMenu The wbAddWBMenu procedure has no arguments Error Code Description AddWBMenuError Error in adding the WB menu Remarks This procedure and the woDeleteWBMenu procedure allows a developer to remove and add the WB menu as desired MACROS THE VBA INTERFACE 153 wbAdjust For additional discussion of the functionality provided see the section entitled Adjustable which refers to the dialog box interface that calls this procedure This routine is also called with appropriate arguments by two of the toolbar buttons This routine is used to either set cells as adjustable or to remove the adjustable attribute All arguments are optional Syntax wbAdjust AdjRange AdjChoice NoErrDialog Argument Required Description AdjRange No This is the range or address of the cells to be rendered adjustable If omitted the default value for AdjRange is the current selection AdjChoice No This is a string to indicate Adjustable or Reset AdjChoice accepts the text Adjust to set the AdjRange as Adjustable or Reset to set the AdjRange t
217. at your system has installed the international language capabilities This can be verified via the Control Panel of the Windows operating system Note English US Chinese Pinyin French France Japanese Katakana 4 What sBest Macros The VBA Interface This section discusses the VBA Visual Basic for Applications interface of What sBest The VBA interface allows the user to write VBA code or macros that execute What sBest commands By using this interface you can build optimization applications that utilize all the power and functionality of What sBest in Excel or any other application offering VBA control The section entitled Usage Guidelines for Macros in VBA introduces some features of the VBA interface such as the Object Browser how to embed your What sBest model in a Visual Basic project as well as how to hide the model The procedures or functions such as Adjust Best and Constraint provided by What sBest are discussed in VBA Interface Procedures The section entitled Tutorial on the VBA Interface is provided to help you get started writing VBA The rest of the section describes the syntax arguments and error codes of particular procedures Usage Guidelines for Macros in VBA Introduction to the VBA Interface of What sBest The very first step in creating a macro for What sBest is to create a reference to the What sBest add in so you can use the add in s attributes and procedures
218. ation Moving resources along routes with limited capacities at minimum expense PIPELINE XLSX Shipping Cost Reduction Minimizing shipping costs on routes with fixed costs while meeting demand SHIPPING XLSX Traffic Congestion Cost Minimization Minimizing shipping costs on a network whose routes have costs that vary with the amount of traffic TRAFFIC XLSX Truck Loading Packing a container with objects of varying sizes to maximize efficiency a knapsack problem TRUCK XLSX Stochastic Models Newsvendor Stock A stochastic model to maximize net profit by deciding how much stock to hold over 2 stages and 1 random parameter for the demand SP_NEWSVENDOR XLSX Investment Planning College A multi period stochastic model planning investments for going to college after 3 Periods SP_INVESTMENTCOLLEGE XLSX Crop Allocation Under Uncertainty A stochastic model to maximize revenue by allocating crops to grow on a specified land area over 2 stages and 1 random parameter for the weather condition SP_CROPALLOC XLSX Put Option A stochastic model to maximize wealth by selling an option at the right time over a multi stage structure and random parameters for the stock returns SP_PUTOPTION XLSX 258 CHAPTER 7 Blending File name HOGFEED XLSX TYPE LINEAR OPTIMIZATION Application Profile The manufacture of animal feed is an example of a blending problem The question is how do you mi
219. ation If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message Stochastic WBSP_VAR Format Help Reference SPVAR A WBSP_VAR cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_VAR stage cells where stage is numeric and cells must refer to variable cells cell address additional message Suggestions There is an incorrectly formatted variable function cell in the model A variable cell must use the format WBSP_VAR arg cells where arg is a numeric value or a cell reference to a numeric value and cells is a reference to the cells you want to apply this timing information The cell reference TROUBLESHOOTING 447 should be to a variable cell For more information on using the stochastic feature refer to section Options Stochastic Solver STRARG String Arguments Found In general What sBest expects all function arguments to be numeric If any unexpected string arguments were found while parsing the workbook What seet will display the following warning message on the WB Status tab Warning Message String Arguments Found Help Reference STRARG Text arguments have been found in formulas Their values have been taken to be zero This can lead to infeasible or sub optimal solutions Please check the returned solution carefully
220. ations of compare such as lt gt symbol for not equal gt lt gt lt SUMIF and VLOOKUP functions Any other operations will return an error message Also a formula cell should return a numeric number rather than a string value Advanced Convert Model Format This feature allows you to convert a non What sBest format spreadsheet optimization model to What sBest format It will try to extract any existing data or information to set the Adjustable Best cells and it will create a new tab W I Constraint_SheetI at the end of the workbook for inserting the constraint functions Convert Model Format 2s This feature will try to convert the model from any other formats into a What sBest format for setting the Adjustables Best and to create a WB _Constraint_ worksheet for the Constraints What sBest will have only one model per workbook The sequence of worksheet tabs may change Current selected worksheet to convert Current Selected Worksheet to Convert What sBest can have one model per workbook but other spreadsheet modeling interfaces can have one model per worksheet The user needs to select the current worksheet to convert then invoke the feature The feature will apply the Adjustable Style for the decision variable cells the WBMIN or WBMAX Name for the Objective cell and create the WB functions in a separate tab WB Constraint _Sheetl at the end of the work
221. avor SAMPLE MODELS 323 Now you are ready to solve the model After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning This warning can be shut off from the General Options dialog box Your solved model appears as follows g The PRICING Worksheet After Solving aaa e g ANG Microso nea TTT kel File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o El s amp s GH Miles per H Gallon 8 0 29 00 12 0 23 00 15 5 19 00 480 73 0 00 Mercurial 0 00 183 59 Cadimac Capacity year 500 00 100 00 200 00 Constraint lt lt lt Price Produced Constraint Rangler 12 39 480 73 lt Mercurial 29 96 183 59 lt Cadimac 40 92 76 23 lt 740 55 gt Produced Requirement Miles Gallon 26 48315 24 324 CHAPTER 7 Media Buying File name MEDIA XLSX TYPE LINEAR OPTIMIZATION Application Profile Media selection or buying is the problem of finding the best way to deliver the desired number of advertising exposures to the target audience by determining the most efficient combination of advertising media purchases Even for small media budgets there can be literally thousands of possible media schedules from which to choose The task is to select from this set an effective schedule to become the media plan What sBest provides a natural format for analyzing a media selection problem You can u
222. be WBUPPER cell value cell address Suggestions There is an incorrectly formatted upper range cell in the model An upper range cell must use the format WBUPPER cell value where cell is a reference to the cell you want the range value on and value is a numeric quantity The cell reference should be to either a constraint cell or an adjustable cell You may use any numeric value for value What sBest will replace value with the actual lower range value the next time you run the solver For more information on range values refer to section Advanced Dual Appendix A Installation Details Installation To install What sBest run the What sBest setup program and follow the prompts Following is a description of the screens that will be seen in the setup program The third screen entitled Setup Type will give a choice between a Default or Specified installation If for some reason you are prompted with a screen not described here follow the directions on it as it has the latest information available Please close all applications Excel included during the installation Version 32 bit 64 bit What sBest 64 bit should be installed with Excel 64 bit on a 64 bit operating system Otherwise install the 32 bit version of What sBest What sBest Example Files Example files can be installed on a local drive or any drive on the network in which you have write privileges It is important that What sBest users avoid
223. be displayed on the WB Status tab Error Message KE RP ROR Stochastic Error Help Reference SPERR Your model must have at least one formula that is dependent upon an adjustable cell and a random cell Refer to the Getting Started section of the online help to learn how to format a stochastic model for What sBest cell address additional message Suggestions There is an incorrectly formatted stochastic function cell in the model or the core model is missing the Adjustable Best Constraint cells A stochastic function cell must use the format WBSP _ cells where cells is a reference to the cells having the argument value For more information on using the stochastic feature refer to section Options Stochastic Solver 444 CHAPTER 8 SPHIST Stochastic WBSP_HIST Format Using the stochastic feature What sBest can return the histogram information on any cells These values tell you how sensitive the solutions are to various stages of the model The WBSP_HIST function is used to request histogram values on any cell If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message KER ROR Stochastic WBSP_HIST Format Help Reference SPHIST A WBSP_HIST cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_HIST number cells where the
224. be linearized automatically by What sBest see Functions and Operators SAMPLE MODELS _ 317 Stratified Sampling File name SAMPLEWB XLSX TYPE NONLINEAR OPTIMIZATION Application Profile This model is useful wherever you need to determine an optimal statistical sampling strategy Opinion polling and market research are two areas in which models similar to this one might be used The Problem in Words In your work in market research for an appliance manufacturer you must determine the consumer s trend toward purchasing your product You need to determine two population means using the smallest least costly sample likely to give reliable results To reduce error you break up the population by income groups You re asking two questions How much do you plan to spend on major appliances next year Onascale of to 100 how likely are you to buy our brand Background The population data looks like this Variance in Response Stratum Income Group Population Question 1 Question 2 1 50 001 400 000 5 1 2 35 001 50 000 300 000 5 2 3 22 501 35 000 200 000 5 4 4 under 22 500 100 000 5 8 You have determined your tolerable upper limits of variance for both sample means and you know the variance by question for each group Objective of Optimization The objective is to determine the best sample size for each stratum while minimizing the cost to obtain the sample 318 CHAPTER 7 The Worksheet Let s l
225. below are the right hand side of the equation 28 CHAPTER 2 If these are not the ranges of cells you want you can specify the cells or ranges by using the button on the right edge of each text box to bring up a cursor for cell selection or type the ranges in However you should use the following table when selecting cells or ranges If the then and the Left hand side Stored In Right hand side includes a should have a should have a single cell single cell single cell same shape and size range single cell single cell same shape and size range range same shape and size range same shape and size range You can relate a left hand side range to a single right hand side cell or a right hand side range to a single left hand side cell What sBest inserts a worksheet function called WB in the host cell s specified in the Stored In text box also known as the constraint cells By clicking on one of the constraint cells and looking at the Excel formula box you can see the WB function that was created For example select the B1 cell choose the WB Constraints command and press OK on the Constraints dialog box to insert the formula WB A1 lt C1 into the cell B1 This formula indicates that the value in Al should be less than or equal to that in C1 This could also be accomplished by selecting cell B1 and pressing the lt toolbar button or typing the WB A1 lt C1 formula directly into the cell
226. best solution found so far after hitting an iteration limit However the same precautions regarding the returned solution apply as when interactively interrupting the solver For more details refer to section Solver Interrupt above LICCAP1 Constraint Limit If your model has more constraints than is allowed for your installation the following error message will be displayed on the WB Status tab Error Message Constraint Limit Help Reference LICCAP1 The number of constraints in this model number of constraints exceeds the limit of constraint limit The model has more constraints than is allowed by your installation You will need to either reduce the size of your model or upgrade to a larger version Suggestions The model exceeds the constraint limit for your installation The capacity limits of your version may be found by running the WB About What sBest command One option is to remove constraint cells from the model until it satisfies the constraint limit Keep in mind that What sBest defaults to forcing adjustable cells to be non negative So any constraints that put a lower bound of zero on the adjustable cells are not required and may be removed Also if the workbook contains multiple independent models you can separate them into different workbooks in order to meet the limit TROUBLESHOOTING 423 If eliminating constraints is not an alternative then you may wish to contact LINDO Systems regarding a lice
227. bilities WBSP_DIST_ NORMAL argument 1 Mean argument 2 Sigma WBSP_DIST PARETO argument 1 Scale argument 2 Shape WBSP_DIST SYMMETRICSTABLE argument 1 Alpha argument 2 Success probabilities WBSP_DIST_ UNIFORM argument 1 Upper limit argument 2 Upper limit WBSP_DIST_ WEIBULL argument 1 Scale argument 2 Shape 94 CHAPTER 3 Distributions with 3 arguments WBSP_DIST HYPERGEOMETRIC argument 1 Population argument 2 Defective argument 3 Size WBSP_DIST TRIANGULAR argument Lower argument 2 Upper argument 3 Mode Correlations You can also specify the correlation information about the random cells Correlation is optional The format is WBSP_ CORR correlation matrix random cells e g WBSP_CORR_SPEARMAN M19 N20 Sheet1 B 13 B 14 meaning the random cells B13 and B14 in Sheet will follow a spearman correlation with the matrix defined in the range M19 N20 This is a 2 column and 2 row matrix for the 2 random cells to correlate As before the entry Place function in cell allows you to place this information in a any cell in the workbook Typically you place this information near the random cell s so that you can quickly observe the correlation information of a cell without calling up any special menus WBSP_CORR_ KENDALL argument matrix WBSP_CORR_ PEARSON argument matrix WBSP_CORR_SPEARMAN argument matrix The NONE choice will actually delete the selected cell ADDITION
228. book ADDITIONAL COMMANDS 129 The user may need to reset the tolerances via the numerous Additional Commands dialog box for the type of the model What sBest will then detect automatically the type of the model once the user starts the solver via the Solve button For instance the workbook has several tabs but you want to convert the model in Sheet Select the tab Sheet go to Advanced and Convert Model Format via the WB menu and press OK You will see the Adjustable cells with a blue like font the Best cell with a blue background and the tab WB _Constraint_Sheet1 for the constraints functions such as WB Sheet1 A1 lt Sheet2 C1 Note This feature creates a new model format but does not remove the existing format Any cells difference that could not be transported will be listed in the status report This feature cannot be invoked via the VBA interface Advanced Parameters This feature allows you to set arbitrary parameters in the LINDO API which is the solver engine used by What sBest In order to solve your model successfully there may be rare occasions when you will need to set an API parameter that is not available through the normal What sBest interface If this is found to be the case you will be provided with a list of settings by a LINDO Systems Technical support representative after investigation of the model Note The Advanced Parameters command should only be used with guidance fro
229. by generating N sample points and construct a finite and tractable scenario tree This is also true for discrete distributions with infinite event space like the Poisson distribution Note Sampling a scenario tree prior to the optimization process is also called pre sampling This is to distinguish this type of sampling from the one that is used during optimization process In What sBest sampling refers to pre sampling unless otherwise is stated SAMPLING N EVENTS FROM Q RB _Q2 o oeR 4 Q ms Ai i q S oO Plo UN Ba SS Ba d Pia 1 N Decision Decision P o 1 N Pied 1 N GE N U P y 1 N Uncountably many scenarios each with A finite set of sampled scenarios each with a point probability of zero a point probability of 1 N Note Because the point probability of each scenario in the original model is zero it is customary to set the probabilities of sampled scenarios to 1 N However the user can always define customized sampling approaches to work with different scenario probabilities Given the parametric distribution of each stochastic parameter What s Best s sampling routines can be used to generate univariate samples from these distributions efficiently The user has the option to use antithetic variates or Latin hypercube sampling to reduce the sample variance MATHEMATICAL MODELING 243 Generating Dependent Samples In certain situations the modeler may
230. can t work the next two shifts 354 CHAPTER 7 Objective of Optimization The objective is to maximize overall staff preference by assigning employees to the shifts they deem most desirable The Worksheet Let s open the ASSIGN sample file and look it over The model consists of four worksheets in one workbook The Mode Worksheet Before Optimization mu an FANN AEN e Microson Excl aS File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o e cmp ISCREEN 1 MULTIPLE SHIFT ASSIGNMENT MODEL Preference Total 0 Mon Tue Wed Thu Fri Sat Sun DAYS REQD 2 1 1 3 1 1 1 Not gt Not gt Not gt Not gt Not gt Not gt Not gt ON ODM amp Wh Mon Tue Wed Thu Fri Sat Sun 1 1 0 0 2 1 1 Not gt Not gt gt gt Not gt Not gt Not gt Tue Wed Thu Fri Sat Sun NITES REQD 0 0 0 1 1 1 gt Not gt Not gt Not gt Preferences SAMPLE MODELS 355 The Model worksheet shows the number of people required for each shift for the week and constraints ensuring these needs are met The best cell also appears in this screen The Assignments Worksheet Before Optimization lais Assicnadsx Microsoft excel ehh File Home Insert Page layout Formulas Data Review View Developer Team What sBest V ei o X Wa Wd cook er cook a Caen lp 100 ___U __ 356 CHAPTER 7 Th
231. can accept the currently selected cells which What sBest has automatically placed in this box You can also type the correct cell range directly into the text box 92 CHAPTER 3 Page Step 3 distributions or correlations Stochastic Support es JV Use Stochastic Modeling I Use Simulation Format Core Stage Distribution scenario Reports Chance Constrained 3 Specify the associated distributions or correlations using the set of WBSP_ functions Refers to WBSP_DIST_DISCRETE_SH z SAS Discrete values A 1 Place function in cell SAS af Insert Specifications Optimization Method Seed for Random Generator Common Size per Stage I Sampling on Continuous Distribution Only tee o This step provides the distributions of the random variables so to specify the distribution information about the random cells The format is WBSP_DIST_distribution parameter_cells random_cells e g WBSP_DIST LOGNORMAL C2 D2 Sheet1 A 2 meaning the random cell A2 in Sheet will follow a Lognormal distribution with the value in C2 for the Mean argument 1 and the value in D2 for the Standard Deviation sigma argument 2 As before the entry Place function in cell allows you to place this information in a any cell in the workbook Typically you place this information near the random cell s so that you can quickly observe the distribution information of a cell without calling up any special menus
232. cccecceeeeeeeeeeeeeeeeeeeeeeeeeeeseeeeeeeseeeaeeeseeeeeeseeaaees 295 Application Profile EE 295 Portfolio Scenario Model 298 Seasonal Sales Factoring e caninin i a a a e ea 304 Exponential SmoothiNg n sreun rin a a a a a aa 308 Application Profiles nenda aaee a radne taeraa 308 Linearization Option Construction Cost Estimation cccccccecceceeeeeeeeeeceeeeeeeeeeeennaees 313 Application Be UE 313 Stated ue e DE 317 ele ere TRUE 317 Cal Gi e e KEE 320 Media Buying nE o E S A S e ees O 324 eelere Tu Re UE 324 Multi Period Inventory Management 327 ele ere TRUE 327 Seele El 330 Geleet Re EE 330 The Building Block Method 334 Application lte EE 334 Waste Minimization in Stock Cutting 339 Application Profiles adr eaea ede ied dal ial 339 Plant Beie 344 Staff Scheduling vcs a news navies lee ad eed ie ead nid dead cee ac 349 elei Re UE 349 Staff Scheduling Preferred Assignment ceeeeeceeeeeeeeeeeeeeeeeeeaeeeeeeaeeeeeeaeeeeeenaneeeneaas 353 Application Profile asin addra nena ies cineindd aaiae ainda Meet a ei daga 353 Staff Scheduling Two Stage Fixed bt 360 Application Profile x i siering iaaa i de aaae aeia A Eie daga 360 Stage 1 Cost Minimization eee iiid air A eat 360 Stage 2 Preference Maximization ccceec cee eee eee e ete eee ae ceee setae eee aeeeeaaeeeeeee 365 Pipeline Optimization cne cei cial ke el eld aes ghee E es 369 eelere Mei e UE 369 Shipping Gost RE
233. cense when you are running the global solver the following error message will be displayed on the WB Status tab Error Message Global Adjustable Cell Limit Help Reference LICCAP5 The number of global adjustable cells in this model number of globals exceeds the limit of global adjustable cell limit The model has more nonlinear adjustable cells than is allowed by your installation of the global solver You will need to either reduce the size of your model or upgrade to a larger version 426 CHAPTER 8 Suggestions The model exceeds the nonlinear adjustable cell limit for your installation of the global solver This limit is easy to hit on some of the smaller capacity versions of What sBest given that they allow only a handful of nonlinear adjustable cells when running the global solver The capacity limits of your version may be found by running the WB About What sBest command Refer to the previous error message LICCAP4 for information on the definition of a nonlinear adjustable cell You will need to reduce the number of nonlinear adjustable cells in the model or turn off the global solver and use the standard nonlinear solver If this is not possible you will need to contact LINDO Systems regarding a license upgrade LICKEY1 Failed to Process License Key When your What sBest license key can t be found read or processed the following error message will be displayed on the WB Status tab Error Message
234. convergence Possible values are Solver Decides None Minimum Medium or Maximum The default setting for Algebraic Reformulation is Solver Decides Note The global solver needs the nonlinear option and the mixed integer option to operate 68 CHAPTER 3 Options Integer Pre Solver The dialog box posted by the Options Integer Pre Solver command appears as follows Heuristic oS Cutoff Criterion Solver Decides v c j Probing Level Solver Decides DI Help m Constraints Cuts Max Passes Relative Limits ee ee Types IV Lattice M Lifting Iw Plant Location Jh Obj Integrality IV Basic IT Cardinality I Disjunctive This command allows you to set a number of options controlling the function of the integer pre solver Integer programming models are inherently difficult to solve This is due to the many possible combinations of values that the integer variables may assume In fact the possible number of combinations grows exponentially with the number of integer variables Given this rate of growth in complexity it doesn t take a whole lot of integer variables to create a problem that is very tough to solve The integer pre solver carefully examines integer models using a number of heuristic procedures The goal of these procedures is to reduce the number of integer variable combinations that need to be examined In some cases the pre solver can deduce a model s solution
235. ctive is to determine the best price for each car to maximize profit while conforming to all regulations and constraints SAMPLE MODELS 321 The Worksheet Let s look at the sample file called PRICING The PRICING Worksheet Before Solving DIN 2 e g rf PRICING xlsx Microsoft Excel gt te File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 CA o El Ss E CAR PRICING MODEL D G Plant Miles per Cost Unit F G H Gallon Rangler i 29 00 Mercurial 10 5 12 5 23 00 Cadimac 17 0 19 00 Production Rangler Mercurial 1 00 1 00 Cadimac 1 00 Capacity year 500 00 100 00 200 00 50 00 12 Constraint lt lt lt 13 14 Price Produced Constraint Demand 15 Rangler 1 00 2 00 lt 1504 00 16 Mercurial 1 00 3 00 lt 486 00 17 Cadimac 1 00 2 00 lt 178 00 18 7 00 0 00 19 20 Produced Requirement 21 Miles Gallon 23 57143 Not gt 24 22 M 4 gt M PRICING 27 Dal il EEES ASean an pwr al A Determine Adjustable Cells The adjustable cells in the model are the quantity of each automobile to produce at each plant B8 F10 and the Price in thousands to charge for each unit B15 B17 B Define Best The best cell is the maximized Total Profit in G16 The formula there is SUMPRODUCT B15 B17 C15 C17 B4 B8 C4 C8 C5 C9 D5 D9 E5 E9 E6 E10 F6 F 10 This is profit minus production costs C Specify Constraints The constraints in the model enforce
236. ctly formatted distribution function cell in the model A correlation function cell must use the format WBSP_CORR arg cells where arg is a cell reference and cells is a reference to the cells you want to apply this correlation type Kendall Pearson or Spearman The cell reference should be to a random cell For more information on using the stochastic feature refer to section Options Stochastic Solver SPDIST1 Stochastic WBSP_DIST 1 Format Using the stochastic feature the user has to associate a distribution to a random cell either discrete or continuous The WBSP_DIST function is used to request a one argument distribution If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message Stochastic WBSP_DIST 1 Format Help Reference SPDIST1 A WBSP_DIST cell with 1 argument is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_DIST arg1 cells where argl is a reference and cells must refer to random cells cell address 442 CHAPTER 8 Suggestions There is an incorrectly formatted distribution function cell in the model A distribution function cell must use the format WBSP_DIST arg cells where arg is a cell reference and cells is a reference to the cells you want to apply this one argument distribution The cell reference
237. customer must be assigned to a postal lockbox so as to minimize the sum of float time expense and monthly fixed operating costs SAMPLE MODELS 285 The Worksheet Let s open the LOCKBOX sample file and look at its design and formulas The LOCKBOX Worksheet Before Optimization mas e g A Locksox tsx Microsoft Excel i S ege File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o El Ss c E F G H BOX LOCATIONS A CUSTOMER LOCKBOX ASSIGNMENTS Monthly Proposed Lockbox Locations Cash Customer Home Flow Locations lew York Atlanta Cincinnal Denver Seattle Office 000 Seattle 5000 Los Angeles 5000 Houston 5000 Philadelphia 5000 Miami 5000 13 Open 0 0 D 0 0 0 14 Cost Month 1 300 1 000 1 100 2 000 s0 15 Fixed Costs s0 so s0 s0 s0 s0 so 16 17 Variable Costs s0 s0 so s0 so s0 s0 18 Daily Cost of Capital 0 027 19 TOTAL OPERATING COST Een 20 21 AVERAGE MAIL DELAY BETWEEN LOCATIONS 37 Customer Home 38 Locations lew York Atlanta Cincinnai Denver Seattle Office Box 39 40 Seattle ane spe se se aper gt P Mot ze 41 Los Angeles gt gt gt gt gt gt P Hot ze 42 Houston gt gt gt gt M t ze M 4 gt gt LOCKBOX 27 al m Bag ss Us In cell C18 the Daily Cost of Capital is entered In this example the cost was calculated based on a hypothetical 10 annual rate for a 360 day year prorated to 027
238. d Linearization Mathematical expressions can be classified according to their characteristics The broadest and most common distinction is between linear and nonlinear expressions What sBest analyzes your model and describes it as linear or nonlinear in the status report under Model Type Linear Expressions If all the terms of an equation are of the first order the expression is said to be linear This means the expression doesn t contain a variable squared cubed or taken to any power other than one a term divided by a variable or variables multiplied by each other In other words proportionality exists That is for every unit increase or decrease in a variable the expression increases or decreases by a fixed amount In their simplest form linear formulas are straight line relationships For example suppose you re buying tomatoes for 1 50 per pound The expression or function used to calculate the Cost C in terms of the amount of tomatoes purchased 7 is CLIT 213 214 CHAPTER 6 As you might expect a graph of this expression for cost is a straight line 60 50 c 40 30 t 20 10 0 5 10 15 20 25 30 35 40 Tomatoes Purchased Ibs Linear expressions can have multiple variables For example if you added potatoes P at 0 75 per pound and apples 4 at 1 25 per pound your cost function would become C 15 7T 0 75 P 1 25 A This new cost expression is linear you could think
239. d before you reinstall What sBest Suggestions First uninstall What sBest from your machine with the Uninstall program You can search for the word uninstall to find a shortcut entitled uninstall What sBest and double click it Otherwise you can manually remove What sBest related files from your machine The location of the What sBest files is indicated at the bottom of the About What sBest dialog box Then to delete the old toolbar use the View Toolbars Customize Excel 2002 command to bring up a list of the available toolbars or right click on the ribbon to select Delete Excel 2007 Scroll down to the What sBest toolbar which may or may not be checked off and click on highlight the words TROUBLESHOOTING 401 What sBest Then click the Delete button to remove the old toolbar Now install What sBest and the new toolbar will be installed without conflict with the old toolbar When I try to close Excel an error appears stating This workbook is currently referenced by another workbook and cannot be closed Problem You have set a reference to WBA XLA or WBA XLAM in the VBA Editor that must be removed before the What sBest add in can be removed and Excel can close Suggestions From the Visual Basic Editor Tools Macro Visual Basic Editor go to Tools References to open the list of references Unselect WBA XLA or WBA XLAM and you should be able to close Excel The Wha
240. d search will be carried out Optimality Tolerance is particularly useful in some integer problems as a means of significantly decreasing the solution time Branching Direction Use the Direction drop down box in the Branching box to govern the preferred direction of branching Branching occurs when the branch and bound manager forces an integer variable that is currently fractional to an integer value When the branching direction is set to Up the branch and bound manager will branch on a fractional integer variable by first forcing it to the next largest integer The reverse is true when this option is set to Down When the option is set to Both the branch and bound manager makes an educated guess as to the best initial branching direction for each fractional variable The default setting is Both Integrality Due to the potential for round off error on digital computers it is not always possible to find exact integer values for the integer variables The two tolerances in the ntegrality box Absolute and Relative control the amount of deviation from integrality that will be tolerated Absolute Specify the absolute amount of violation from integrality that is acceptable in the Absolute text box Specifically if Z is the closest integer value to X X will be considered an integer if X I lt Absolute Integrality Tolerance The default value for this tolerance is 000001 Although one might be tempted to set this tolerance to 0
241. d compatibility with earlier versions of What sBest Direction also accepts the numbers for lt 2 for and 3 for gt 4 for lt c 5 for c 6 for gt c 7 for None RHS Yes RHS is the right hand side of the constraint equation It can be a range or a value see the Remarks below ConLoc Yes ConLoc is the range to store the constraints NoErrDialog No Any argument passed causes all What sBest error dialog boxes from the wbConstraint routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to get any possible returned What sBest error number Useful in an embedded application of What sBest Error Codes Description Con_BadLHSArg Bad LHS argument Con_BadDirectionArg Bad Direction argument MACROS THE VBA INTERFACE 157 Con_BadRHSArg Bad RHS argument Con_BadConLocArg Bad ConLoc argument Con_RangeSizeError LHS must be same size as ConLoc Con_ProtectedSheetError Unable to enter constraints on a protected sheet Remarks LHS and ConLoc ranges must be the same size RHS can be a range or a value Example To enter the constraint H8 gt 10 into cell I8 enter wboConstraint H8 gt 10 Ig or wbhConstraint Cells 8 8 gt 10 Cells 8 9 To constrain H8 H10 to be less than or equal to J8 J10 and store the constraints in 18 110 enter wboConstraint H8 H10 lt
242. d constraints It also tells you the appropriate quantities to produce and the total usage of each component Note that profit is now 33 000 considerably higher than the 31 000 attained by simply building as many Deluxe models as possible What s Best If It s often useful to explore your optimization model from various angles For example what if you learn that the 20 Deluxe computer towers remaining from the What sBest answer found above G16 E16 will be obsolete after the current production run In that case it might be better to maximize the utilization of this inventory than to maximize profit Try this by making Total Usage of Deluxe computer towers cell E16 your best cell to be maximized This is done by selecting cell E16 choosing Best from the WB menu clicking OK and then re solving GETTING STARTED 19 What sBest will maximize the value of cell E16 without regard to the former objective of maximizing Total Profit Note that the resulting production of 50 Deluxe units completely exhausts the obsolete inventory but that profit has dropped from 33 000 to 25 000 Now suppose for financial reasons profit must be at least 32 000 This constraint can be manually entered by simply typing WB G6 gt 32000 in a convenient cell in this case let s use H6 Optimizing again with the new constraint in place results in the production of 40 units of each model a profit of 32 000 and a surplus of 10 Deluxe to
243. d in files The Default setup is recommended for English language versions of Windows This will install the What sBest add in files in Excel s Library folder On the other hand should you choose the Specified setup the add in files will be installed in a directory that you specify The Specified option is recommended for non English versions of Windows or network installations At this point What sBest has enough information to begin copying files Once the files are done copying a Finish button should appear After clicking Finish Excel will open You may receive a message that wbintr xls contains macros You must then select the Enable Macros button in order to finish installation Where are the What sBest add in files installed in my computer The Default installation will automatically transfer the program files to the Library subdirectory of your main Excel directory usually C Program Files Microsoft Office Office10 Library LINDOWB for Excel 2002 or in C Program Files Microsoft Office Office14 Library LINDOWB for Excel 2010 TROUBLESHOOTING 403 You should find the following files CONOPTx DLL LIBIOMP5MD DLL LINDOx_0 DLL LINDOCU_xx DLL LINDOPRx DLL LINDOWBEF DLL LINDOWBIL DLL LNDWBxxx LIC MOSEKx _0 DLL MXST32 LIB README WRI VCREDIST_x86 EXE WBA XLA Excel 2003 or WBA XLAM Excel 2007 and later WBINTR XLS WBOPT DLL WBOPTLINK EXE WBUNCHADD EXE The Help file will be stored in the
244. d on observations so far Stage 2 beginning the second set of random variables are observed etc This staging information is inserted into the sheet with the WBSP_VAR and WBSP_RAND functions as follows In the drop down list you can select a WBSP_ function with its associated arguments ADDITIONAL COMMANDS 91 Variables WBSP_VAR Use this function to associate a Stage to an Adjustable Constraint or formula cell The format is WBSP_VAR stage cells_with_this_stage e g WBSP_VAR 0 Sheet1 A 2 means cell A2 in Sheet is in Stage 0 The entry Place function in cell allows you to place this information in a any cell in the workbook Typically you place this information near the decision cell so that you can quickly observe the staging information of a cell without calling up any special menus Randoms WBSP_RAND Use this function to associate a Stage to a Random cell The format is WBSP_RAND stage random_cells_with_this_stage e g WBSP_RAND 1 Sheet1 A 2 meaning cell A2 in Sheet will be at Stage 1 The NONE choice will actually delete the selected cell Refers To Specify the random cell on which to apply the distribution Alternately you can accept the currently selected cells which What sBest has automatically placed in this box You can also type the correct cell range directly into the text box Place function in cell Specify the cell in which to write the WBSP_ function Alternately you
245. daily This figure is important in calculating the expense due to float time caused by mail delay In H7 H11 the Monthly Cash Flow from each customer is shown Cells B27 F31 display the average mail delay in days between customer sites and proposed lockbox locations In G27 G31 the average delay from customer locations to the home office is found Finally in B14 G14 the fixed operating Cost Month associated with each potential lockbox site is entered Note that no fixed cost specific to the crediting of deposits is associated with the home office cell G14 since this is part of the assumed cost of doing business A Determine Adjustable Cells The adjustable cells indicate whether or not cash is to be routed from a given customer to a proposed lockbox location B7 G11 and whether or not a lockbox is opened at a given site B13 G13 These cells display a figure to show if a customer is assigned to a lockbox location 1 or not 0 286 CHAPTER 7 B Define Best The best cell is the sum of all operating and float costs in H19 A cost summary broken down into subtotals of fixed and variable costs is found in A15 H19 Let s look at the formulas used to determine these costs Considering first the variable costs associated with a lockbox in New York City the formula in cell B17 is B7 B27 H 7 B8 B28 H 8 B9 B29 H 9 B10 B30 H 10 B11 B31 H 11 1000 C 18 Thus for the NYC lockbox the average mail delay from each customer loca
246. dd in names are entered using the following dialog box Function Support x Function Support By checking this option every function will be supported in the model Otherwise What sBest will treat user written functions as unsupported functions and will read the cell as a constant equal to its numeric value at the start of optimization This support of user functions will make the model bigger more complex and so may make solution time longer In Microsoft Excel 2002 you may need to adjust a setting from the menu Tools Options Security MacroSecurity TrustedSources so as to grant any project access Thus grant any project access Check the box Trust Access to Visual Basic Project save your model and reopen Excel In Microsoft Excel 2007 adjust the security setting from the Excel Options then click on Advanced TrustCenter TrustCenterSettings Enable macros and grant the same access in the Macro Settings tab In case of your add in has been digitally signed you will need to enable this add in to run your model In some situations a time delay may occur after enabling the add in Refer to the What sBest sample file Shipping MacroFunctions xlsm for an example of valid user defined function usage The default setting is False unchecked ADDITIONAL COMMANDS 127 Advanced Statistical Functions This feature allows you to view the specific statistical functions available for What s Best Lis
247. del Globally Optimal During the solution search the solver found the best possible solution that satisfies all the constraints The message Solution Status GLOBALLY OPTIMAL will be displayed in the status report upon successful solution of a linear model There is no better answer that satisfies all constraints Locally Optimal A locally optimal outcome applies to a nonlinear model when the solver has found the best solution within a local area that satisfies all of the constraints In other words no better solution exists within that local area This means it is possible there is a locally optimal solution outside this immediate area that provides a better answer It may be wise to consider re solving the model with different starting values for the adjustable cells in attempting to investigate other local optima Optimality Conditions in Nonlinear Models After successfully solving a nonlinear model in addition to reporting a solution status of locally optimal the status report also indicates whether the optimality conditions are SATISFIED or UNCERTAIN A mathematician might refer to these optimality conditions as the Kuhn Tucker conditions A layman on the other hand might prefer to think of the optimality conditions as the flatness conditions Geometrically for functions with no constraints satisfaction of the optimality conditions means the objective function is flat the slope is zero in the neighborhood of the returned solution
248. del does not satisfy this condition You must disable the quadratic solver by turning off quadratic recognition and then re solve This will cause the general purpose nonlinear solver to be invoked Suggestions The Quadratic Recognition option is controlled with the WB Options Nonlinear Solver command When this option is enabled the nonlinear solver uses algebraic preprocessing to determine if an arbitrary nonlinear model is actually a quadratic program in which case it can be passed to the faster quadratic solver The quadratic solver assesses the model to determine if it is convex If the model is found to be non convex you will receive this error message At which point you must either reformulate the model so that it becomes convex or turn off quadratic recognition and use the general purpose nonlinear solver Refer to Overview of Mathematical Modeling for a discussion of the concept of convexity in math programs 438 CHAPTER 8 RUNTIME Runtime Limit Reached By default What sBest does not put a limit on the total time that the solver will run However by using the Runtime Limit option on the General Options dialog box posted by the Options General command the user may limit the number of iterations When the program exceeds the specified runtime limit the following warning message will be displayed on the WB Status tab Warning Message KH KK E EE EE EE EE EE EE EE EE EE EE INTERRUPTED KEE E EE EE EE EE
249. dle If such a solution does not exist What sBest will not be able to find a feasible solution to the model Node Selection The branch and bound solver has a great deal of freedom in deciding how to search the branch and bound solution tree Use the Node Selection drop down box to control the order in which the solver selects branch nodes in the tree If you examine the pull down list for the node selection option you will see the following options Solver decides This is the default option What sBest makes an educated guess regarding the best node to branch on Depth first What sBest spans the branch and bound tree using a depth first strategy Worst bound What sBest picks the node with the worst bound Best bound What sBest picks the node with the best bound In general Solver decides will offer the best results Experimentation with the other options may be beneficial with some classes of models Strong Branch Use the Strong Branch text box to specify a more intensive branching strategy during the first n levels of the branch and bound tree where n is the option s setting During these initial levels What s Best picks a subset of the fractional variables as branching candidates What sBest then performs a tentative branch on each of the variables in the subset selecting as the final candidate the variable that offers the greatest improvement in the bound on the objective Although strong bra
250. dvanced Parameters window The workbook options are General Options Linear Solver Options Nonlinear Solver Options Global Solver Options Integer Pre Solver Options Integer Solver Options and Stochastic Solver 41 42 CHAPTER 3 The algorithms used by the solvers are as follows The linear solver in What sBest uses either a primal simplex dual simplex or barrier method The Solver Method default setting of Solver decides selects the primal simplex method The What sBest nonlinear solver uses a generalized reduced gradient GRG algorithm The What sBest global solver combines a series of range bounding techniques within a brand and bound framework to find global solutions to non convex NLPs Finally the integer solver provided in What sBest uses a branch and bound algorithm also referred to as the branch and bound manager ADDITIONAL COMMANDS 43 Integers Integer Binary The ntegers Integer Binary command allows you to restrict your adjustable cells to being integers What sBest allows you to define integers in either binary or general format A binary integer will return a zero or one whereas any nonnegative whole number 0 1 2 3 will be returned for a general integer The nteger dialog box appears as follows Integer Binary Xs To create an integer range specify the cell or cell range you wish to make integer in the Refers to text box Then enter a name in the Integer Names in Workbook te
251. e If What sBest can t parse a particular name the following warning message will be displayed on the WB Status tab Warning Message Unsupported external value or range in the Name list Help Reference NAME Check name value or the validity of the link Name will be taken as a 0 number Name name Suggestions What sBest does not support names containing any of the following links to external workbooks formulas and symbols Verify all names using Insert Name Define remove any unused names or copy the external data directly into the current workbook You may need to call LINDO Systems for assistance NLINCELL Nonlinearities Present Assuming the Nonlinearity Present checkbox is checked a model containing nonlinear expressions will produce the following warning message on the WB Status tab Below the message What sBest provides the names of the cells containing nonlinear relationships Warning Message Nonlinearities Present Help Reference NLINCELL The cells below contain nonlinear expressions If these cells are used only for reporting then for efficiency they should be included in a WBOMIT range refer to documentation In some cases nonlinear cells may be linearized automatically by the Linearization option that is set in the General Options dialog box This warning can be turned off with the Nonlinearity Present checkbox in the General Options dialog box cell addresses listed at bottom
252. e F5 F7 is forced to be equal to its total Supply H5 H7 In B9 E9 the amount shipped to each intake center B8 E8 is forced to be equal to its demand B10 E10 In B23 E25 the amount shipped along each route B5 E7 is required to be less than or equal to that route s maximum capacity minus Epsilon 01 in cell B33 see note below 378 CHAPTER 7 Note As traffic Flow approaches the Limit the Time Penalty goes to infinity Observe for instance the formula for Warehouse 1 Unit 1 in cell B23 B13 B5 1 B5 B18 When Flow B5 Limit B18 the formula to calculate time is undefined because it results in division by zero The user should build models that avoid such mathematically undefined regions Therefore rather than constraining the flow along each route to be less than or equal to its limit we ve constrained it to be less than or equal to the limit minus a small amount we call Epsilon Now let s solve the model The TRAFFIC Worksheet After Solving igs ec Se TRAFFIC xlsx Microsoft Excel Lo 2 File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o E ZS f D E TRAFFIC FLOW Unit 1 Unit 2 Unit 3 Unit 4 Warehouse 1 200 8 456 4 311 2 131 6 Warehouse 2 239 4 409 8 49 8 1 0 Warehouse 3 459 8 333 8 238 9 267 5 Total K 900 E 1200 3 600 gt 400 Demand 900 1200 600 400 RATE Warehouse 1 39 14 11 14 Warehouse 2 27 9 12 9 Warehouse 3 24 14 17 13 LIMIT 30 Warehouse 2 124
253. e Model Reduction is a linear solver option and is set in the Linear Solver Options dialog box For most models the default option settings should offer the best performance in a standard running environment However as you build more complex models you may benefit from trying new option settings or be required to change the settings to get a valid of good solution In order to effectively use the options the user should understand the four solver architecture of What sBest and the types of options that are available The four classes of solvers available in What sBest are linear nonlinear global and integer The downloadable and solver suite versions of What sBest are supplied with a linear solver a nonlinear solver global solver and an integer solver Larger versions of What sBest are equipped with linear and integer solvers only A nonlinear solver and a global nonlinear solver are provided optionally for additional fees The linear solver generally runs in primal simplex mode but it can be set to dual simplex or the barrier method if the barrier option is purchased What sBest options apply only to the current model That means options are defined as Excel names in the workbook and are not saved for other workbooks The What sBest option names usually start with WBxxx and thus are separated alphabetically from the user defined names The Reset to Default command resets the workbook options but not options defined in the A
254. e The Never Created selection means that What sBest will not insert a status report By selecting Only on Error Warning What sBest will insert a status report worksheet entitled WB Status only if an error or warning from calculation is encountered If there are no errors or warnings then no status report is inserted The status report contains the model s classification statistics options selected and any error messages or warnings generated during the last attempt to solve the model To view the status report just click on the WB Status tab of your workbook The information presented in the status report is discussed in the Solve section or the Solution Outcomes section in Overview of Mathematical Modeling The What sBest default is Always Created meaning that a status report is created and inserted into the workbook upon each solve Solution Report Select the Solution Report checkbox to tell What sBest you would like a solution report created when the model is solved The next time you solve What sBest will generate a worksheet called WB Solution containing a listing of the ABC cells and their locations types values and formulas as well as sensitivity analysis dual values for the adjustable and constraint cells or the detailed report with the objective coefficients ranges Click on the WB Solution tab to see the solution report The default is not to create a solution report 56 CHAPTER 3 Here s an example of the so
255. e VBA is case insensitive to the procedure name when it is called so the procedure could alternately be called with its name typed entirely in upper case De as VBADJUST instead of wbAdjust MACROS THE VBA INTERFACE 145 Named arguments such as shown above are necessary when you are skipping over some arguments With some programming languages it is possible to skip an argument by leaving it blank This is not possible with VBA Named arguments must be used instead INVALID whbSetGeneralOptions False True True VALID whbSetGeneralOptions goStatusReport True goSolutionReport False goWmBlank True When calling procedures with multiple arguments using named arguments allows you to list the arguments in any order you choose Using named arguments can also make the code easier to read Error messages you might encounter learning VBA When initially learning to run What sBest using VBA code the user may encounter the following error messages which are easily resolved Sub or Function not defined This error message is often the result of not having WBA XLA checked as an available reference Checking it as a reference makes the What sBest procedures available to your Visual Basic code Instructions for setting this reference are provided at the beginning of this section Invalid outside procedure This message is often the result of using parenthesis without the CALL keyword Either put the key
256. e Assignments worksheet shows individual employees who are assigned to weekly shifts A 1 indicates that a staff member has been assigned to a particular shift A 0 means he isn t working that shift The Work cell by each name specifies the exact number of shifts each one should work during the week Since no employee can work more than 1 shift during any 24 hour period the maximum number of shifts any employee can work during the week is 7 The Preferences Worksheet Before Optimization l is ANd Microsoft Excel a a Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ai o ER X N eum en H Wa Ra pooh e A e 8 Wa coon HAEH Model SAMPLE MODELS 357 Each employee ranks his five most preferred shifts for the week on the Preferences worksheet Employees can specify preferences for more than 5 shifts during the week as long as they follow the same procedure e g each employee can rank his first seven choices from 7 to 1 However each em ployee would still be assigned the exact number of shifts specified in column B of the Assignments worksheet p The Constraints Worksheet Before Optimization KI ed gt o Gy e Agen ade Microsoft Excel a File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ai o El X P gt i Model Assignments lt Preferences Constraints l M gt mS oo OA
257. e an integer array of length T number of stages in the model and give in each position the number of nodes to be created in that stage By default stage 0 will always one node thus the Oth index in the array will be one Other positions in the array corresponding to the number of nodes in stages 1 2 7 1 may take any positive integer values In this framework each node represents a block realization of all the stochastic parameters in that stage and will have a conditional probability of UN where Nt represents the number of nodes in stage t Specify the sample size per stochastic parameter In the method the user should provide an integer array of length S the number stochastic parameters in the model and give in each position the sample size for that stochastic parameter In either case What sBest will automatically construct a finite scenario tree with specified dimensions In a case where both stochastic parameters are normally distributed each belonging to a different stage Therefore creating N nodes per stage has the same effect as creating N samples per stochastic parameter whenever there is a single stochastic parameter per stage 244 CHAPTER 6 Note Sampling a scenario tree is not limited to stochastic parameters that follow parametric distributions It is also possible to use sampling for models which already have a finite scenario tree This is especially useful when the original tree is finite but still too big to
258. e constraints These constraints are contributing to the infeasibility of the model Unbounded Variable warning that the debugger feature will list the unbounded variables These constraints are contributing to unbound the model Support Lookup Functions warning that the Lookup functions will be read and processed otherwise these functions will be treated as unsupported functions The default is to display all warnings except the Reference to Blank Cell and the Infeasible Constraint debugger warnings Update Links Select the Update Links button to update all What sBest functions in the current workbook to point to the present location of the What sBest add in file WBA XLA or WBA XLAM When a file is opened that contains What sBest functions created on a system in which the What sBest program files were in a different location Excel displays a message about automatic links and asks Update all Linked Information You may reply No to this dialog box given that the Excel link update won t update the links to the What sBest add in If you now look at a cell containing one of the What sBest functions you will see that it contains the path of the What sBest add in file at the time the function was created For example a function of the form 58 CHAPTER 3 WB A1 lt B1 has a prepended path and appears something like this C PROGRAM FILES MICROSOFT OFFICE OFFICE10 LIBRARY wba xla WB A1
259. e expected improvement to the objective were we to obtain perfect information about the random outcomes As such this is a expected measure of how much we should be willing to pay to obtain perfect information regarding the outcomes of the random variables Possible flag values are Disable False or Enable True The default setting is to enable calculation ADDITIONAL COMMANDS 103 Calculation for Expected Value of Modeling Uncertainty This Expected Value of Modeling Uncertainty EVMU is the absolute value of the difference EV EVEM It is a measure of what we can expect to gain by taking into account uncertainty in our modeling analysis as opposed to mistakenly assuming that random variables always take on their mean outcomes Possible flag values are Disable False or Enable True The default setting is off the EVMU is not calculated Note The above approach for computing EM and EVMU makes unambiguous sense only for models with a stage 0 and a stage 1 If there are later random variables in stages 2 3 etc then there are complications For example for decisions in later stages we have seen the outcomes from the random variables in earlier stages so considering these random variables to take on their mean value does not make sense For models with additional stages beyond 0 and 1 EVMU will merely be an approximation of the true expected value of modeling uncertainty Note Computing these expected value statistics can
260. e model The SHIPPING Worksheet After Optimization Glaf ls SHIPPING xlsx Microsoft Excel vol Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o Ys SHIPPING COST REDUCTION E G H SHIPPING CDST REDUCTION Total Units From From Demand Demand Shipped Steel Mill 1 Cost Steel Mill 2 Cost Constraint Plant To Plant A 50 200 0 500 gt 50 Plant B 0 300 90 400 gt 50 500 30 600 gt Output Capacity Output Capacity 100 lt 100 120 lt 150 i Costs 35 000 54 000 Total Cost 89 4 gt WB Status SHIPPING J al Mm Ready 7 Sp 100 The least cost solution results in shipping costs of 89 000 D Dual Values The solution recommends shipping nothing from Mill 2 to Plant A To find out how much your total cost will increase if you transport anything between these two points use the Advanced Dual command to display in an empty cell the dual value for cell E6 Then optimize again and you ll find a dual value of 200 This means that your Total Cost would increase by 200 if you were to ship one unit along that arc If you perform the same operation for cell B7 the amount shipped from Mill 1 to Plant B you ll find a dual value of zero Dual values are generally positive for adjustable cells that have a zero value in the solution An exception to this occurs in cases where there are multiple solutions as in the current problem Because no penalty is
261. e most appropriate solver Barrier What sBest uses the barrier method assuming you have purchased a license for the barrier solver Otherwise the dual solver will be used Primal The primal solver will be used exclusively e Dual The dual solver will be used exclusively In general Solver Decides will yield the best results The barrier solver can t make use of a pre existing solution so Barrier usually won t give the best results In general Dual will be faster than Primal for reoptimization during branch and bound Cold Start Use the Cold Start option to control the linear solver that is used by the branch and bound solver at each node of the solution tree when a previous solution is not present The Warm Start option discussed above determines the solver to use when a previous solution does exist The available options are Solver Decides What sBest chooses the most appropriate solver at each node Barrier What sBest uses the barrier method assuming you have purchased a license for the barrier solver Otherwise the dual solver will be used Primal The primal solver will be used exclusively Ducal The dual solver will be used exclusively 76 CHAPTER 3 In general Solver Decides will yield the best results However experimentation with the other options may be fruitful Optimality The Optimality box contains three tolerances Absolute Relative and Time to Rela
262. e nonlinear solver The dialog box posted by the Options Nonlinear Solver command appears as follows Strategies IT Crash Initial Solution V Quadratic Recognition Use Lindo Crash IV Presolve Iv SLP Direction Iw Selective Constraint Evaluation SLP Solver Steepest Edge J Gather Information for Starting Point Optimatility Tolerance 0 0000001 Iteration Limit for Slow Progress 100 Help The nonlinear solver is an option on larger versions of What sBest You can try the nonlinear solver in the Demo version of What sBest or contact LINDO Systems to purchase a nonlinear solver license for a larger version For more information regarding the difference between linear and nonlinear models see Linear vs Nonlinear Expressions and Linearization Crash Initial Solution Use LINDO Crash Check the Crash Initial Solution or Use LINDO Crash checkbox to have What sBest s nonlinear solver invokes a heuristic for generating a good starting point when solving a model If this initial point is relatively good subsequent solver iterations should be reduced along with overall runtimes The two checkboxes invoke two different internal strategies for the purpose of collecting data The default setting for Crash Initial Solution and Use LINDO Crash is off 62 CHAPTER 3 SLP Direction Check the SLP Direction checkbox to have What sBest s nonlinear solver use successive linear programming SLP techniques
263. e of the variable ii cell address of the variable In this problem the Area Allocated to each crop is an adjustable that has to occur at stage 0 Random Parameters Enter the yield information for all the crops under the various weather scenarios Then declare the Yields of each crop as a random variable This is done by using the function WBSP_RAND This function requires two parameters i stage of the variable ii cell address of the variable In this problem the Yields per Acre of the crop are the random variables that are realized at stage 1 Stage Information for Recourse Variables Declare the stage information for each recourse variables The following variables adjustables are assigned a stage using the function WBSP_ VAR a Quantity Sold b Quantity Purchased The stage is 1 because these variables depend on the random variables and therefore take a value only at stage 1 Stage Information for the Constraints and the Objective Function The What sBest interface will automatically assign the objective function and all the constraints at stage 1 which depend on the stage value of the previous variables The user can also assign these variables to a stage 1 using the WBSP_ VAR function 386 CHAPTER 7 Step 3 distribution information for the random parameters Declare a joint discrete distribution for the yields of the various crops This is done by using the function WBSP_DIST_DISCRETE_SV Thi
264. e source link to the add in The following error message will be displayed on the WB Status tab Error Message ERROR Multiple Add in Links Help reference ADDINLINK The workbook contains multiple links to the What sBest add in Only one source should be defined in the workbook Make sure to correct the add in link reference via the menu Edit Links or OfficeButton Prepare EditLinksToFiles and remove the corrupted link Then update the workbook links via the menu WB Options General UpdateLinks save the file and reopen it Suggestions Make sure of the location of the current add in via the Excel menu Tools Add ins or OfficeButton ExcelOptions Add Ins Go You may need to reset the add in by browsing to the installation location Remove any corrupted or wrong add in link from your workbook via the menu Edit Links or OfficeButton Prepare EditLinksToFiles Reset the links on the worksheet to the What sBest functions via the menu WB Options General UpdateLinks Save the file close Excel and reopen it TROUBLESHOOTING 409 ARITHERR Arithmetic Error Many mathematical operations are not defined e g division by zero What sBest tries to avoid such errors but this is not always possible When an irresolvable numerical error occurs the following error message will be displayed on the WB Status tab Error Message Arithmetic Error Help Reference ARITHERR What sBest encountered an
265. e were some outcomes under which our final wealth fell short of our target wealth of 80 This report gives complete detail on what to do each period For example at the beginning we should split our 55 by investing 41 479 into Stocks and 13 521 in Bonds Notice the interesting policy in period stage 2 If our wealth is well below 80 i e 64 or if our wealth is above 80 then we invest all of our portfolio into Stocks If our wealth is intermediate i e 71 428571 then we invest all portfolio into bonds The reasoning is that if we know we are going to fall short of our target or if we have already achieved our target then we might as well invest in the instrument with highest expected returns Stocks On the other hand if our beginning wealth stage 2 is 71 428571 then if we put all our money into bonds then we are guaranteed to just achieve our target of 80 242 CHAPTER 6 Monte Carlo Sampling In stochastic programming where one or more stochastic parameters have continuous or discrete but infinite event space there are an infinite number of possible scenarios making the model computationally intractable For such cases Monte Carlo sampling also called pre sampling can be used to approximate the problem to work with a finite scenario tree As illustrated in the figure below if the model has a single stochastic parameter with a continuous distribution such as the Normal Distribution one can discretize the event space simply
266. ean bound for a minimization problem Based on the decomposition structure the solver divides the original problem into several subproblems or blocks and solves them almost independently exploiting parallel processing if multiple cores are available BNP may perform better than the default MIP solver if a the number of linking constraints is small b the number of blocks is large and they are of approximately the same size and c the number of available processors or cores is large e g 4 or more Also there may be some models for which BNP finds a good solution and good bound more quickly than the default MIP algorithm although it may take longer to prove optimality The Blocks option for the BNP solver controls the number of subproblems or blocks that the model will be partitioned into Possible setting for the Blocks parameter are Off This will disable the BNP solver in which case the standard MIP solver will be used to solve all mixed integer linear programs N A positive integer greater than or equal to 2 indicating the number of independent blocks to try and partition the model into via one of the graph partitioning algorithms provided by Whats Beet The actual heuristic used is chosen with the Heuristic parameter The default setting for Blocks is Off i e the BNP solver will not be used on integer programming models 82 CHAPTER 3 The Block Heuristic parameter controls the heuristic used to parti
267. ear expression is called linearization What sBest can perform different degrees of linearization in the pre processing stage of the solution MATHEMATICAL MODELING 2415 process on the ABS IF MAX and MIN nonlinear spreadsheet functions as well as all logical operators See Chapter 6 Functions and Operators for a comprehensive list Ideally all nonlinear expressions would be converted to linear equivalents so the linear solver can be used instead of the nonlinear solver For an example of a simple nonlinear to linear conversion consider the following equation X Y 10 As written this equation is nonlinear because of the division by Y By simply multiplying both sides of the equation through by Y this can be converted to the equivalent linear equation X 10 Y By utilizing as many nonlinear to linear conversions as possible the nonlinear model might possibly be reduced to a linear model When a nonlinear model can be fully linearized the payoff can sometimes be enormous e g finding a solution where none could be found before or reducing solution time from days to seconds The sample model Linearization Option and Construction Cost Estimation demonstrates the benefits of successful linearization The What sBest linearization option cannot reduce all nonlinear models to linear models nor does the effort necessarily improve the solution time In some exceptional cases it may be better to run What sBest with linearization
268. earliest version of What sBest became available in 1984 for VisiCalc and What sBest has been under continuous development since then Models have been built for What sBest that solve problems in virtually every field of professional endeavor The Sample Models are provided to demonstrate the range of applications for What sBest What sBest 13 0 includes major solver enhancements to increase speed and reliability on broad classes of linear integer quadratic and general nonlinear models Other significant enhancements include an improved global solver an updated pre solver and greater user control over the solution process LI Positive Semi Definite POSD SDP This feature is an additional benefit to the Conic Solver for models being convex quadratic e The Semi Definite Program SDP Positive Definite POSD feature adds a constraint on a matrix to be positive semi definite including integer variables This can estimate a covariance matrix for a portfolio for instance e Specify any symmetric range by using the function WBPOSD on the adjustable cells this will define the lower triangular matrix LI Nonlinear Solver Programming e Improved default settings for NLP s gives 5 average speed improvement e Faster processing of long nonlinear expressions in NLP s e g 1000 s of terms as found in nonlinear regressions with 1000 s of observations xiv LI Global Solver e Global solver supports more fu
269. ecommunications Insurance O O What other optimization package have you used What will be your primary application of this product ADDITIONAL COMMANDS 139 Use the Register command to register your version of What sBest online You will need a connection to the Internet for this command to work Enter the personal information you deem relevant and select the Register button Your information will be sent directly to LINDO Systems via the Internet Once your registration is complete the following dialog box will appear on your screen Thank you Select the OK button to be returned to the main Excel environment LINDO Systems is constantly working to make our products faster and easier to use Registering your software ensures that you will be kept up to date on the latest enhancements and other product news You can also register through the mail or by fax using the registration card included with your software package CheckUpdate Turn the CheckUpdate command on to have What sBest automatically check every time you start the software if there is a more recent version of What sBest available for download on the LINDO Systems website You will need an Internet connection to the Internet for this command to work When you issue the CheckUpdate command or start a version of What sBest with CheckUpdate enabled What sBest will search the Internet to see if an updated version of the software is available fo
270. ecourse variable that has to be decided at stage 0 WBSP_VAR 0 D18 Then the other adjustables belong to their respective period For instance D23 belongs to the stage 5 Random Parameters Specify the stage information for the stock return This is done by using the function WBSP_RAND This function requires two parameters i stage of the variable ii cell address of the parameter In this problem the return in cell B19 occurs randomly at stage 1 WBSP_RAND 1 B19 Then the random cell in B23 occurs at stage 5 392 CHAPTER 7 Other Variables The What sBest interface will automatically assign the objective function and all the constraints at stage 1 which depend on the stage value of the previous variables The user can also assign these variables to a stage 1 using the WBSP_VAR function For instance the following variables are assigned a stage 1 because they are dependent of the random parameter which is at stage 1 a Price of stock this period cell C19 b Wealth this period cell E19 It would have been possible to define these variables for taking a value only at stage 1 WBSP_VAR I C19 D19 E19 Also the constraint in D26 belongs to stage 5 SAMPLE MODELS 393 Step 3 distribution information for the random parameters Specify a discrete distribution for the stock return parameter This is done by using the function WBSP_DIST_ DISCRETE SV This function takes in two parameters i the
271. ect to changes in either the right hand side of a constraint or an adjustable cell value As with the derivative of a linear function a dual value in a linear model has a constant value over a range In nonlinear models the dual value is similar to the derivative of a nonlinear function it is valid at the point where it s evaluated but it may change immediately as you move from that point Dual Values in Integer Problems Dual values for problems with integer variables cannot be usefully interpreted because of the way the branch and bound technique solves integer models If a dual value is requested in an integer model What sBest will return a value However this value is of no practical use Valid Ranges for Dual Values You may also wish to determine the upper and lower ranges of any specified dual value Changing the right hand side of a constraint or using more or less of a resource as described above eventually will cause a change in the dual value The valid range for a dual value is the amount of change in the right hand side of a constraint or in resource use in an adjustable cell that is possible before a change in the dual value will occur The range over which the use or availability of a resource or the right hand side of a constraint can decrease before the dual value changes is called the ower range The range over which the use or availability of a resource or the right hand side of a constraint can increase before the d
272. ed Lagrangian Decomposition 5 Simple Benders Decomposition StochasticSeed StochasticSeed is a cell reference or an integer greater than 1 indicating the seed value for random generator StochasticSampI Size StochasticSampISize is an integer greater than 1 indicating the default number of scenarios per stage StochasticSamp Cont StochasticSamp Cont is a True False flag indicating whether or not to use this option StochasticEVWS StochasticEVWS is a True False flag indicating whether or not to use this option StochasticEVEM StochasticEVEM is a True False flag indicating whether or not to use this option 194 CHAPTER 4 StochasticEVPI StochasticEVPI is a True False flag indicating whether or not to use this option StochasticE VMU StochasticEVMU is a True False flag indicating whether or not to use this option StochasticRepScenHoriz StochasticRepScenHoriz is a True False flag indicating whether or not to use this option StoOpt_BadStochasticSolverMethodArg StoOpt_BadStochasticSeedArg StoOpt_BadStochasticSamp ContArg StoOpt_BadStochastick VWSArg StoOpt_BadStochasticE VEMArg StoOpt_BadStochasticEVPIArg StoOpt_BadStochastickE VMUArg StoOpt_BadStochasticRepScenHorizArg Example If one wished to set all the stochastic support options the simplest syntax would be wbSetStochasticOptions 2 2027 False False False False True False To set one or more options named arguments should be used wbSet
273. ed here causes all What sBest error dialog boxes from the wbStochasticFunction routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number Useful E P N BN MACROS THE VBA INTERFACE 201 in an embedded application of What sBest Sto_BadFunctionNameArg Sto_BadCellRangel Arg Sto_BadCellRange2Arg Sto_BadCellRange3Arg Sto_BadPlaceInCellArg Sto_BadCellRange1CellRange2Arg Sto_BadCellRange1 CellRange2CellRange3Arg Bad CellRangel CellRange2CellRange3 argument Examples To set a stage information to a variable cell the simplest syntax would be wbStochasticFunction WBSP_VAR 1 0 0 0 A2 A3 0 To set a distribution to a random cell wbStochasticFunction WBSP_DIST LOGNORMAL 0 C2 D2 0 A2 A3 0 wbStochasticHistogram This routine can be used to set the stochastic histogram seen in the Stochastic Support dialog box All arguments are required except for the error code For additional discussion of the options available through this routine see the section entitled Options Stochastic Solver Syntax wbStochasticHistogram NumberBins Arglist Place_in_ cell NoErrDialog NumberBins Yes NumberBins is an integer between 1 and 255 indicating the number of bins for the reporting cell Arglist Yes ArgList is a listing of cell 202 CHAPTER 4 references for indicatin
274. ed in order for it to appear in the optimal solution of HOGCHANC This is a good number to have handy when negotiating to get a lower price Note In nonlinear models the ranges over which dual values are valid may be very small Before basing a pricing or purchasing decision on a dual price or reduced cost in a nonlinear model you should test the returned value by making the specified change to the variable or constraint using Adjustable Remove Adjustable on the variable and re solving SAMPLE MODELS 267 Box Design File name BOX XLSX TYPE NONLINEAR OPTIMIZATION The Problem in Words As a manufacturer of electronic equipment you must design a cabinet for your new product that meets the specifications of various departments within your organization at minimum cost Background Your engineering department has determined that the equipment requires a volume of at least 1512 cubic inches and that a minimum surface area of 888 square inches will suffice to dissipate heat Marketing will find it easiest to sell the finished device if the footprint of the cabinet is no more than 252 square inches Finally your designers have decreed that for aesthetic reasons the ratio of height to width should be 618 1 That is between 518 and 718 inclusively The sheet metal from which the cabinet will be made costs 05 per square inch Extra labor required on the front and back panels raises the cost for these components to 10
275. ee Steps to What sBestl 0 ccecececcccceceeeeeeeeeeeeeeeeeseceaeeeeeeeeeteetenneeeeees 9 TUTORIAL eiid i tidal de diel eed ee i r ad 10 The XYZ Production Problem cccccccceeccccesececceeeeeecetedencnedenenecesedeaaaeeeteaecesedeaceeeedenenesedes 10 The ABC Siz eege degt isin be edb cate edt det Eet 12 What s Best deteegegek idee tel dds eb ahead ded eve Haden Geet added dee 18 Working While SOlVING 22 ccecceceteeeeeneeedececeeeedeneeedeneneeedebenededaenseeddueceeedetenededeeeneeteds 19 The N Xt Ste EE 19 2 ABC S THE BASICS OF WHAT SBEST uo cccecsseeceeseeeeeeeeneeeeseeeeeeeseeeeeenseeneeensseeeeenees 21 AGjuStab EE 22 Make Adjustable cr sree tite ith ee Eege e dEr 22 Remove Adjustable eer EENEG 23 Make Adjustable amp Free or REMOVE Free 23 Free osc E eeh a ee a ae ha loo a de ee len EE dee EE 24 BeOS EE ada ual cadet met Min cantante A cede ms ain caiee tam Hes case mt eos 25 lee GS sce EAE EN AE A EE E E iva hae 25 En E A A ETE A E ETE E E ere 26 GOnstfaliints saan enee eee ten edel E deuehaaae 27 Left Hand Side LHS Right Hand Side RHS and Stored Im 27 Usage Guidelines for Constraints 0 cece ee eenee ee etne seer eeeeeeteeeeetieeeeeseeeeetieeeen 29 Constraint related Problems s sasssseessssesernesennnesssnneetnnnssnnnnasnnnnnsttnnennnanastennnnnnneeenneenna 31 Explicitly Specifying Convexity to the Solver 0 2 ececeeeeeneeeeeeeteeeeeeeneeeeeenaeeeeetteeeeeenaaes 3
276. eececeerseeccereentecersnensegesenecdentseeeeerenneadeesnensegensnece 105 REI Le EE 106 Use Simulation Forma eeng deed EE Ed 108 Aptos Reset to Default ie eea E EE E E R 109 Lee MER LC 110 FOr CellURAN GO EE 111 FREPOM ON TiVO eeh Re eeh e Ee Eed ege 111 BIER IG 111 Upper Range and Lower Range cccccccceeeseteeeeeeeneeeeeeceeeeesaeeeeeenaeeeeesnaeeeesenaeeeeeeaas 111 Report Information lt s2cccs s8 ec tateetaets d ad Edel ec 111 Usage Guidelines for Dual Values 112 Dual Value of a Constraint Cell Shadow Price 0 cc eee eeceeee eee eeeeeeeeeeeeeneeeeeenaeeeeeeaas 112 Dual Value of an Adjustable Cell Reduced Coste 114 Dual Value of Zero and Multiple Optma enn 117 Dual Values in Nonlinear Problems cccceeeeeeceeeeeeeeeeeecneeeeeeaeeeeeeaeeeeeeaeeeeeenaeeeeeeaas 117 Dual Values in Integer Problems cececeeeeeneeeeeeneeeeeeaeeeeesaeeeeeeaeeeseeaeeeeeenaeeeeeeaas 117 Valid Ranges for Dual Values eeeceeeceeeeceeceeeeeeeeeeeeeeeeeeeeseeeeeeseeeeeeeseneaeeeseneaeeeeeeaaees 117 Constraint Range Eege EE gees Drees dn 118 vi 4 Adjustable Gell RINES sirita o r E TEENE A ERT eed ahah ensue EERS 120 Lee D EE 124 OMIT Names in Workbook and Refers to 124 Usage Guidelines for Omit ceirar aas er AE E A ETE AERE 125 What TO Om t Ee ee kee ek ek 125 WhatiNot To OM eene Aiea eed ented ait eh ie ee Ee E 125 Advanced FUNCtION Support ee cececceecececcee cece eeeeeeceeaeeeeeeeeesaaeaeeeeeeese
277. eet WBSOS range reference Note Each variable in an SOS set counts against the integer variable limit imposed in limited versions of What sBest SOS sets are supported for linear models only Cardinality Related to the SOS capability discussed above What sBest also supports cardinality sets of variables via the WBCARD function The cardinality feature allows you to specify a set of variables with a cardinality of N meaning that at most N of the variables in the set will be allowed to be nonzero As with SOS sets cardinality sets help the integer solver branch more efficiently and they reduce the number of variables and constraints in your models The syntax for the WBCARD declarations is as follows written in the selected cell of the spreadsheet WBCARD number range reference Note Each variable in a CARD set counts against the integer variable limit imposed in limited versions of What sBest CARD sets are supported for linear models only ADDITIONAL COMMANDS 47 Select Any Cells This reference field allows you to select any of the Adjustable cells that will be part of the set You can select multiple range by holding the Control Ctrl key Then click on Add to store them in the List of Selected Cells field List of Selected Cells This field will list all the cells that are part of an SOS or CARD set You can modify the list by clicking on Add or Remove buttons Place the Function in Cells Speci
278. eger Nonlinear Integer Linear Quadratic Nonlinear Linear For further information on these categories see the section entitled Linear vs Nonlinear Expressions and Linearization Solution Status This field gives the status of the final solution The list of possible states is Globally Optimal Infeasible Unbounded Feasible Infeasible or Unbounded Near Optimal Local Optimal Locally Infeasible Cutoff Numerical Error Unknown Unloaded Loaded and Unknown Error See Solution Outcomes in Overview of Mathematical Modeling for more information ABCs 39 Optimality Condition This shows the optimality condition for nonlinear models either Satisfied or Uncertain See Solution Outcomes for more information Objective Value Assuming your model contains a best cell to be maximized or minimized this field displays its final value Direction Assuming your model contains a best cell this field displays its direction The direction will be listed as either Maximize or Minimize Solver Type This shows the type of any extended solver in use over and above the standard linear and nonlinear solvers Possible extended solvers are Global Branch and Bound or Multistart Tries This shows the current number of tries or iterations needed to solve the model Infeasibility This shows the total amount by which all constraints are violated When this value is reported as zero all constraints are satisfied However on integer models
279. elete MACROS THE VBA INTERFACE 169 This statement removes the WBFREE range name thereby returning the adjustable cells contained in the former range to normal status WBINT For additional discussion of the functionality provided see the section entitled nteger which refers to the nteger dialog box having a General option button that calls this procedure This routine is used to build general integer ranges named WBINT The adjustable cells contained in these ranges will be set to non negative integral values by the What sBest solver Syntax WBINT IntName Refers_to Argument Required Description IntName Yes IntName is a string that refers to the range being made integer Refers_to No Refers_to is the range or address of the cell s to be specified as integer If omitted the default is the current selection Error Codes Description Int_BadIntNameArg Bad IntName argument Int_BadRefers_toArg Bad Refers_to argument Int_ProtectedSheetError Unable to set integer cells on a protected sheet Int_CreateError Error setting integer cells Remarks The use of integer variables can dramatically increase total solution time Example To constrain cell F6 to be a general integer using the range name staff enter WBINT staff F6 To Remove If you wish to delete a WBBINT range name using VBA instead of the Delete button on the Integer Binary dialog box you can use Acti
280. ell This is referred to as goal seeking or backsolving If you solve a model in which no best cell has been specified a No Best Cell Specified warning appears in the status report after the solution process has completed This warning is intended to notify the user that the specification of a best cell may have been inadvertently omitted You may turn this warning on or off by the No Best Cell checkbox in the General Options dialog box posted by Options General command Cell range Specify the cell to be maximized or minimized in this text box by using the button on the right edge to bring up a cursor for cell selection Alternately you may accept the currently selected cell which is automatically selected by What sBest You may also type the cell range to be specified as the best cell directly into the text box ABCs 27 Constraints The dialog box posted by the Constraints command appears as follows SS Left Hand Side LHS Right Hand Side RHS Psst Pe se ft Stored in ass mm es x Specify any square range for POSD by using the function WBPOSD Define one symmetric range per WBPOSD function Range matrix Place function in cell This command is used to specify the resource constraints in your model To define a constraint you must supply the left hand side of the constraint the right hand side of the constraint and the host cell where the constraint should appear These go in the Left
281. em loading the What sBest solver Solve_ErrorRunningSolver There was a problem running the What sBest solver Return Value The return value is the same of the Solution Status argument Example Sub On JustSolve Error goto errorhandler Dim lngSolutionStatus as Long S wb ID Se olve the current model Solve IngSolutionStatus isplay the results lect Case IngSolutionStatus Case 1 MsgBox The model is Globally Optimal Case 2 MsgBox The model is Globally Optimal amp Range WBMAX Case 3 MsgBox The model is Infeasible Case 4 MsgBox The model is Unbounded Case 5 MsgBox The model is Feasible Case 6 MsgBox The model is Infeasible or Unbounded Case 7 198 CHAPTER 4 MsgBox The model is Near Optimal Case 8 MsgBox The model is Locally Optimal Case 9 MsgBox The model is Locally Infeasible Case 10 MsgBox The model is Cutoff Case 11 MsgBox The model is Numerical Error Case 12 MsgBox The model is Unknown Case 13 MsgBox The model is Unloaded Case 14 MsgBox The model is Loaded Case Else MsgBox Solution status unknown End Select Exit Sub Errorhandler Msgbox Error number is amp Err amp Description wbError Err End Sub H wbStochasticChanceConstrained This routine can be used to set the stochastic support functions seen in the Stochastic Support dial
282. emand for Time Period I must be met by using some combination of sources 1 2 and 3 The ending inventory is equal to starting inventory plus the sum of amounts purchased from each source less the unit demand You must not only satisfy the demand for each period but also minimize the amount of inventory held over Obviously it s in your interest to purchase as much as possible from your least expensive source Source 1 However demand in some periods exceeds Source 1 s capacity Objective of Optimization The objective in the Inventory model is to minimize the total cost and determine how much material to buy from each source in each time period to meet customer demand at lowest purchase and holding costs 328 CHAPTER 7 The Worksheet Let s look at the INVENT worksheet and note that Source 1 is obviously the best bargain D21 However as demand rises from period to period B6 B18 Source 1 with a capacity of 180 won t suffice to meet demand The INVENT Worksheet Before Solving Ss Bea Mo pm e nis INVENT xlsx Microsoft Excel kalak File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o Eil ZS INVENTORY PLANNING MODEL F G H INVEINTORY PLANNING MODEL Time Purchase From Source Ending Cost Per Period Demand Met 1 2 3 Inventory Period 0 0 100 Not lt 100 200 180 Not lt 280 560 220 Not lt 500 1 000 150 Not lt 650 1 300 100 Not lt 750 1 50
283. emoved from the cell and you will see the font color revert from blue or the font color you defined for the Adjustable style to the original color After solving a model you may wish use Remove Adjustable to fix some of the adjustable cells at their new values turning them into constants and solve again for the remaining adjustable cells Make Adjustable amp Free or Remove Free Select this to take the referenced cells and either set them as adjustable and free capable of assuming negative as well as positive values or remove their free status Making this selection and clicking OK will post the Free dialog box to facilitate setting or removing the free status For further discussion see the section entitled Free Refers To Specify the range of cells that are to be made adjustable or fixed in this text box by using the button on the right edge to bring up a cursor for cell selection Alternately you can accept the currently selected cells which What sBest has automatically placed in this box You can also type the correct cell range directly into the text box Note Adjustable cells should not be locked or hidden on a protected sheet 24 CHAPTER 2 Free The dialog box posted by selecting the Make Adjustable amp Free or Remove Free command in the drop down list in the Adjustable dialog box appears as follows WS g Free Names in Workbook By default adjustable cells are restricted to being greater than or equal
284. en and you will find a new toolbar What sBest and menu WB specific to the What sBest program These are discussed in the The What sBest Environment Menu and Toolbar section If you do not find the WB menu present please go to Tools Add ins and check the What sBest entry or try reinstalling What sBest You may be prompted for a license key the first time the software runs You will find your What sBest license key enclosed with your CD Please enter the license key exactly as it appears including all hyphens If you have requested and received a license key via e mail you may copy and paste it directly into the space provided Ctrl C to copy Ctrl V to paste If you would like to run a trial version of What sBest 150 constraints 300 variables and 30 integers no license key is required and just click Trial here If you have misplaced your license key you will need to contact LINDO Systems GETTING STARTED 5 You can now start building and solving models using the What sBest menu and toolbar integrated in the Ribbon bar in Excel version 2010 IO a pe iS i eT x Home Insert Page Layout Formulas Data Review View Developer Team f What sBest A ei o E ES V A K Make Adjustable Je Minimize lt Less Than one Integers E Locate E license SP Language English S ES Remove Adjustable A Maximize 7 gt Greater Than Options Heip
285. en nature s decision as well as our previous decisions we make a recourse decision x1 x0 1 taking into account that 2 0 at the beginning of stage 2 Nature takes a set of random decisions 12 leading to realizations of all random events in stage 2 and 2 1 at the end of stage 2 having seen nature s decision as well as our previous decisions we make a recourse decision x2 x0 1 x1 2 taking into account that T 0 At the beginning of stage T Nature takes a random decision T leading to realizations of all random events in stage T and T 1 at the end of stage T having seen all of nature s T previous decisions as well as all our previous decisions we make the final recourse decision x7 x0 w1 x1 2 uT This relationship between the decision variables and realizations of random data can be illustrated as follows Decision x Decision seul t Stage t 1 Stage t Each decision represented with a rectangle corresponds to an uninterrupted sequence of decisions until the next random event And each random observation corresponds to an uninterrupted sequence of random events until the next decision point Note A stage is the pair random event followed by a decision The initial stage 0 is special in that it consists only of our first decision The final stage may be special in that it may consist of just a random event with no explicit final decision MATH
286. epresent them in the range B16 E16 B16 is the intercept coefficient C16 is the coefficient for square feet D16 is the coefficient on the number of bedrooms and finally E16 is the coefficient on the number of baths B Define Best We want to minimize the Max Error which is computed in cell H16 with the formula MAX H4 H13 The range H4 H13 contains the amount of Error in our forecast for each of the historical cost observations For example cell H4 contains the formula ABS F4 G4 In words this is the absolute value of the difference of the Actual Cost F4 minus the Predicted Cost G4 This gives us the amount of forecast error on the first observation Cell H16 simply takes the maximum of all these error terms This of course is our objective and we tell What sBest to minimize it SAMPLE MODELS 315 C Specify Constraints This is an unusual model in that it doesn t make use of any limited resources so no constraints are required You are almost ready to solve the model but first you will need to set a couple of options on the General Options tab First you will need to set the Linerization Degree to Maximum to have the What sBest linearizer automatically convert this otherwise nonlinear model to linearity Next you will need to reduce the Big M Coefficient from its default value of 100 000 to 1 000 Linearized models are very sensitive to this parameter If Big M is too large you can end up with poorly scaled m
287. equirements for each of the six products are the same as in the Product Mix problem SAMPLE MODELS 335 Objective of Optimization The objective of optimization is to maximize total profits The total profit is the sum of individual plant profits minus the sum of the shipping costs from the individual steel mills The Worksheet Let s look at the BLOCK sample file The BLOCK worksheet was built by directly combining the SHIPPING and PRODMIX worksheets After combining one copy of the Shipping Cost Reduction model with three copies of the Product Mix model we performed only slight modifications to link the four individual problems into one comprehensive model The model is laid out in a 3D workbook on four separate worksheets a shipping sheet and three separate manufacturing sheets The first worksheet is Shipping built by copying the original Shipping Cost Reduction problem into cell Al of a new workbook This sheet gives information on the amount of steel that has been shipped from each steel mill to each manufacturing plant a breakdown of shipping costs and total costs The Shipping Worksheet Before Optimization Fa e g 0S BLOCK xlsx Microsoft Excel kala Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o EN 8 Je SHIPPING COST REDUCTION E E G H From Total Units From Demand Demand Steel Mill 1 Cost Shipped Steel Mill 2 Cost Constraint by Plant To 0 2 PlantA 0 5 Not gt 80
288. equires 200 tons of wheat and 240 tons of com to feed his cattle For domestic use he requires 100 tons of beans He can either grow these crops or buy them from the market The plantation cost for the crops is given by 150 acre wheat 230 acre corn and 260 acre beans The crops can be sold in the market at 170 ton wheat 150 ton corn and 200 ton beans Any shortfall can be purchased from the market at 238 ton wheat and 210 ton corn and 270 ton beans The yields in tons acre of the crops depend on the weather The farmer believes that the weather can be good fair bad or very bad with equal probability If the yield of a crop is y in fair weather then the variation of the yield with weather is given by Good 1 2y Fair y Bad 0 8y Very bad 0 6y The yields in tons acre of the various crops under the various weather scenarios are Wheat Corn Beans Good 3 3 6 24 Fair 2 5 3 20 Bad 2 2 4 16 Very bad 1 5 1 8 12 The farmer has to decide how much land to allocate to each crop so as to maximize his profit 384 CHAPTER 7 The Worksheet The worksheet has two sections 1 A section where we enter the data the adjustables constraints randoms and the objective function for the problem This is similar to the section that we create for solving a deterministic optimization problem 2 A section where we enter the stochastic information Information can be entered directly onto the spread
289. er Solver K Best Solutions Desired Number e Specify Reporting Cells Iw Create Report We also define the cells to look at via the button Specify Reporting Cells here all the Adjustable cells select the range of cells or cell by cell select the cell to refer then click Add You can modify or delete an entry by clicking on the cell reference in the list Cell H3 has the formula WBIKB_REP F3 F10 Select any cells to report multiple selection holding the Ctrl key WBBINf List of selected cells select and change by Add or Remove Knapsack WBBINf 86 CHAPTER 3 This means that we would like to generate the 5 best solutions to the model We then click OK and then run the Solve command The solver sees that the K Best feature is being requested and it automatically generates the 5 best solutions to the model At which point we are presented with the following dialog box Select the Desired Run Values for the Trade off Cells WBMAX 25 000000 RIDIKNAPSACK IFIO 1 0000 RIDIKNAPSACK IFS 0 0000 RIDIKNAPSACK IFS 0 0000 RIDIKNAPSACK IFS 0 0000 RIDIKNAPSACK IFE 0 0000 RIDIKNAPSACK IF 0 0000 RIDIKNAPSACK IFS 1 0000 RIDIKNAPSACK IFS 1 0000 Report solution into the spreadsheet This Selection Take Default In the Preview window we see that the solver was able to find 5 feasible next best solutions to the model The solutions are ranked in order by their objective values There
290. er determines zero dollars should be allocated for that source In this example the optimizer determines that zero dollars should be allocated for the Herald By using the Advanced Dual command you would find that the total cost 6 220 will be increased by 500 for every 1 000 spent on the Herald Dual values for cells B16 G16 would give the dollar cost of requiring a thousand more exposures Multi Period Inventory Management File name INVENT XLSX TYPE LINEAR OPTIMIZATION Application Profile What if your product is made from materials that are in limited supply and require special or expensive storage facilities In such a situation you have to keep purchasing and inventory costs down but still keep enough stock to meet demand If you use perishable resources or materials subject to supply limitations you may encounter problems like this one The Problem in Words Your production demands vary over thirteen time periods Raw materials available at varying costs from three different suppliers must occasionally be held in sufficient quantity from time period to time period to meet production needs A holding cost associated with inventory held over further complicates the picture How can you determine how much inventory to hold and which supplier to use while minimizing total cost and meeting your customers demand for the product Background You know the unit demand for each of the thirteen time periods For instance the d
291. er discrete or continuous The WBSP_DIST function is used to request a three argument distribution If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab TROUBLESHOOTING 443 Error Message KT RROR Stochastic WBSP_DIST 3 Format Help Reference SPDIST3 A WBSP_DIST cell with 3 arguments are incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_DIST arg1 arg2 arg3 cells where argl arg2 and arg3 are references and elle must refer to random cells cell address Suggestions There is an incorrectly formatted distribution function cell in the model A distribution function cell must use the format WBSP_DIST arg1 arg2 arg3 cells where arg arg2 and arg3 are cell references and cells is a reference to the cells you want to apply this three argument distribution The cell reference should be to a random cell For more information on using the stochastic feature refer to section Options Stochastic Solver SPERR Stochastic Error Using the stochastic feature the user has to associate the stochastic information to a core model The set of WBSP_ function is used to set the information If the arguments of these functions are not correctly specified or if any piece of information can not be loaded the following error message will
292. ess Suggestions There is an incorrectly formatted dual cell in the model A dual cell must use the format WBDUAL cell value where cell is a reference to the cell you want the dual value on and value is a numeric quantity The cell reference should be to either a constraint cell or an adjustable cell You may use any numeric value for value What sBest will replace value with the actual dual value the next time you run the solver For more information on using dual values refer to section Advanced Dual 452 CHAPTER 8 WBLOFORM Lower Range Cell Format If requested What sBest can return ranging information Range values tell you over what range a particular dual value is valid The WBLOWER function is used to request lower ranges If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message Lower Range Cell Format Help Reference WBLOFORM A lower range cell is incorrectly formatted Correct the formula in the cell below The format should be WBLOWER cell value cell address Suggestions There is an incorrectly formatted lower range cell in the model A lower range cell must use the format WBLOWER cell value where cell is a reference to the cell you want the range value on and value is a numeric quantity The cell reference should be to either a constraint cell or an adjustable cell You may use any numeric value fo
293. essions 218 SMOOTH XLSX 308 SOCP 251 Solution Outcomes 220 Solution Status 38 220 INFEASIBLE 221 Locally Optimal 220 NUMERICAL ERROR 221 Optimal 215 UNBOUNDED 221 Solution Time 39 Solve command 33 Solver decides 78 Solver Method 59 Solver Type 39 SOLVERGOP 438 SOLVERR 439 Solving 33 Interrupting 220 no feasible solution found 221 optimality conditions 220 Unbounded 221 Solving Second Order Cone Programs 251 SOS1 45 SOS2 46 SOS3 46 SPCONFLICT 440 SPCORR 441 SPDIST1 441 SPDIST2 442 SPDIST3 442 Special Ordered Set 45 Specified 4 Specify Constraints 16 SPERR 443 SPHIST 444 SPRAND 444 SPREP 445 SPSTSC 446 SPVAR 446 SQRT 205 Staff Scheduling 349 Staff Scheduling Preferred Assignment 353 Staff Scheduling Two Stage Fixed Shift 360 STAFF XLSX 349 Standard Deviation 288 Starting What sBest 7 Statistical functions Error Not a valid bookmark in entry on page 208 Steepest Edge 60 63 Stochastic 225 Stochastic Monte Carlo Sampling 242 STRARG 447 Stratified Sampling 317 Strictly convex concave 218 String Support Maximum String Length 128 STRLIST 447 Strong Branch 78 STRRES 448 Sub or Function not defined 147 406 SUM 205 SUMIF 207 448 SUMIFWBSOLVER XLS 449 SUMPRODUCT 205 Supported Functions and Operators 205 System Requirements 3 T TEMPFILE 449 Textbook 2 The ABC s 21 The Building Block Method 334 Time to Relative 77 To
294. est Excel file format Suggestions What sBest requires workbooks to be saved in Excel 97 format or higher You will need to work with a more current Excel file format Resave the file using the File Save As command in Excel When presented with the file save dialog box select a more current file format from the Save as type dropdown box TROUBLESHOOTING 411 FORMULA1 Formula Parsing If What sBest was unable to parse a cell formula in your workbook the following error message will be displayed on the WB Status tab Error Message Formula Parsing Help Reference FORMULAI An error occurred while attempting to parse the cell formula listed below Check the formula in this cell for potential problems such as complex nested functions or text strings as arguments Some Excel functions also require a specific format cell address Suggestions In rare instances if a formula becomes too complex What sBest may not be able to successfully parse it Things to check for are nested functions that are many layers deep in which case you may want to break the formula up into multiple cells Another possibility is that you have used a text string as part of the formula Finally some Excel functions must follow a specific format in order to be parsed by WB You may need to contact LINDO Systems for assistance FORMULA2 Unsupported Functions What sBest does not directly support all the functions available
295. estion 2 0 014 al il 2 10 The solution tells you the minimal sample sizes that yield reliable results within the tolerances you ve set This data could be used to calculate the probable success of a marketing plan or in forecasting demand for next year s production 320 CHAPTER 7 Car Pricing File name PRICING XLSX TYPE NONLINEAR OPTIMIZATION The Problem in Words You manufacture three automobile models each with its own price structure and miles per gallon rating at your five plants An increase in sales of any one model results in a small decrease in sales of the two others The models compete for production capacity in your five plants Also the federal government has imposed an lower limit on the average fleet mileage of your entire production which makes sales of low mileage cars more desirable You need to set the prices of the three models of automobiles so profit is maximized at the five plants while staying within the federal fleet gas mileage requirement of 24 miles per gallon Background Your known values are the cost of manufacturing each model at each plant the miles per gallon for each model and the annual production capacity at each plant You also know price quantity relationships among the models called demand curves by economists These demands are dependent upon the price of each car related to the prices of the other cars Objective of Optimization The obje
296. etermine Adjustable Cells The adjustable cells in US5 AF16 of FIXED show whether a person is assigned to a work pattern There are 12 adjustable cells corresponding to each individual being assigned indicating what one of the 12 possible work patterns that person is assigned to A 1 in an employee s row indicates that he is assigned that column s schedule number B Define Best The best solution is the one that maximizes total preference score for the group Total preference is shown in AH19 This is the sum of the preference subtotals for each employee C Specify Constraints Constraints are of the following three types No more work patterns must be assigned than recommended by the stage 1 optimization X19 Employees must be assigned to only the work patterns selected in stage 1 U17 AF17 and e Fach person should be assigned to only one work pattern AGS AG16 Now let s solve the model The FIXED2 Worksheet screen 2 After Optimization a g UF FIXED2 xlsx Microsoft Excel FE lole File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o El X Al P ajrRis tT u v w x Y N oooooooococoeoeoco m MPLOYEE ASSIGNMENTS TO SCHEDULES 10 b ab ah N Schedule Staffed LLOYD DIANE TOM JOANNE DAN JIM SUSAN JOY JOHN 2 0 0 0 0 0 0 0 0 0 0 0 0 0 ooooccococococo c e oooocoocococoeco ooeoeooonocoecoew ooococoswcooc
297. eturn for the scenarios to be greater than or equal to the Desired Return Now let s solve the model After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning This warning can be shut off from the General Options dialog box Your solved model now appears as follows n The DNRISK Worksheet After Solving Kl H Ir e g nis DNRISK xlsx Microsoft Excel 777 SEN File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ai o El 3 E Downside Risk Portfolio Model E Downsidell isk Portfolio Model Stock 1 Stock2 Stock3 0 0 0 0 0 0 Scenario Downside Forcing Scenario Return Risk Constraints 1 7 1 14 4 16 9 0 0 100 0 gt 5 6 10 7 3 5 0 0 100 0 gt 3 8 32 1 13 3 0 0 100 0 gt 8 9 30 5 73 2 0 0 100 0 gt 9 0 19 5 2 1 0 0 100 0 gt 8 3 39 0 13 1 0 0 100 0 gt 3 5 7 2 0 6 0 0 100 0 gt ON Dm amp wh Average Desired Threshold Budget Investment Return Return Return Equals 100 Percent 0 0 Not gt 13 0 11 0 Not Average Squared Downside Risk S7 al D ETE The Average Squared Downside Risk in cell D19 has been minimized to 2828 298 CHAPTER 7 Portfolio Scenario Model File name PORTSCEN XLSX TYPE NONLINEAR OPTIMIZATION The Problem in Words There are a variety of ways to measure the risk of a portfolio In this model you need to observe the changes in the opt
298. example you can obtain a description of the error and provide it to the user or perhaps provide the user with further information as the code example below demonstrates However if your code that calls the What sBest procedure does not have error handling then Excel handles any What sBest error with a run time error message that can sometimes disguise the error For details see the section entitled Run time Errors Code Sample One below sets the selected cell s as adjustable and solves the model while providing the user with information in case there is an error setting adjustable cells on a protected sheet The code also displays a description of any other error NOTE ON CODE SAMPLE ONE What sBest has defined error numbers beginning at 30001 These error numbers should not be used in your code since they are subject to change Instead use the error codes stored in the wbErr structure as shown in the example below What sBest provides a function to return the error text for these wbErr codes This function is similar to Excel s Error function The wbError function takes an error code or error number as an argument and returns the error text CODE SAMPLE ONE Sub mySub On Error GoTo ErrorHandler Trap any What sBest error wbhAdjust Make current cell adjustable wbSolve Solve the model Exit Sub ErrorHandler Process any What sBest error If Err wbErr Adj ProtectedSheetError Then
299. f employees To get integer answers you could round the fractional cell values One possibility is as follows Round From To Cell G8 Number Starting on Monday 79 33333 80 Cell G10 Number Starting on Wednesday 19 33333 20 Cell G11 Number Starting on Thursday 39 33333 39 Cell G13 Number Starting on Saturday 29 33333 29 After entering these new integer values in the adjustable cells you ll find a new solution with a total of 221 employees and 44 200 as the minimum cost Therefore dual values in this case provide us with the theoretical since fractional people are imaginary minimum increase in total cost 67 instead of the actual increase in total cost 200 for a feasible solution Note Before using any dual values in a pricing hiring or purchasing decision be sure to investigate the ranges over which they are valid In some problems dual values may be valid over only an infinitesimal range See Additional Commands for a discussion of valid ranges for dual values SAMPLE MODELS 353 Staff Scheduling Preferred Assignment File name ASSIGN XLSX TYPE LINEAR OPTIMIZATION Application Profile Staff scheduling is usually a very costly and laborious job In institutions where there are several daily shifts and the staff can rotate between shifts during the same period the task is even more complicated The scheduler must match the organization s requirements with the preferences of individual employees Larger
300. f FLOWNET xlsx Microsoft Excel 2 6 File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o El X G PRESSURE BALANCE Destination Cc D E Zo mnmpcomb Wi 2 3 4 5 6 7 8 d 10 11 12 13 Pressure Parameter 1 Flow Parameter 1 Note The pressure parameter equals 1 for incompressible fluids and electricity and 2 for gases The flow parameter equals 1 for electricity 1 852 for H2O and between 1 8 and 2 for other fluids ARC FLOW PRESS BALANCE lt 3 Hal vlrh mn CHE A Determine Adjustable Cells The adjustable cells are the Pressures at each Node Arc Resistance C15 H15 and the Flow along each arc the cells outlined above in the range C4 J11 of the Arc Flow worksheet To facilitate modeling the problem nonadjustable zeroes have been entered for arcs where there is no flow This increases the number of numeric cells in the model In your own models you may want to minimize the number of numeric cells B Define Best No best cell is defined in this example since our objective is simply to balance the flows along the arcs and satisfy demand at the nodes C Specify Constraints The constraints in this model are twofold First conservation of flow requires that the amount entering an arc must equal the amount exiting that arc Arc Flow C13 H13 As an example here s the formula in C13 WB SUM C4 C11 ARC RESISTANCE C13 SUM C4 H4 274 CHAPTER 7
301. f What sBest MACROS THE VBA INTERFACE 175 Error Codes Description IKBest_BadArgListRepArg Bad ArgList argument KBest_BadRefersToRepArg Bad Refers_to argument IKBest_ProtectedSheetRepError Unable to set KBest cells on a protected sheet Example To define an KBest trade off range F3 F10 and place the function WBIKB_REP in H3 enter wbIntegerSolverK BestReport F3 F10 H3 See sample Knapsack_KBest xlsx WBOMIT For additional discussion of the functionality provided see the section entitled Advanced Omit which refers to the dialog box that calls this procedure This routine is used to build WBOMIT ranges which are areas of the worksheet that What sBest will ignore while solving If you wish to delete a WBOMIT range name using VBA instead of the Delete button on the Omit dialog box you can use Active Workbook Names WBOMITmyRangeName Delete This statement removes the WBOMIT range name Syntax WBOMIT OmitName Refers_to Argument Required Description OmitName Yes OmitName is a string that refers to the range that is to be ignored Refers_to No Refers_to is the range or address of the cell s to be ignored If omitted the default is the current selection Error Codes Description Omit_BadOmitNameArg Bad OmitName argument Omit_BadRefers_toArg Bad Refers_to argument Omit_ProtectedSheetError Unable to set omit cells on a protected sheet
302. f data covering 2 years 8 The SMOOTH Worksheet Before Solving mas e GF VIS SMOOTH xlsx Microsoft Excel ec he Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o ER Expahential Smoothing Model Sum Squared Squared Sales Predicted Error Error 1 10 1 10 1 52 0 00 Not 1 10 0 18 7 40849 1 76 0 00 0 00 3 10 Bounds 1 86 0 00 0 00 346 Alpha 0 00 Not gt lt 1 57 0 00 0 00 2 46 1 64 0 00 0 00 2 69 1 64 0 00 0 00 2 69 2 12 0 00 0 00 4 49 1 39 0 00 0 00 1 93 2 29 0 00 0 00 5 24 1 67 0 00 0 00 2 79 2 42 0 00 0 00 5 86 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 DDD EH HE e KOENEN E 312 CHAPTER7 The solution is shown below a The SMOOTH Worksheet After Solving i ed SS EF TAN SMooTHter Micros Excel ohh File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ai o X Expdhential Smoothing Model Sum Squared Squared Sales Predicted Error Error 1 10 1 10 1 52 1 34 Leg 1 76 1 58 0 18 Bounds 1 86 1 74 0 08 Alpha 056 gt lt 1 57 0 03 1 64 0 00 1 64 0 00 2 12 0 23 1 39 0 27 2 29 0 45 0 11 0 37 0 10 0 11 0 00 0 11 0 05 0 04 0 01 1 2 3 4 5 6 7 8 9 HAH SAMPLE MODELS 313 Linearization Option Construction Cost Estimation File name LINEARZ XLSX TYPE NONLINEAR
303. ferent processes This number can be set between 1 and 32 depending on the computer capabilities The default setting is 1 There is also a choice for the threads Solver Decides Use the best performing multithreading solver on average either concurrent or parallel for model type when the number of threads is greater than 1 otherwise it runs single threaded Parallel Preferred Prefer parallel over concurrent but use concurrent if an appropriate parallel solver does not exist Parallel Only The solver will run the parallel mode Concurrent Preferred Prefer concurrent over parallel but use parallel if an appropriate concurrent solver does not exist 54 CHAPTER 3 Concurrent Only The solver will run the concurrent mode Hide Status Window on Solve Check this option if you would like to hide the Status Window while the What sBest solver is running The default setting is off Linearization The linearization options offer significant performance gains to some nonlinear models by replacing nonlinear operations with mathematically equivalent linear operations An example of such performance gains may be seen in the sample model entitled Linearization Option and Construction Cost Estimation Degree Many nonlinear operations such as abs x and min x y can be replaced by linear operations that are mathematically equivalent The ultimate goal is to replace all the nonlinear operations in a model with equivale
304. finding better solutions when a non convex model has several local optima Note The multistart capability is an optional component of the What sBest solver and is packaged as part of the global solver option Your particular installation may not have the global option enabled in which case enabling Multistart Attempts will cause a warning to be generated when solving If you are interested in adding the multistart capability please contact LINDO Systems The default setting for Multistart Attempts is Solver Decides Optimality Specify the global solver s optimality tolerance in the Optimality text box in the Tolerance box This tolerance indicates that candidate solutions must beat the incumbent solution by at least this amount to become the new best solution The default setting for Optimality is 0 000001 Delta Specify the delta tolerance the global solver s convexification process in the Delta text box in the Tolerance box This tolerance is a measure of how closely the additional constraints added as part of convexification should be satisfied The default setting for Delta is 0 0000001 ADDITIONAL COMMANDS 67 Variable Bound Specify the maximum magnitude of variable bounds used in the global solver s convexification process in the Variable Bound text box in the Limit box Any variable bound with a magnitude in excess of this value will be truncated to this setting Setting this parameter appropriately helps the
305. fined by either the menu command Constraints or the toolbar buttons lt gt Once you ve specified the ABC s you can solve your worksheet model and find the best answer to your problem 10 CHAPTER 1 TUTORIAL This tutorial will introduce you to What sBest by showing you how to solve a simple linear problem called the XYZ Production Problem You should open the sample problem file XYZ XZLS located in the WB directory in your C drive so you can finish formulating the model in this tutorial The other sample models have been completely formulated for you and are ready to solve Please note that the following discussion uses Excel naming conventions such as C 5 D4 throughout The XYZ Production Problem XYZ Corporation builds two computer models the Standard and the Deluxe The Standard has a profit per unit of 300 and the Deluxe has a profit per unit of 500 The two models are produced from three components the Standard computer tower the Deluxe computer tower and a hard drive Standard Model Deluxe Model _ Profit per Unit 300 500 Problem What combination of Standard and Deluxe computer towers will maximize XY Z s profit from the components currently in stock Unless specified otherwise during installation the XYZ XLS file was copied to the WB subdirectory If you haven t already done so open the XYZ XLS sample file GETTING STARTED 11
306. function is the equivalent of SUMPRODUCT but instead of multiplying terms row by row the terms are multiplied row by column and then summed The syntax is WBINNERPRODUCT Rangel Range2 Rangel or The cell range containing the column or row to multiply and sum Range2 Rangel and Range can only be one dimensional ranges and the ranges must be the same size and shape Note Nesting of the VWBINNERPRODUCT function is not recommended In other words the function WB A1 lt WBINNERPRODUCT B2 B4 A3 A5 should be avoided 5 Logistic Cumulative Distribution WBLOGISTIC This function returns the cumulative distribution function for the Logistic distribution The syntax is WBLOGISTIC A B C Cumulative distribution function for the Logistic distribution with location parameter A and scale parameter B It returns the probability that an observation from this distribution is less than or equal to C 210 CHAPTER 5 6 Logistic Probability Density Distribution WBLOGISTICDENS This function returns the probability density function for the Logistic distribution The syntax is WBLOGISTICDENS A B C Probability density function for the Logistic distribution with location parameter A and scale parameter B It returns the probability density at C 7 Logistic Inverse Distribution WBLOGISTICINV This function returns the inverse of the Logistic distribution The syntax is WBLOGISTICINV A B C Inverse of L
307. fy the host range of cell you would like to see the SOS or CARD function to be placed in the spreadsheet What sBest automatically fills this box with the current cell selection If the selection already contains a WBSOSx or a WBCARD function then What sBest will display the cells argument into the List of Selected Cells 48 CHAPTER 3 Integers Semi continuous The Integers Semi continuous command allows you to support Semi continuous variables via the following dialog box Semi continuous EE Lower Bound A 1 Upper Bound SAS S Select any cells multiple selection holding ae Lx SAS1 B List of selected cells select and change by Add or Remove Cancel Add Remove Place the function WBSEMIC in cell ex a mm Many models require certain variables to either be 0 or lie within some nonnegative range e g 10 to 20 Variables with this property are said to be semi continuous Modeling semi continuity in What sBest in the past meant having to add an additional 0 1 variable and two additional constraints The syntax for the WBSEMIC declaration is as follows written in the selected cell of the spreadsheet WBSEMIC lower bound upper bound range references This will restrict the variable in the range references to be either 0 or to lie within the range lower_bound upper_bound Note Each semi continuous variable will be counted against any integer variable limit for your
308. g of string text argument in formulas goWrnIrreConst No 1 True goWrnIrreConst is a True False flag indicating whether to provide warning of irreconciliable constraints or not goWrnInfeasConst 0 False goWrnInfeasConst is a True False flag indicating whether to provide warning of infeasible constraints or not goWrnUnboundVar No 0 False goWrnUnboundVar is a True False flag indicating whether to provide warning of unbounded variables or not goWrnSupLookupFct Ne 1 True goWrnSupLookupFct is a True False flag indicating whether to provide warning of supported lookup functions or not Error Codes Opt BadFeasibilityToleranceArg Opt_BadIterLimitArg Opt_BadRuntimeLimitArg Opt_BadSelectRefersToArg Opt_BadNumberThreadsLimitArg Opt_BadThreadChoiceArg Opt_BadMinimizeExcelArg Opt_BadHideStatusArg 180 CHAPTER 4 Opt_BadStatusReportArg Opt_BadReportsLocationArg Opt_BadSolutionReportArg Opt_BadNonlinearityArg Opt_BadNoObjectiveArg Opt_BadBlankCellsArg Opt_BadUnsupportedFunctionArg Opt_BadStringArgumentArg Opt_BadIrreConstraintArg Opt_BadInfeasConstraintArg Opt_BadUnboundVarArg Opt_BadSupLookupFctArg MACROS THE VBA INTERFACE 181 Example Arguments should be provided as follows If one wished to set all the options the simplest syntax would be wbSetGeneralOptions 0 0000002 77 88 1 0 2 True False False 1 0 2 222222 1 1 1 False
309. g the cells to display in the stochastic report Place_in_cell Place_in cell is a cell reference to specify the cell in which to write the WBSP_HIST function NoErrDialog Any argument passed here causes all What sBest error dialog boxes from the wbStochasticHistogram routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number Useful in an embedded application of What sBest Sto_BadNumberBinsArg Sto_BadPlaceInCellArg Sto_ProtectedSheetRepError Examples To set several reporting cells so to display the histogram report the simplest syntax would be wbStochasticHistogram 0 Sheetl C 1 wbStochasticReport This routine can be used to set the stochastic reporting cells seen in the Stochastic Support dialog box All arguments are required except for the error code For additional discussion of the options available through this routine see the section entitled Options Stochastic Solver Syntax wbStochasticReport ArgList Place_in_cell NoErrDialog MACROS THE VBA INTERFACE 203 references for indicating the cells to display in the stochastic report Place_in_cell Place_in cell is a cell reference to specify the cell in which to write the WBSP_REP function NoErrDialog Any argument passed here causes all What sBest error dialog boxes from the wbStochasticFunction routine to be su
310. global solver focus on more productive domains The default setting for Variable Bound is 10000000000 Use of Bound Specify how to impose the above variable bound limit on the model variables in the Use of Bound drop down box in the Limit box Possible values are Solver Decides None All Variables or Selected Variables The default setting for Use of Bound is 0 or Solver Decides Branching Direction Specify the direction to branch first when branching on a variable with the Branching Direction drop down box The branch variable is selected as the one that holds the largest magnitude in the measure Possible values are Solver Decides Absolute Width Local Width Global Width Global Distance Absolute Violation or Relative Violation The default setting for Branching Direction is 0 or Solver Decides Box Selection Specify the node selection rule for choosing between all active nodes in the global solver s branch and bound tree in the Box Selection drop down box Possible values are Solver Decides Depth First Worst Bound or Best Bound The default setting for Box Selection is 0 or Solver Decides Algebraic Reformulation Control the extent of algebraic reformulation e g whether x y x is replaced by x y x with the Algebraic Reformulation drop down box The algebraic reformulation process is crucial in building a tight convex envelope to enclose the nonlinear nonconvex functions thereby helping to improve overall
311. gument Int_BadRefers_toArg Bad Refers_to argument Int_ProtectedSheetError Unable to set integer cells on a protected sheet Int_CreateError Error setting integer cells Remarks Integer variables can dramatically increase total solution times 156 CHAPTER 4 Example To constrain cell F7 to be a binary integer using the range name OnOff enter WBBIN Onoff F7 To Remove If you wish to delete a WBBIN range name using VBA instead of the Delete button on the Integer Binary dialog box you can use Active Workbook Names WBBINOnOff Delete This statement removes the WBBIN range name thereby returning the adjustable cells contained in the former range to normal status wbConstraint For additional discussion of the functionality provided see the section entitled Constraints which refers to the dialog box that calls this procedure This routine is also called with appropriate arguments by the three toolbar buttons displayed above This routine inserts a constraint formula within the selected cell Syntax wbConstraint LHS Direction RHS ConLoc NoErrDialog Argument Required Description LHS Yes LHS is the left hand side of the constraint equation Direction Yes This is a string to indicate what type of constraint lt less than or equal to gt greater than or equal to equal to lt c convex gt c concave or c convex For backwar
312. h Proposed Demand City Monthly Supply Fixed Open City Atlanta Boston Chicago Denver Omaha Portland Cost Plant Oo NON amp Co N h Baltimore 10 Cheyenne 11 3alt Lake City 12 Memphis B Wichita 14 15 Operating Cost 15 250 16 Trans Cost 3 800 3 200 6 658 600 4 130 13 200 Trans Costs 31 588 17 18 TOTAL OPERATING COST 4 19 20 21 22 23 24 25 ki 4 4 gt gt 1 WB Status Shipping Costs Amount Shipped S7 Som o O 348 CHAPTER 7 The Amount Shipped Worksheet After Optimization mias c gae ANLO Microsoft Excel Sm x File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o El X Amount Shipped Monthly Proposed Demand City Supply 5 Supply Supply Capacity Boston Chicago Denver Omaha Portland imitation in Tons Baltimore Cheyenne 45 leet Demand 16 Demand 17 18 ER EAR 21 Be M 4 H WB Status Shipping Costs_ Amount Shipped 8 Meu J Plants are open in Baltimore Cheyenne and Memphis 19 110 and 112 of the Shipping Costs worksheet Total Operating Cost in J18 of the Shipping Costs worksheet has been minimized to the optimally low figure of 46 838 Since the constraint in HO of the Amount Shipped worksheet is not binding you know that additional sales out of Baltimore are possible SAMPLE MODELS 349 Staff Scheduling File name STAFF XLSX TYPE LINEAR OPTIMIZATION Ap
313. h Next forms are available Please consult the Visual Basic or Excel Help for more information After running the macro the adjustable cells and the best cell for each increment are copied to the table in the range L2 S22 The row is incremented each time through the variable Table that is always two greater than the Count the iteration number In this way a convenient report is created providing sensitivity analysis of the profit unit of Product 2 As shown here there are changes in the optimal solution when the profit unit for product 2 is 50 or greater In addition to simply having the macro increment the profit unit for product 2 through a range the profit unit values could have been read from a database or a text file This model is a looping version of the Product Mix model VBA Interface Procedures What sBest provides a set of Visual Basic Procedures that allow models to be built and automated using Visual Basic for Applications VBA commands These procedures are the same ones that are called when What sBest commands are selected from the WB menu or the What sBest toolbar For example the Solve procedure invoked in a macro is also invoked when you press the button on the What sBest toolbar If you wish to automate the creation of a What sBest model or if you wish to incorporate What sBest as a part of a larger application then you will find these procedures to be invaluable They make it relatively easy to i
314. he General Options dialog are saved with the workbook and are therefore called workbook options All workbook options are reset to default settings every time you create a new workbook You may also use the Reset to Default command to return all workbook options in the current model to their default values with the exception of the Advanced Parameters options Discussion of the General Options follows below Feasibility Tolerance You can specify the amount of violation that will be tolerated in a model s constraints with the Feasibility Tolerance text box Increasing the feasibility tolerance can allow you to find a feasible solution to a model that was previously infeasible For example changing a feasibility tolerance would be useful if you have a poorly scaled model with very large and very small coefficients that is nearly feasible You would know that the model is nearly feasible if you found the slack values to be small The best solution would be to rescale the model but setting the feasibility tolerance offers a simpler alternative By entering a larger feasibility tolerance you allow the solver to tolerate slight constraint violation such as a few pennies in a budget of tens of thousands in order to reach a feasible solution The default value for feasibility tolerance is 0 0000001 Iteration Limit You can specify a limit on the number of tries or iterations undertaken during the solution process with the Iteration Limit Iterations
315. he Problem in Words The first stage is to determine the lowest cost schedule that meets all staffing requirements You can determine this schedule independent of specific personnel availability or characteristics You know staffing requirements for each day of the week It s not important how these daily requirement figures are obtained as long as they accurately reflect staffing needs They could be based on the output of another model such as a queuing model or an extrapolation of historical figures We also make the following assumptions in this model There is only one skill level of staff employees are interchangeable Staffing requirements or Full Time Equivalent requirements FTEs can be met with either full time employees working five days per week or part time or pool employees that can be hired on a daily basis e Each full time employee cannot work more than 4 days in a row You could incorporate other assumptions with minor changes to the model Background An employee s schedule for one time period is called a work pattern Each employee can be scheduled under one of several work patterns For example a full time employee working five days a week can either work Monday through Friday or Tuesday through Saturday These work patterns can be represented as follows Pattern Mon Tue Wed Thu Fri Sat Sun 1 1 1 1 1 1 0 0 2 0 1 1 1 1 1 0 A one indicates that the employee is working and a zero that he is off
316. he Visual Basic Editor is called via Tools Macros from the main Excel menu bar If you do not create this reference then any attempt to use the What sBest attributes or procedures will produce the error message Sub or Function not defined Building and Solving a Basic Model Let s revisit the XYZ Production problem discussed in the Tutorial of Getting Starting We will look at how the ABC s of a model can be specified using Visual Basic Unless specified otherwise a sample file named XYZVBA XLSM was copied to the WB subdirectory during installation Along with the main XYZ worksheet there are two VBA modules called ABC e and Dual The ABC s module has three procedures in it BuildXYZ which uses Visual Basic to build and solve the model MaxDeluxe which changes the objective to maximizing the use of Deluxe computer towers and solves the new model and MaxDeluxe2 which uses the same objective as MaxDeluxe but imposes a restriction that profit must be greater than or equal to 32 000 You will notice that the code to build the model is very straightforward For information on the complete syntax for each of the functions refer to the section on Procedures The BuildXYZ procedure is listed below Sub BuildXYZ Dim lngSolutionStatus As Long Go to line label Handler for code that handles error On Error GoTo Handler Make Quantities to Produce C5 D5 Adjustable 148 CHAPTER 4 wbAdjust ESDI Make
317. he adjustable cells and or functions of the adjustable cells For instance resources will never be unlimited At some usage level resources will be exhausted Another example would be that orders must be filled A cost minimization model with no constraints to fill orders would minimize cost by producing nothing which clearly is not an optimal answer to the real world problem Constraints are used to indicate these types of limitations It would be unusual for a model to have no constraints So when What sBest encounters such a situation it displays the following warning on the WB Status tab Warning Message No Constraint Cells Help Reference NOCONST The solver recognized no valid constraints The model either contained no constraint functions or only constraint functions that did not depend on any adjustable cells If the model was developed for an earlier version of What sBest the constraints may need to be converted to the current format for constraint functions 436 CHAPTER 8 Suggestions You will need to add at least one constraint cell to the model Constraints can be created with the WB Constraints command You may also want to refer to section The ABC s Three Steps to What sBest for detailed information on how to create a constraint cell On rare occasions it may actually make sense to have an unconstrained model This would be a model where you need to find the extreme point of an objective function dependent upo
318. he arguments by tracking its dependencies or references The argument cell should be declared only once cell address Suggestions There is a conflicting declaration of the argument cell in the Stochastic timing functions The timing functions must use the format WBSP_RAND arg cells for randoms or WBSP_VAR arg cells for variables where arg is a numeric value or a cell reference to a numeric value and cells is a reference to the cells you want to apply this timing information The cell reference should be declared once without cross or duplicated references For more information on using the stochastic feature refer to section Options Stochastic Solver TROUBLESHOOTING 441 SPCORR Stochastic WBSP_CORR Format Using the stochastic feature the user has to associate a distribution to a random cell either discrete or continuous The WBSP_CORR function is used to request a one argument correlation If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message XE RROR Stochastic WBSP_CORR Format Help Reference SPCORR A WBSP_CORR cell with 1 argument is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_CORR arg1 cells where argl is a reference and elle must refer to random cells cell address Suggestions There is an incorre
319. he cells D8 D10 to no longer be adjustable enter wbAdjust D8 D10 Reset or wbAdjust Range Cells 8 4 cells 10 4 Reset wbBest For additional discussion of the functionality provided see the section entitled Best which refers to the dialog box that calls this procedure This routine is also called with appropriate arguments by the either of the toolbar buttons displayed above This routine is used to create a best cell replacing any previously defined best cell All arguments are optional Syntax wbBest BestCell BestChoice NoErrDialog Argument Required Description BestCell No This is the cell or address of the cell to be the best cell If omitted the default value for BestCell is the current cell BestChoice No This is a string to indicate whether the best cell should be minimized or maximized BestChoice accepts MIN or MINIMIZE upper or lower case for minimize MAX or MAXIMIZE upper or lower case for maximize and NONE upper or lower case to remove any previous best cell If omitted the default value for BestChoice is minimize For backwards compatibility with earlier versions of What sBest BestChoice also accepts the numbers 1 for Minimize 2 for Maximize and 3 for None NoErrDialog No Any argument passed here causes all What sBest error dialog boxes from the wbBest routine to be suppressed Instead the error number is delivered in this return argument Pass an i
320. he solver press on to the true optimal solution without immediately resorting to a relative optimality tolerance discussed above On the other hand if after running for a while it becomes apparent that the optimal solution won t be immediately forthcoming then we might want the solver to switch to using a relative optimality tolerance The Time to Relative tolerance can be used in this manner This tolerance is the number of seconds before the branch and bound solver begins using the relative optimality tolerance So for the first n seconds where n is the value of the Time to Relative tolerance the branch and bound solver will not use the relative optimality tolerance and will attempt to find the true optimal solution to the model Thereafter the solver will use the relative optimality tolerance to confine its search The default value for the Time to Relative tolerance is 100 seconds Tolerances The Tolerances group box contains three miscellaneous tolerances for controlling the branching strategy used by the branch and bound solver The three tolerances are Hurdle Node Selection and Strong Branch We discuss each of these in the sections that follow Hurdle Enter a value in the Hurdle text box if you know the objective value of a solution to a model This value is used in the branch and bound manager to narrow the search for the optimum More specifically What sBest will only search for integer solutions in which the objective is bet
321. heet during successive runs This makes possible for other sheets to keep their cells reference from this report for displaying a specific data The solver writes a series of solution in the created tab WB Stochastic and WB Histogram with the expected value and displays the first default scenario or a selected scenario on the spreadsheet Please refer to the section Guidelines for Stochastic Modeling for a tutorial and information on how to use Stochastic Support effectively Expected Value of Objective The Expected Value of Objective EV is the expected value for the model s objective over all the scenarios and is the same as the reported objective value for the model This value is provided by default in the report The user can directly request the value on the spreadsheet by inserting the function in a cell WBSP_MEAN cellref value The cell will display the mean value requested for the cellref For instance enter WBSP_MEAN B 22 0 in any cell After solving this function will display the mean value of 2106 49622433202 for the objective cell in B22 102 CHAPTER 3 Calculation for Expected Value of Wait and See Model s Objective The Expected Value of Wait and See Model s Objective EVWS reports the expected value of the objective if we could wait and see the outcomes of all the random variables before making our decisions Such a policy would allow us to always make the best decision based on the outcomes for
322. her or not to use this support Error Codes Description AdvFunc_BadAdvFunctionSupportArg Bad AdvFunctionSupport argument MACROS THE VBA INTERFACE 177 Example If one wished to set all the function support options the simplest syntax would be wbSetFunctionSupport True or by the named argument wbSetFunctionSupport AdvFunctionSupport True Note The AdvFunctionSupport argument should be set to TRUE in order to use the other arguments wbSetGeneralOptions This routine is used to set the What sBest general options These options constitute the majority of the options seen in the General Options dialog box All arguments are optional For additional discussion of the options available through this routine see the section entitled Options General Syntax wbSetGeneralOptions goFeasTol golterLimit goRuntimeLimit goNumberThreadsLimit goThreadChoice goIndSlack goAutoSelectFreeIntOmit goMinimizeExcel goHideStatusWindow goLinearizationDegree goLinearizationDelta goLinearizationBigM goStatusReport goStatusReportBegEnd goSolutionReport goWrnNonlinear goWrnBest goWmBlank goWrnFunction goWrmStringArg goWrnIrreConst goWrnInfeasConst goWrnUnboundVar goWrnSupLookupFct Argument Required Default Description goFeasTol No 0 0000001 goFeasibilityTol is a positive number indicating the amount of violation tolerated in cons
323. how What sBest successfully met the minimum steel needs of each plant while efficiently using the other raw materials on hand SAMPLE MODELS 339 Waste Minimization in Stock Cutting File name CUTSTOCK XLSX TYPE LINEAR OPTIMIZATION Application Profile Consider a product produced in rolls or sheets fabric sheet metal or carpeting A manufacturer of this product is constantly faced with a problem His machinery produces rolls of a single standard width but he must sell to an unstandardized marketplace This model applies linear programming to the problem of cut patterns Given the sizes required the amount of each size demanded and the cut patterns available the model minimizes the waste cost associated with meeting demand The Problem in Words You re the production manager in a sheet metal plant You turn out rolls of sheet metal of a particular width Your customers use your product in different ways requiring rolls of different widths To accommodate their needs you can cut a roll of sheet metal into more than one narrower roll Your goal is to waste as little of the sheet metal as possible by choosing patterns that best utilize the width of a roll and closely matching the length requirements of various sizes Each wasted edge strip and each length of metal cut to an unneeded width adds to your total waste cost You must select cut patterns that meet customer needs and minimize total waste costs Background Your fac
324. iables offering the highest absolute rate of improvement toward the objective This preference is acted upon regardless of how far other variables have to move in tandem with the chosen variables Since these other variables may quickly hit a bound the resulting gain for the objective may actually be quite small The pricing mode called Steepest Edge takes a different approach of more painstakingly selecting variables according to the actual improvement in the objective Because the objective s gain is higher per iteration with Steepest Edge fewer iterations of somewhat longer duration are required The default value for Dual Pricing is Solver Decides Primal Pricing For the primal simplex algorithm there are two primary methods The Partial method prices a small subset of variables each iteration and intermittently prices out all the variables to determine a new subset of interesting variables Devex prices out all columns during each iteration using a steepest edge approximation Use of the thorough steepest edge algorithm means that Devex results in fewer overall iterations though each iteration is longer than it would be under the Partial method Devex is useful with degenerate models but it is generally difficult to predict in advance what method to use The default value for Primal Pricing is Solver Decides ADDITIONAL COMMANDS 61 Options Nonlinear Solver This command allows you to set a number of options controlling th
325. ic Cardinality Disjunctive ADDITIONAL COMMANDS 73 Options Integer Solver The dialog box posted by the Options Integer Solver command appears as follows This command allows you to set a number of options controlling the function of the integer solver To understand the operation of the integer options it is useful to understand how integer problems are normally solved With the default option settings What sBest solves integer problems using the following steps 74 CHAPTER 3 1 What sBest begins by solving the continuous relaxation i e the original model with integer restrictions removed This gives an optimistic bound on the objective of the true integer model because the objective of the integer restricted model could never be better than the objective of the continuous approximation 2 After solving the continuous relaxation What sBest uses a process called branch and bound to find the optimal integer solution Branch and bound implicitly enumerates all possible integer solutions in an intelligent fashion minimizing the number of solutions that have to be explicitly examined However the number of potential solutions grows exponentially with the number of integer adjustable cells Thus models with a large number of integers may take a very long time to solve Options such as the optimality tolerances set limits upon how exhaustively this branch and boun
326. ich you will want to add your own application To demonstrate some of the range of applications for What sBest sample models are provided with the software and many are explained in Chapter 8 Sample models 2 CHAPTER 1 Optimization Models Optimization helps you find the answer that yields the most desirable result the one that attains the highest profit output or happiness or the one that achieves the lowest cost waste or discomfort Often these problems involve making the most efficient use of your resources including money time machinery staff inventory etc Optimization problems are classified as linear or nonlinear depending on whether the relationships in the problem are linear with respect to the variables What sBest can solve both linear and nonlinear problems with optional integer restrictions For more information on optimization and the solution process please refer to Overview of Mathematical Modeling For additional reference we recommend the LINGO textbook Optimization Modeling with LINGO or the LINDO textbook Optimization Modeling with LINDO both by Linus Schrage and available through LINDO Systems Non Optimization Models Non optimization models do not have a cell defining an objective function that is to be maximized or minimized A common purpose of such models is to solve an equation What s Best can find values that satisfy sets of equations or satisfy circular references Similarly What
327. ideline ccccceccceeeeeeneeeeeeeneeeeeeeeeeeeeaeeeeeeceeeeesiaeeeeeenaeeeeeeaas 223 Scale the Model to a Reasonable Range of Une 223 Simplify Relationships nseoosenenneneeeeeennnrtnsreerrttnrenssttttttnnttesttntntnnnnestttnnnnnn teen tenn nnmnnn 224 Reduce Integer Hestrichons 224 Guidelines for Stochastic Modeling assseeeessneeesrnessnnessnnesrnnnesnnnansnnnneeninnastannnnnnnandtnnnena 225 Multistage Decision Making Under Uncertainty 0 c ccccceeeesteeeeeeneeeeeeeneeeeeenaeeeeeeaas 225 Recourse M delS asii iiie aai deed 227 Defining an SP Model in What sBest Simple 2 Stage Example ccccceeeeeeeee 228 Defining an SP Model in What sBest Multi Stage Exvample 236 Sampling 2 Scenario Tree eie aeaa E E E E 243 Guidelines for Chance Constrained Modelmg 244 Solving Second Order Cone Progorams srie aiei Ri a i kii 251 T SAMPLE MODELS Esseg ge eg see sed ARARE A A AASA ENER RTRA 255 Blendi DEE 258 Application Ree UE 258 Chance Constrained Blendmg 263 Application Ree UE 263 e 267 Flow Network Modeling reide ir e R EEEE EE 270 Bond Portfolio Optimization ae a e a eE ee aae a aati 278 Application Profile ne tsen ere a laa eet aan dan dpe a aee ai 278 Beier eler lee Le EE 284 Markowitz Portfolio Problem 288 Application Profile eea nern d eea ae a eadra a eiT 288 Portfolio with Transaction Coste 292 Application d e UE 292 Portfolio Minimizing Downside Risk 0 c
328. ient s initial investment while covering his cash flow needs over the next five years In other words you wish to know the minimum amount of cash that should be allocated among all the available bonds which will maintain the required cash inflow over the next five years 280 CHAPTER 7 The Worksheet To get started let s examine the BONDS worksheet Look it over for a minute to see how it s designed The BONDS Worksheet Part 1 Before Optimization 1 Kg ON cel ae kela Zl a 2 e g O BONDS xlsx Microsoft Excel 2 6 File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ai CH Es fe AVAILABLE i i D E F Asking Interest Units Investment Year of Maturity 1 0 996 10 5 0 0 0 00 0 997 10 5 0 0 0 00 2 0 923 10 75 0 0 0 00 0 987 11 2 0 0 0 00 0 993 11 8 0 0 0 00 1 061 12 0 0 0 00 0 883 10 0 0 0 00 1 102 12 6 0 0 0 00 0 889 10 2 0 0 0 00 TOTAL COST Year 0 Year 1 Year 2 Year 3 Year 4 Amount Covered 0 00 0 00 0 00 0 00 0 00 Notze T Not gt T Not gt T Not gt Mot ze Cash Flow Need 17 00 62 00 23 00 35 00 62 00 HAH BONDS 2 al Mm ESO 100 A Determine Adjustable Cells Adjustable cells are the units of bonds purchased for each bond quoted E4 E12 B Define Best The Best possible solution is the particular mix of units of bonds purchased that result in minimum initial investment in cell F14 Examine the form
329. ier option LICOPT4 Mixed Integer Solver Not Licensed If you attempt to use the mixed integer programming solver option without a license the following error message will be displayed on the WB Status tab Error Message KE RROR Mixed Integer Solver Not Licensed Help Reference LICOPT4 The license for your installation does not allow for use of the mixed integer solver option 430 CHAPTER 8 Suggestions The mixed integer programming solver is an optional feature You ve attempted to use the mixed integer solver with a copy of What sBest that does not have an appropriate license You will need to either disable any integer options WB Options Integer Pre Solver WB Options Integer Solver or contact LINDO Systems regarding a license upgrade that includes the mixed integer option LICOPT5 Stochastic Solver Not Licensed If you attempt to use the stochastic solver option without a license the following error message will be displayed on the WB Status tab Error Message Stochastic Solver Not Licensed Help Reference LICOPTS The license for your installation does not allow for use of the stochastic solver option Suggestions The stochastic programming solver is an optional feature You have attempted to set up a stochastic model with a copy of What sBest that does not have an appropriate license You will need to either disable any stochastic featuress WB Options Stochastic Solver WB Advanced Stoch
330. ified Create Report Using the Function WBIKB_REP The general format is WBIKB_REP cells_to_be_reported e g WBIKB_REP Sheet1 B 1 Sheet1 B 2 meaning the cells B1 and B2 of Sheet will appear in the K Best Report After solution a new tab WB _KBest will be created It will have one column for every cell to be reported and one row for every run 80 CHAPTER 3 Select the checkbox to tell What sBest you would like a KBest report created when the model is solved The next time you solve What sBest will generate a worksheet called WB _KBest containing a listing of the cells and their values Click on the WB _KBest tab to see the KBest report ADDITIONAL COMMANDS 81 Branch and Price Solver The Branch and Price BNP Solver contains two parameters Blocks and Heuristic Branch and Price Solver Blocks off es Heuristic GPi v The BNP solver is a mixed integer programming solver for solving models with block structures like the following Minimize c k x k Subject To xX A k x k d linking constraints x k in X k for all k decomposition structure where d c k and x k are vectors and A k is a matrix with appropriate dimensions x k contains decision variables and X k denotes a linear feasible domain for x k The BNP solver is a hybrid of branch and bound column generation and Lagrangean relaxation methods It can help to find either the optimal solution or a better lower bound the Lagrang
331. ight the range F15 F17 then choose Constraints from the WB menu and click OK Note that the Constraints dialog box has E15 E17 entered as Left hand side LHS G15 G17 entered as Right Hand Side RHS F 15 F 17 entered in Store in and lt less than or equal to being the default is entered as the constraint type Alternately you may use the lt toolbar button after selecting the range to store the constraints See The ABC s for more information on these defaults Automatic Generation of a Constraint H 10 Product Component Requirements 11 12 Components Quantity Required Total Number 13 Standard Deluxe Usage In Stock 14 Standard Tower 1 0 60 Deluxe Tower 1 50 Hard Drive 1 2 120 18 19 4 E XYZ lt 2 Ready 2 Count 3 SO 100 16 CHAPTER 1 At this point let s briefly summarize what we have done so far The XYZ Worksheet Before Optimization GI No Go ils TT yz se Microsoft Excel re eee xX File Home Insert Page Layout Formulas Data Review View Developer Team What sBest VY ei o El ZS B cC D E F G XYZ COMPUTER CORPORATION PRODUCTION PLAN D a e H Standard Deluxe A i PROFIT Quantity to Produce poo g Profit per Unit 300 500 Product Component Requirements 1 2 3 4 5 6 7 8 9 10 11 12 Components Quantity Required Total Number Standard Deluxe Usage In Stock 15 Standard Tower 1 16 Deluxe Tower 17 Hard Drive 1 18 19 VAN XYZ
332. imal investment allocations resulting from the minimization of risk as measured in three different ways and determine the best measure of risk for your lifestyle Background Once again there are three assets this time with twelve equally likely expected return scenarios Scenarios are outcomes of events with an influence on your analysis Fed raises interest rates by 0 5 point Fed lowers interest rates by 0 25 point housing starts up etc This model calculates three different measures of risk variance semi variance and downside risk You can minimize each of the three and get different levels of each asset that achieve your target return of 15 each offers the lowest risk depending on which of the three measures you select Variance is a measure of the fluctuation of the expected return However this measure of risk considers a scenario that returns 5 above the target to be as desirable as a scenario that returns 5 below the target You re probably only worried about the risk that the return will be below your target return Both Semi variance and downside risk look only at the risk that your return will be below the target Downside risk minimizes the difference between the target and returns below the target The semi variance minimizes the difference between the target and the square of the returns below the target Therefore it puts a higher weight on larger differences below the target Objective of Optimization The ob
333. in Excel If any unsupported functions references are found in any of the cell formulas the following warning message will be displayed on the WB Status tab Warning Message Unsupported Functions Help Reference FORMULA2 The cells listed contain spreadsheet functions that are not defined in What sBest The numeric values for these cells are taken from the spreadsheet directly without recalculation cell addresses listed at bottom of tab Suggestions Cells in your model can reference Excel functions that are not supported by What sBest However these cells values will be fixed at their calculated values at the start of the solve command The list of cells referencing unsupported functions may be found at the end of the report Supported functions and operators are listed in the Supported Functions and Operations section If the unsupported cells are used for reporting only they can be included in a WBOMIT range see the section entitled Advanced Omit If they are necessary to the actual optimization model they must be expressed or approximated in terms of equivalent operations supported by What sBest If you cannot approximate the unsupported functions reformulate the problem to eliminate all such functions 412 CHAPTER 8 This warning may be disabled with the Unsupported Function warning checkbox in the General Options dialog box posted by the Options General command Using linked worksheets may also ca
334. incurred in moving from one optimal solution to another such a problem is said to have multiple optima there is more than one combination of adjustable cells that give the same minimum cost 376 CHAPTER 7 Traffic Congestion Cost Minimization File name TRAFFIC XLSX TYPE NONLINEAR OPTIMIZATION Application Profile In the earlier SHIPPING network problem the cost to transport your product from a supply point to a demand point was fixed However in some network problems the costs vary with the amount transported along each arc If you ve ever driven to or from a major city during rush hour you ve experienced this phenomenon As the number of cars on the road increases the cost in terms of time required of getting from point A to point B increases In many cases the cost does not increase linearly For example doubling the traffic on a lightly traveled road may not double the travel time but doubling the traffic again may effectively grind the flow of vehicles nearly to a halt The Problem in Words As Quartermaster of a military base you need to distribute uniforms from three warehouses to four intake centers within the base Background You know that the time required to go from a particular warehouse to a particular unit obeys the following formula Time Rate Flow 1 Flow Limit Where Rate time required to transport one unit if there is no congestion along this route Flow amount of product mo
335. ing the model The value is updated periodically in the course of solving Infeasibility This shows the total amount by which all constraints are violated When this value is reported as zero all constraints are satisfied However on integer models all integer restrictions may not be satisfied Objective This shows the current value of the cell to be maximized or minimized Solver Type This shows the type of specialized solver in use if any and will be either Global Branch and Bound or Multistart Best Obj This shows the objective value of best feasible solution found Obj Bound This shows the theoretical bound on the objective for integer or nonlinear programming models What sBest initially determines this value by solving the problem without integer restrictions It then tightens this bound as it searches more branches of the solution tree The objective bound is useful information in that it is a limit on how good a value the objective can attain On long running models you might want to interrupt the solver once the best solution is sufficiently close to the theoretical limit Steps This shows the number of solver iterations Active This shows the number of pending subproblems to be solved Numerics This shows the total number of numeric cells in the model Adjustables This shows the total number of adjustable cells in the model Integers Bin This shows the number of adjustables cells with integer binary restrictions
336. ing to units of thousands of dollars OMITTED Omitted Cell Reference Cells within WBOMIT ranges De cells that have been omitted from the optimization via the WB Advanced Omit command cannot be referenced in cell formulas that lie outside WBOMIT ranges When this situation is encountered What sBest will display the following error message on the WB Status tab Error Message Omitted Cell Reference Help Reference OMITTED The solver has been halted because the following cells are contained in WBOMIT ranges and have been referenced by formulas that are not contained in any WBOMIT range cell addresses TROUBLESHOOTING 437 Suggestions There are several options here Remove the omitted cells that are being referenced i e the cells listed in the error message from all WBOMIT ranges Place the cells referencing the omitted cells in WBOMIT ranges too Eliminate the references to the omitted cells from the un omitted cell formulas QUAPREC Quadratic Recognition A quadratic program QP is any model that is linear with the exception of product terms involving two variables e g 3 X Y If you have enabled the Quadratic Recognition option and you try and solve a quadratic programming model that is non convex the following error message will be displayed on the WB Status tab Error Message Quadratic Recognition Help Reference QUAPREC The quadratic solver requires that the model be convex The mo
337. int 15 lt lt Stage 1 decision and constraint 16 lt lt Stage 1 non negativity constraint 17 lt lt Stage 0 cost computation 18 lt Stage 1 holding cost computation 19 lt Stage 1 shortage cost computation 20 lt lt Stage 1 revenue computation 21 22 lt Stage 1 expected value maximize 23 24 25 Model Scenario Tree READY 3 c D E F G gt SP_NEWSVENDOR xlsx Excel 7 amp x HOM INSER PAGE FORM DATA REVIE VIEW DEVEL Team What Lindo Sys fe Stochastic Scenario Optimization Y H J K L M a Stochastic data Step 2 Stage information WESP_VAR Q TC stage 0 WESP RAND WESP_var Step 3 Distribution information WESP_DIST_NORMAL Mean Demand Standard Deviation Step 4 Sample size STSC Stage Scenarios a Step 5 Reporting cells REP IST e 5 For this specific problem the five steps mentioned earlier are Step 1 The core model is described numerically in column B and in words in columns A and C Step 2 We specify cell B11 as a stage 0 decision variable by inserting the expression WBSP_VAR 0 B11 into cell 16 We can enter this expression directly or using the Stochastic Support dialog box We specify cell B12 as a stage 1 random variable by inserting the expression WBSP_RAND 1 B12 into cell I8 The cell B13 is the recourse decision adjustable at stage 1 WBSP_VAR I B13 Step 3 We tell What sBest that de
338. ints that you know have convex feasible regions but you suspect might not be identified as convex by our solver What sBest allows special constraint types lt c gt c and c to allow users to identify constraints that have convex feasible regions For example suppose we have the constraints x3 2 x y y 3 lt 6 x gt 5 eae The feasible region of this set of constraints happens to be convex The user is justified in writing x43 2 x y y 3 lt c 6 More generally if f x is any function on the left hand side and the user writes Aix lt c b The solver will assume that the feasible set for this constraint is convex This is true for example if fx is a convex or quasi convex function Loosely speaking a quasi convex function is uni modal if you pour water into it only one puddle would form A convex function is also quasi convex If you have the constraint f x gt b and you know that f x is a concave function then you are allowed to write Aix gt c b Finally if you have the constraint f x b and you know that fx is a quasi convex function then you are allowed to write Ax c b The interpretation is that we require f x b however the feasible region to the relaxation f x lt b is convex Similarly if you have the constraint f x b and you know that f x is a quasi concave function then you are allowed to write Ax c b The interpretation is that we requi
339. ion WBCARD 10 20 Sheet1 B 1 Sheet1 C 1 C 3 wbintegerSos For additional discussion of the functionality provided see the section entitled Integer Special Ordered Set which refers to the Special Ordered Set Cardinality dialog box that calls this procedure This routine is used to build the SOS ranges WBSOSx Adjustable cells contained in these ranges will be restricted to integral values by the What sBest solver If you wish to delete a SOS function using VBA instead of deleting it on the spreadsheet you can use Selection Clear This statement clears the selected cell from any of its content Syntax wbIntegerSos TypeSos ArgList Refers_to NoErrDialog TypeSos TypeSos is an integer that refers to the type of the SOS 1 for type 1 2 for type 2 3 for type 3 ArgList ArgList is a string list of range or cells reference separated by a comma Refers_to Yes Refers_to is the range or address of the cell s to be specified as SOS NoErrDialog No Any argument passed here causes all What sBest error dialog boxes from the wbIntegerSos routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number Useful in an embedded application of What sBest 174 CHAPTER 4 IntSos_BadTypeSosArg Bad TypeSos argument IntSos_BadRefersToArg Bad Refers_to argument IntSos_ProtectedSheetError Unable to set i
340. ion argument MACROS THE VBA INTERFACE 183 Example If one wished to set all the options the following would work wbSetGlobalOptions True 4 0 0001 0 000001 100000000 Ly 2p kg 2 To set individual options here setting Mu tistart Attempts to 4 named arguments should be used wobSetGlobalOptions GlMultistartAttempts 4 Note The global solver needs the nonlinear option and the mixed integer option to operate wbSetintegerOptions This routine is used to set the What sBest integer options displayed in the Integer Solver Options dialog box All arguments are optional For additional discussion of the options available through this routine see the section entitled Options Integer Solver Syntax wbSetIntegerOptions BranchingDirection AbsoluteIntegrality RelativeIntegrality WarmStartLP ColdStartLP AbsoluteOptimality RelativeOptimality TimeToRelativeOptimality HurdleTolerance NodeSelectionTolerance StrongBranchTolerance K Best kK BestReport BNPBlocks BNPHeuristic Argument Required Default Description BranchingDirection No 0 Both BranchingDirection is an integer indicating the preferred direction of branching 0 Both 1 Up 2 Down Absolutelntegrality No 0 000001 AbsoluteIntegrality is a fractional value indicating the absolute amount of violation from integrality that is acceptable for the integer variables Relativelntegrali
341. ion of the options available through this routine see the section entitled Options Linear Solver Syntax wbSetLinearOptions LinearSolverMethod ScaleModel Reduction PrimalPricing DualPricing Argument Required Default Description LinearSolverMethod No 0 Solver Decides LinearSolverMethod is an integer indicating the linear solver method to employ 0 Solver Decides 1 Primal Simplex 2 Dual Simplex ScaleModel No 1 True ScaleModel is a True False flag indicating whether to scale model Reduction No 1 True Reduction is a True False flag indicating whether to use model reduction PrimalPricing No 0 Solver Decides Primat Pricing is an integer indicating what primal pricing method to use 0 Solver Decides 1 Devex 2 Partial DualPricing No 0 Solver Decides DualPricing is an integer indicating what dual pricing method to use 0 Solver Decides 1 Partial 2 Steepest Edge Error Codes Description 190 CHAPTER 4 LinOpt_BadScaleModelArg Bad ScaleModel argument LinOpt_BadReductionArg Bad Reduction argument LinOpt_BadLinearSolverMethodArg Bad LinearSolverMethod argument LinOpt_BadDualPricingArg Bad DualPricing argument LinOpt_BadPrimaltPricingArg Bad PrimalPricing argument Example If one wished to set all the linear solver options the simplest syntax would be wbSetLinearOptions 3 False T
342. ity Cell Format 451 WBDUFORM Dual Cell Fommat tanne ne nn 451 WBLOFORNM Lower Range Cell Format 452 WBSEMICFORM Semi continuous Cell Format 453 WBSOSFORNM Special Ordered Sets Cell Format nsnssssssennneesseenrtnnsensrrenrrnnseeerenne 454 WBUPFOR M Upper Range Cell Fommzat nn 454 APPENDIX A INSTALLATION DETAILS 2 cccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeseseeesneneeeeeeeneees 455 lin tall tion WEE 455 What sBest Example Files niin e e a EaR 455 Setup Typs EE 455 WhatsBesthAdd in Files tune a a edel 456 Locati n of the Add In Piles rirni a e r e E a R 456 Installation Related Problems c ecccceceeeeeeeeeeeaeeeeeeeeeseseanaeeeeeeeeesesanaeeeeeeeeeeenaees 456 Settings for Microsoft Excel 2007 2010 2013 456 Settings for Microsoft Excel 1004 20072 457 tele DT CEA ce tall 459 Location of the Add In Files and Update Links 460 Uninstall EE 462 APPENDIX B CONTACTING LINDO SYSTEMS c ceeeeeceeeceeeeeeeeeeeeeeeeeeeeseneneeeeeeeenees 465 WWW indo COM EE 465 PREFACE xiii Preface What sBest 13 0 makes available to your Microsoft Excel spreadsheet program a highly developed solver capable of performing linear integer quadratic general nonlinear global and stochastic optimization on the most difficult of problems What sBest gives you access to this solver from within Excel and may either be run directly or called from within Visual Basic The
343. jective is to determine the percent to invest in each asset while minimizing the risk of the entire portfolio using the risk measure that is most important to you SAMPLE MODELS 299 The Worksheet Let s look at the supplied PORTSCEN sample file mas e eoe PORTSCEN xisx Microsoft Excel Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 CA o ER Ss File Al The PORTSCEN Worksheet Before Solving Leet se f PORTFOLIO SCENARIO MODEL im OD on amp Lo cC PORTFOLIO SCENARIO MODEL OOnNONMEWH 10 11 12 Asset 1 0 0 130 0 110 3 121 6 95 4 92 9 105 6 103 8 108 9 109 0 108 3 103 5 117 6 Expected Return Target Return Return gt Target 20 Invest Total 100 21 22 SSES PORTSCEN Asset 2 0 0 122 5 129 0 121 6 72 8 114 4 107 0 132 1 130 5 119 5 139 0 92 8 171 5 0 0 115 0 Not gt Not z Asset 3 0 0 114 9 126 0 141 9 92 2 116 9 96 5 113 3 173 2 102 1 113 1 100 6 190 8 E Prob 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 F Return 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G Difference Forcing Constraints Over 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Variance Semi Variance Downside Risk H Under 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
344. l art and U a1 ut t are the lower and upper bounds generated by outcomes up to stage t for all t 1 7 is one of the relational operators lt or gt and x0 and xt x w1 w2 ut t are the decision variables unknowns for which optimal values are sought The expression being optimized is called the cost due to initial stage plus the expected cost of recourse Note What sBest can solve linear nonlinear and integer multistage stochastic programming problems 228 CHAPTER 6 Scenario Tree When the probability distributions for all random variables are discrete and finite then there are only a finite number of outcomes in each stage With each random parameter fixed to one of its possible outcomes one can create a scenario representing one possible realization of the future Enumeration of all possible combinations of outcomes allows us to represent all scenarios in a tree with each scenario being a path from the root of the tree to one of its leaves The nodes visited by each path correspond to values assumed by random parameters in the model Defining an SP Model in What sBest Simple 2 Stage Example There is a relatively straightforward five step process for setting up an SP model in What sBest All the information about the SP features is stored explicitly openly on the spreadsheet The five steps are Step 1 Define a core or deterministic model as a regular deterministic
345. lable this model would be reformulated to minimize total material costs Otherwise very expensive material might be purchased although it would be used efficiently Another model might also take into account the value of End Waste that could be re entered in inventory li 4 a 100 kala Home Insert Page Layout Formulas Data Review View Developer Team What sBest Y o X SAMPLE MODELS 343 35 25 Pattern A d 434 feet Hg Ze 2 25 Pattern C 448 fest TE S Pattern D 725 feet mm CR Los Feet SE End Waste M Note that the optimized cutting plan includes no footage cut to Pattern B in cell G5 Also end waste occurs only in the 35 width E13 344 CHAPTER7 Plant Location File name PLANTLOC XLSX TYPE LINEAR OPTIMIZATION This problem is related to the class of network or routing problems In such problems the variables usually include multiple choices of transportation routes to and from a number of points of origin and destination with differing shipping and operating costs associated with each possible route The Plant Location problem is similar to the SHIPPING sample model but allows greater latitude of decision making in that the points of origin plant locations are variable Manufacturers and wholesale businesses are likely to encounter problems of this sort in matching existing customer demand to product availability and minimal transportation costs Background
346. lerance command 78 Tolerances 77 Toolbar 7 ToolBar command 135 Tools Add ins 4 Tools Macros 147 474 INDEX Tools References 147 Trademarks 2 Traffic Congestion Cost Minimization 376 TRAFFIC XLSX 376 TRANSPOSE 205 Trend 304 Trial Version 134 Tries 39 Truck Loading 379 TRUCK XLSX 379 TRUE 205 Tutorial 10 on the VBA Interface 147 Types 72 U JNBOUNDED 221 449 ncertainty 225 INDEFREF 450 pper Range 111 sage Guidelines for Dual values 112 for Omit 125 Use of Bound 67 Leef ore ang caer V Valid Ranges for Dual Values 117 Variable Bounds 67 Variables 134 integer 2 44 Variance 298 VBA 145 147 151 170 175 VBA Interface Procedures 151 VBA Interface Tutorial 147 Visual Basic Editor 147 for applications VBA 143 204 VLOOKUP 207 431 VLOOKUPWBSOLVER XLS 431 W Warm Start 75 Waste Minimization in Stock Cutting 339 WB formula 28 WB Menu 4 7 21 WB Solution 36 56 WB Status 36 55 WB _ Histogram 58 WB _ Stochastic 58 wbAddAdjustableStyle 152 wbAddBestStyle 152 wbAddWBMenu 152 wbAdjust 153 wbBest 154 WBBIN 155 WBCARDFORM 451 wbConstraint 156 wbConstraintPOSD 157 wbDeleteReports 158 wbDeleteWBMenu 158 WBDUAL Formula 110 wbDualValue 159 WBDUFORM 451 WBERLANG 208 WBERLANG D 208 wbError and Error Codes 160 WBEXPOINV 209 WBFREE 168 WBINNERPRODUCT 209 WBINT 169 wbinteger 170 whIntegerCard 171 whbIntege
347. lly displays Ready but displays other messages when either Excel or What sBest is performing some activity that may be prolonged For further information on the What sBest add in see the Add ins section GETTING STARTED 9 Developing a Model in What sBest The ABC s Three Steps to What sBest There are three steps to setting up a model to be solved by What sBest Throughout this help file you ll find them referred to again and again We call them the ABC s Adjustable Best and Constraints A Identify Adjustable Cells The adjustable cells are the cells in the worksheet that What sBest can adjust in its quest for a solution In mathematical programming terms these are called variables These can be defined using either the menu command Adjustable or the toolbar button KX B Define Best The best cell is the goal or objective of your solution Typically this is to maximize or minimize an adjustable cell or some function of the adjustable cells What sBest allows only one best cell in the model No best cell is needed when equation solving or goal seeking The menu command Best or the toolbar button ie 7 can be used to define the best cell C Specify Constraints The constraint cells identify any limitations in a model For example Raw materials used in production must be less than or equal to raw materials on hand The constraint cells enforce these restrictions They are de
348. lope is equal to zero Continuing to the right begins to lead uphill and retreating to the left leads up the hill you just came down You are in a valley the lowest point in the immediate neighborhood a local minimum but is it the lowest possible point You can t determine that given the information available to you at that particular point This is an extreme example and not typical of well formulated nonlinear problems Nonlinear solvers do their best to tackle such nonlinear models by seeking a local optimum from the starting points supplied by the user This provides the user with the opportunity to explore the available local optima MATHEMATICAL MODELING 217 What sBest takes the initial values of the adjustable cells as starting points in its search for a locally optimum solution Therefore if you solve this model with different starting values for B3 and do not use the Global Solver then What sBest may return a different local minimum Attempting to solve the model with a starting value between 5 and 6 for B3 is likely to lead to a local minimum at 5 518 which happens to be the global optimum You may try other starting values to find other local optima For some problems you may find that observing the results of solving the model several times with different initial values can help you find the best solution Convexity Ifa function is convex then it has a single global optimum If a function is not convex it may have mul
349. lse flag indicating whether or not to use this support AdvStringLength No 20 AdvStringLength is an integer between 1 and 255 indicating the maximum string length 196 CHAPTER 4 Error Codes Description AdvStr_BadAdvStringSupportArg Bad AdvStringSupport argument AdvStr_BadAdvStringLengthArg Bad AdvStringLength argument Examples If one wished to set all the string support options the simplest syntax would be wbSetStringSupport True 10 To set one or more options named arguments should be used wbSetStringSupport AdvStringSupport True Note The AdvStringSupport argument should be set to TRUE in order to use the AdvStringLength argument wbSolve For additional discussion of the functionality provided by this routine see Solve This routine is used to solve the active model Syntax wbSolve SolutionStatus ExcelOpen NoErrDialog Argument Required Description SolutionStatus No SolutionStatus is a return integer on the condition of the solution Globally Optimal 1 Globally Optimal 2 Infeasible 3 Unbounded 4 Feasible 5 Infeasible or Unbounded 6 Near Optimal 7 Locally Optimal 8 Locally Infeasible 9 Cutoff 10 Numerical Error 11 Unknown 12 Unloaded 13 Loaded 14 Unknown Error other where 1000 is an interruption from a calculation error and 2000 is an interruption by the user Excel
350. lution Check the solution carefully it may be sub optimal or infeasible 420 CHAPTER 8 Suggestions When a model is interrupted there are certain instances when What sBest will be able to return the best solution found so far The best way to determine if an incumbent solution exists is by checking the Best Obj field in the What sBest Solver Status window If this field contains a numeric value then there is an incumbent solution that can be returned If this field does not contain a numeric value then a valid solution does not exist In which case the values returned by the solver will not be valid Keep in mind that at best the returned solution is most likely sub optimal Furthermore whenever you interrupt the solver you should check the final infeasibility value on the WB Status tab of the returned workbook An infeasibility value significantly different from zero means that some constraints are violated in the returned answer and the solution is not valid Note Ifa feasible integer solution is found for an integer optimization model restoring the best integer solution may take some time after the initial interrupt So don t be concerned if the solver doesn t interrupt immediately when the model contains integer adjustable cells The solver is just busy returning to the incumbent solution TROUBLESHOOTING 421 INVMOD Invalid Model If you attempt to solve a model that is clearly not formatted for What s
351. lution report WB Solution for the XYZ sample model covered earlier H S5 e Dis XYZ xlsx Excel 7 0 O xX HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys v Al ad fe What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A B Cc D E a 1 What sBest 13 0 d 0 Sep 20 2014 Lib 9 0 1889 103 64 bit Solution 2 3 DATE GENERATED Oct 14 2014 09 27 AM 4 5 OBJECTIVE INITIAL 6 CELL VALUE VALUE TYPE DECREASE a a 8 X Z G6 3 300000e 004 0 000000e 000 MAXIMIZE 9 10 COEFFICIENTS 11 XYZ C5 3 000000e 002 5 000000 12 XYZ D5 5 000000e 002 5 000000 13 14 ADJUSTABLE INITIAL 15 CELLS VALUE VALUE TYPE REDUCED COST DECREASE a 5 17 XYZ C5 6 000000e 001 0 000000e 000 C 0 000000e 000 Infinity 18 XYZID5 3 000000e 001 0 000000e 000 C 0 000000e 000 Infinity 19 90 RB Binswe C Cemntinusne RF Brea T ntecren WN Frea Tntecen cl hd WB Status WB Solution XYZ Ka al Note that creating solution reports may dramatically increase runtimes on large models Beginning or End Select the Beginning or End radio button to tell What sBest whether to place any reports status and or solution report at the beginning of the worksheet tabs far left or at the end of all worksheet tabs far right The default is to insert the reports at the Beginning ADDITIONAL COMMANDS 57 Warnings These checkboxes allow you to select the warnings you wish to display in the
352. m LINDO Systems technical support 130 CHAPTER 3 The parameter names and their values are entered using the following dialog box Parameters m The Advanced Parameters command should only be used under the guidance of LINDO Systems technical support Real valued parameters have names beginning with WBLS_DPARAM while integer valued parameters names begin with WBLS_IPARAM The WB Options Reset to Default command will not reset the custom parameters defined in this window Instead you must delete them individually using the Delete button pictured above In addition What sBest will accept two names for providing the instruction list and a parameter file in a standard format e WBFORMAT will produce a MPI MPS or LTX file format in the specified destination for instance C Temp modelname mpi The parameter file is provided as a PAR and CSN ADDITIONAL COMMANDS 131 e WBFORMATSP will produce the formatted files related to a Stochastic Program model for instance C Temp stochasticmodelname without extension for MPI SSMPI STOCH TIME _1 STOCH The parameters file is provided as PARAM TXT and PARAM PARAM CSV e WBFORMATLOG will produce the formatted files related to an output log file from the calculation library for instance C Temp logname txt There is also an hidden name that the user can setup as WBCALCxxx with a range value which actually tells What sBest to re
353. mand has a Normal distribution with mean 80 and standard deviation 20 by inserting the expression WBSP_DIST_ NORMAL I15 116 B12 into cell 113 MATHEMATICAL MODELING 231 Step 4 We tell What sBest how many scenarios to use in each stage Oe the sample size by inserting the expression WBSP_STSC I21 J21 into cell 119 Step 5 We specify that we want a scenario by scenario report on the amount ordered the demand lost sales and profit by placing the expression WBSP_REP B11 B12 B13 B22 in cell 124 We request a nine bin histogram of Profit by placing the expression WBSP_HIST 9 B22 in cell 125 There is also an Options Stochastic Solver dialog box for setting various SP related options 232 CHAPTER 6 Stochastic Support IV Use Stochastic Modeling Support Core Stage Distribution Scenario Reports Chance Constrained 2 Specify the stage information for the Variables Adjustables Geen EE Stage Refers to wes lo ss a Place function in cell A 1 mj SE Specifications Optimization Method Seed for Random Generator Common Size per Stage Iw Sampling on Continuous Distribution Only oto za l MATHEMATICAL MODELING 233 The SP NEWSVENDOR Worksheet After Optimization Al x Given all costs and prices in Stage 1 atthe en Step 1 ON DO Wh H cc SP_NEWSVENDOR xlsx Excel 2 P HOM INSER PAGE FORM DATA REVIE VIEW DEVEL Team
354. mes and click on the Remove button The WBSP_REP function will be placed in the current selection of the field Place the function WBSP_REP in cell Output Report eX Select any cells to report multiple selection holding the Ctrl key A 1 List of selected cells select and change by eg Add or Remove Place the function WBSP_REP in cell SAS1 ADDITIONAL COMMANDS 99 Here s an example of the stochastic report for the SP_ NEWSVENDOR sample model H S co IN Zo SP_NEWSVENDOR xlIsx Excel P D x HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys v Al A fe What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A BC B E F BEN 1 What sBest 13 0 d 0 Sep 30 2014 Lib 9 0 1889 103 64 bit Stochastil 2 Lj 3 DATE GENERATED Oct 14 2014 09 39 AM 4 5 6 STOCHASTIC INFORMATION 7 8 CLASSIFICATION DATA Current Capacity Limits CR A 10 Adjustables 1800 Unlimited 11 Integers Binaries 0 Unlimited 12 Constraints 1599 Unlimited 13 Nonlinears 0 Unlimited 14 RANDONS 1 15 STAGES 2 16 NODES 201 17 SCENARIOS 200 18 19 Expected Value EV 2 11E 03 _2n Exnactad Valua of Wait and Gee Madel Nhiectinea RUNS 2 90F1N2 x D WB Status WE Stochastic WB _Histogram Model See D Jl nl Once created the WB _ Stochastic report will stay on the workbook and the solver will just clear the sheet during successive runs Thi
355. mped from the Wells to each Pump to equal the sum of amounts pumped from that Pump to the Refineries Third demand at the Refineries must be satisfied These constraints are in cells E12 H12 and require that the sum of amounts pumped from the Pumps to each Refinery is greater than or equal to the demands in E11 H11 Finally the capacities of the pipelines cannot be exceeded The constraint formulas in B29 C31 and E29 H31 one for each arc accomplish this result 372 CHAPTER 7 Now let s solve the model The PIPELINE Worksheet After Optimization aas e goe ELINE xlsx Microsoft Exc al File Home Insert Page layout Formulas Data Review View Developer Team What sBest V ai o X f PIPELINE NETWORK PROBLEM MONTHLY PUMPING VOLUME Pumped From Inflow To Refinery No Well 1 Well 3 Outflow 2 3 Through Pump A 50 7 27 Pump B 41 36 30 Pump C 45 0 PUMPING COSTS Well 1 Well 2 Ref 1 Through PumpA 1 50 3 15 5 00 Well Pumping Costs 338 40 Refinery Pumping Costs 1 092 65 Total Pumping Costs 751 431 05 WB Status What sBest has returned a minimized Total Pumping Cost of 1 431 05 Note that all Pumps are in use SAMPLE MODELS 373 Shipping Cost Reduction File name SHIPPING XLSX TYPE LINEAR OPTIMIZATION Application Profile This problem is typical of the class of network problems that generally involve the shipping of goods through transportation networks or
356. mprovement in the objective for an increase in the constraint s right hand side value A positive dual implies that the objective will improve when increasing the right hand side while a negative implies that the objective will suffer On maximization problems as we have shown above a positive dual value means that increasing the right hand side of the constraint will cause the optimal objective to improve or increase On the other hand for minimization models if the sign of the dual is positive then the optimal objective value will decrease as the right hand side increases 114 CHAPTER 3 Note Ifthe constraint on Deluxe computer tower usage WB E16 lt G16 is not tight i e E16 is not equal to G16 but is less than 50 then the dual value is 0 Increasing the right hand side from 50 to 51 would not affect the optimal solution and consequently would not change the best cell value Note When taking the dual value of a constraint be sure to specify the cell containing the constraint function not the right hand side of the constraint Dual Value of an Adjustable Cell Reduced Cost The dual value of an adjustable cell is the rate at which the best cell would be penalized if an adjustable cell with an optimal value of zero were forced into the solution even though it is not optimal to do so If the adjustable cell is a positive number the dual value will always be 0 The dual value of an adjustable cell is often referred to as
357. n Data Total Cells This shows the total number of numeric cells in the model These are the cells useful to the model containing the Numerics Strings and the Constraints Numerics This shows the number of cells displaying a numeric value These are Adjustable Constant and Formula cells Adjustables This shows the total number of adjustable cells in the model Continuous This shows the number of Adjustable cells with a continuous range 0 infinity 38 CHAPTER 2 Free This shows the number of Adjustable cells with a free range infinity infinity Integers This shows the number of Adjustable cells with integer restrictions on a range 0 infinity Binaries This shows the number of Adjustable cells with binary restrictions 0 1 Constants This shows the number of cells containing a constant number or an unsupported function converted into its constant value This does not count the constant arguments within a formula Formulas This shows the number of cells containing a usefull formula to the model This does not count the constant arguments within a formula Strings This shows the number of cells containing a string of characters or an unsupported function converted into its string value This does not count the string arguments within a formula Constraints This shows the total number of constraint cells in the model Nonlinears This shows the number of adjustable cells that appear nonlinearly i
358. n Loaded of each item in D6 D11 B Define Best The best solution is the one that maximizes the value of the load in cell B15 The formula there SUMPRODUCT B6 B11 D6 D11 multiplies each individual item s value times the Proportion Loaded and sums them C Specify Constraints There are two constraints The first in D15 specifies that the Total Weight of Load C15 remain less than or equal to the Maximum Load Weight E15 The second in E6 E11 requires that the number of each item loaded onto the truck is less than or equal to 1 SAMPLE MODELS _ 381 Now let s solve the worksheet TRUCK Worksheet After Optimization by Conventional Method S mmm X a 3 e g S TRUCK xlsx Microsoft Excel Sa Home Insert Page Layout Formulas Data Review View Developer Team What sBest VY ai o YS f D TRUCK LOADING Maximum Proportion Proportion Value Weight Loaded Loaded 22 500 7500 0 33333333 24 000 7500 g 8 000 3000 9 500 3500 11 500 4000 9 750 3500 Total Value Total Weight Maximum of Load of Load Load Weight 31 500 10000 10000 M 4 WB Status TRUCK J al Mm Ready 23 oO 100 You ll notice that the What sBest solution recommends loading 33 of item 1 and all 100 or 1 of item 2 While this is the best solution if fractions of items can be loaded it may be difficult to load or sell one third of a piano To eliminate the fractions you could do s
359. n argument Pass an integer to use any possible returned What sBest error number Useful in an embedded application of What sBest Sto_BadCellRangelArg Bad CellRangel argument Sto_BadPlaceInCellArg Bad PlaceInCell argument Sto_BadRangeChoiceArg Bad RangeChoice argument Examples To set a Stage Scenario table the simplest syntax would be wbStochasticStageScenario Sheet B 1 C 3 D1 SET 0 wbUpdateLinks For additional discussion of the functionality provided by this routine see the description of Update Links in the section entitled Options General This routine is used to update the links to the WB constraints and functions Syntax wbUpdateLinks The wbhUpdateLinks procedure has no arguments Error Codes Description UpdateLinksProtectedError Unable to update links on a protected sheet UpdateLinksHiddenError Unable to determine if there are constraints in hidden cells on protected sheets Remarks This procedure is provided because Excel does not properly update links of add in functions 5 Functions and Operators What sBest supports many mathematical and logical functions of Excel and also adds some functions of its own List of Supported Functions and Operators The following Excel functions and operators are supported by What sBest Functions ABS ASIN ATANH CHIINV EXPONDIST GAMMADIST JF LOGINV MOD NORMINV NPV PRODUCT ROUND SIGN
360. n on the right edge of the text box to bring up a cursor for cell selection Binary WBBIN Select the Binary radio button in the Integer Type box to cause What sBest to constrain the current range of cells specified in the Refers to text box to have a value of zero or one Binary integer variables 0 1 are useful in making Yes No Open Close or Buy Sell decisions and formulating piecewise linear functions If a cell is specified as binary What sBest will find the best solution that returns a 0 or 1 in that cell General WBINT Select the General radio button in the Integer Type box to cause What sBest to constrain the range of cells specified in the Refers To text box to be a positive whole number General integer variables 0 1 2 can be useful when answers with fractions are of limited or no value Some examples are personnel scheduling buy sell decisions involving round lots and discrete loading models If a cell is specified as general integer What sBest will find the best solution that returns a whole number in that cell Runtime Concerns in Integer Problems The use of integer variables can considerably increase the time required to find optimal solutions In most nonlinear models that include integer variables your chances of reaching an optimal solution in a reasonable amount of time are diminished further unless the problem is extremely rudimentary or ADDITIONAL COMMANDS 45 constrained in very specific ways To im
361. n result in clear on screen messages and instructions for remedying the errors If for instance you specify installation to a non existent directory the setup program asks you if you want to create such a directory now or quit installation Missing spreadsheet software found configuration files and incorrect spreadsheet releases are all handled similarly If after following all on screen instructions and referring to Troubleshooting you still have trouble installing What sBest please call LINDO Systems Settings for Microsofte Excele 2007 2010 2013 Via the Ribbon select File Office Button Excel options INSTALLATION DETAILS 457 Popular Show Developer tab in the Ribbon File Office Button Excel options Manage Excel Add ins Go Check _What sBest or Browse to WBA XLAM usually in C Program Files Microsoft Office Office12 Library LINDOWB File Office Button Excel options Trust Center Trust Center Settings Macro Settings Enable all macros possibly Trusted Publishers to LINDO Systems Inc Settings for Microsofte Excele 1997 2003 Via the Menubar select Tools Add ins Check _What sBest or Browse to WBA XLA usually in C Program Files Microsoft Office Officel 1 Library LINDOWB Tools Customize Toolbars Check _What sBest Tools Options Security Macro Security Security Level to medium 458 APPENDIX A Trusted Publishers to LINDO Systems Inc Note A previous add
362. n the model We say that a variable appears nonlinearly in a formula when that formula is nonlinear with respect to changes in the variable For instance consider the nonlinear expression X Y 2 This expression is nonlinear with respect to Y but it is linear with respect to X Thus Y would be counted in the nonlinear count while X would not Coefficients This shows the total number of coefficients in the best cell and all formulas dependent on adjustable cells Variables This shows the total number of adjustable cells constraint cells and cells containing formulas dependent on adjustable cells that influence the best cell This information appears after an automatic linearization Minimum and Maximum coefficients These are the largest and smallest absolute values of coefficients appearing in the model When the ratio of these two values becomes very large the model is said to be poorly scaled Poorly scaled models can lead to numerical round off errors in the solver These values are supplied with their location to assist you in tracking them down Note that lt RHS gt signifies the Right Hand Side of a constraint If the location given is this means that no specific cell location is available and that the coefficient appears in a constraint added to the model as part of the linearization option Model Type What sBest examines your model to determine which of six types your model falls under Integer Quadratic Int
363. n unconstrained adjustable cells In this case you may want to create a single vacuous constraint cell in order to avoid this error message ep X gt 1 e20 NUMERICAL Numerical Error In some cases models will not be numerically stable In such a case the solver will not be able to continue when numeric values become too large and the following error message will be displayed on the WB Status tab Error Message Numerical Error Help Reference NUMERICAL The optimizer encountered numerical errors while solving and was unable to continue the optimization Scaling the model s coefficients so that they don t cover as large a range may be helpful in eliminating this error Suggestions Typically this error message occurs when a model is poorly scaled A model is poorly scaled when the ratio of the largest coefficient to the smallest coefficient in the model s formulas is too high If this error occurs on a nonlinear model then you can try a different starting value If this doesn t seem to help then you should try rescaling your model What sBest displays information on the WB Status tab regarding the values for the largest and smallest coefficients and where they are located in the workbook This information can be useful in tracking down the poorly scaled parts of the model Changing the units of measure in your model may help to improve scaling For example if your model contains dollar amounts you may want to try switch
364. nching is useful in tightening the bound quickly it does take additional computation time So you may want to try different settings to determine what works best for your model The default Strong Branch setting is 10 levels ADDITIONAL COMMANDS 79 K Best Solutions The Desired Number parameter is used to set the number of solutions desired as part of the K Best solutions feature of What sBest s mixed integer solver The Specify Reporting Cells is used for selecting the trade off cells m K Best Solutions Desired Number 1 Specify Reporting Cells Create Report Whenever this value is greater than 1 say K What sBest will return up to K unique solutions to the model with respect to the 0 1 variables These solutions will have the property that they are the next best solutions available in terms of their objective values If there are K or less alternate optima in the 0 1 variables then these solutions will be listed Less than K solutions may be returned if a sufficient number of feasible solutions do not exist Please refer to section Usage Guidelines for K Best Solutions for an example of the use of the K Best feature Select any cells to report multiple selection holding the Ci key Le Sheet1 SAS 1 List of selected cells select and change by geet Add or Remove Place the function WBIKB_REP in cell Sheet1 8 1 Teea The default Desired Number is 1 with no reporting cells spec
365. ncorporate What sBest into a Microsoft Excel or Access application or any other application offering Visual Basic for Applications All of the following procedures with arguments requiring cells can accept either range objects or the address of the cell s Note VBA is case insensitive to the procedure name when it is called so any procedure could alternately be called with its name typed entirely in lower case e as wbaddadjustablestyle instead of wbAddAdjustableStyle All of the What sBest procedures available are listed below with details on their syntax arguments error codes and any return values Some also include examples of using the procedure or remarks The procedures with arguments that require cells can accept either range objects or the address of the cell s Argument with square brackets and around them are optional non bracketed arguments are required 152 CHAPTER 4 wbAddAdjustableStyle This routine is used to add the adjustable style to a workbook that does not have one yet Syntax wbAddAdjustableStyle The wbAddAdjustableStyle procedure has no arguments Error Codes Description Adj_CreateStyleError Error Creating an Adjustable style Remarks Because this procedure is called by the wbAdjust procedure in most cases it should not be necessary for the developer to call it directly whAdaBestStyle This routine is used to add the best style to a workbook th
366. nctions such as cdf and inverse cdf of distributions such as Normal Exponential Logistic from the available set of functions LI Linear Solver Programming e The Simplex Linear Programming algorithm implementation has been improved for speed and robustness The performance improvements compared to previous version is 90 for Primal Simplex and 45 for the Dual Simplex LI Mixed Integer Solver Programming The Mixed Integer Programming solver includes a number of new features e Knapsack related cuts improvements significantly faster solving times on models with certain knapsack like constraints e Improved default node selection rules improves performance on most MIP s e New branching variable rule options maximum coefficients and neighborhood branching which can reduce number of branches on certain MIP s models e Perspective reformulation capability gives improved performance on quadratic portfolio models with semi continuous variables for instance min buy quantities Q Pre solver Improvements e The preprocessing for Linear Mixed Integer Programming can significantly reduce the coefficient density of certain dense matrices LI Stochastic Support improvements e Added a function WBSP_MEAN so the user can place the Expected Value for any random cell anywhere else in the spreadsheet This value for the Objective cell is already given in the Status Report LI Statistical Functions The user can define two additional p
367. ned from Selling Planting Cost Purchase Cost Y Problem Statement Model Scenario Tree Al D D m 70 SAMPLE MODELS 389 The SP_CROPALLOC Worksheet After Optimization H S5 e DO SP_CROPALLOC xlsx Excel 7 P D x HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys d Al E fe Farm Planting Decisions in Face of Crop Yield EEN B c D E F G HI J Ha 4 Step1 5 Data Note yield and price data are completely artificial arbitrary wh Selling Cost Unit Quantity Planting Price Unit ShortfalliB Yield Acre 6 Crops Required CostiAcre forExcess ought random Good 7 Wheat 150 170 Fair 8 Corn 230 150 6 Bad H Beans 260 200 J Very Bad Ee 10 ti Total Area 500 Step 2 12 Declare the area alloca 13 WBSF 14 Adjustables Area Quantity Quantity Purchase 5 Crops Allocated Harvested Gold d Declare the yield of eac 16 Wheat W in 0 200 WBSP_ 7 Corn 0 0 0 240 18 Beans 500 12000 11900 Declare the sold and pu 19 Shortfall Purchased WBSF 20 Excess Sold WBSF 71 Objective Maximize Profit Amount Obtained from Selling Planting Cost Purchase Cost Y LL WB _Histogram Problem Statement Model Scenario Tree 4 a Ur READY H 70 The solver writes a series of solution in the created tab WB _Stochastic with the expected value and displays the first scenario on the spreadsheet 390 CHAPTER 7 Put Option File name SP_PUTO
368. nformation File is created upon request of LINDO Systems by clicking the Info button It contains the Machine Name the User Name and the Disk Identification Number This file USERINFO TXT can then be sent to LINDO Systems so to create the full license key for academic purpose By default this file will be created in the What sBest add in folder but a different folder can be selected usually in the local disk drive Upon request of LINDO Systems this USERINFO TXT file is created to contain the Machine Name the User Name and the Disk Identification Number This file should then be sent to LINDO Systems to create the full License Key Select Destination Folder Browse Create e O Also you may need to verify where your license key is stored The license file LNDWBxxx LIC is located in the same directory as the What sBest add in files The About What sBest will show your license capacity currently installed If you have lost your license key please contact LINDO Systems 138 CHAPTER 3 Register The dialog box posted by the Register command appears as follows Serial Number werc1 1234567890 Educational License Linear Barrier Conic Nonlinear Global Integer Stochastic Professional Name Phone Email What is your company s primary business Education Consulting Manufacturing Accounting Government Agricultural Medical Financial Marketing Other Tel
369. nformation can be entered directly onto the spreadsheet or via the set of dialog boxes Step 1 core model 1 Data and Formulas Specify the initial price 100 the strike price 99 and the risk free rate 5 The price stock of this period price of the previous period 1 the stock return of this period This is written in the cells C18 to C23 The wealth of this period the wealth of the previous period 1 the risk free rate the decision to sell strike price price stock of this period This is written in cells E18 to E23 SAMPLE MODELS 391 2 Adjustable Cell There are 6 adjustable cells in cells E18 to E23 one for each period The meaning is 1 for selling 0 for holding 3 Objective Function The objective function is to maximize the wealth at the end of period 5 cell E28 4 Constraint Cell There is one constraints in D26 of the model The total number of selling decisions has to be one 5 Random Cell There are 5 random parameters in cells B19 to B23 one at each period expressing the uncertainty of the stock return Step 2 stochastic information for stage Decision Variables Specify the stage information for the decision to sell or to hold which is a decision variable adjustable This is done by using the function WBSP_VAR This function requires two parameters i stage of the variable ii cell address of the variable In this problem the decision in cell D18 is a r
370. nimizing the use of integer restrictions can drastically reduce the solution time In instances involving larger numbers you may find that solving the model without integer restrictions and then rounding yields acceptable answers in a fraction of the time the integer model requires MATHEMATICAL MODELING 225 Guidelines for Stochastic Modeling So far we worked with deterministic mathematical programs where model parameters e g coefficients bounds etc are known constants A stochastic program SP is a mathematical program linear nonlinear or mixed integer in which some of the model parameters are not known with certainty and the uncertainty can be described with known probability distributions Applications arise in several industries e Multi period financial portfolio planning with uncertain prices interest rates and exchange rates e Exploration planning for petroleum companies e Fuel purchasing when facing uncertain future fuel demand e Fleet assignment vehicle type to route assignment in face of uncertain route demand e Electricity generator unit commitment in face of uncertain demand e Hydro management and flood control in face of uncertain rainfall e Optimal time to exercise for options in face of uncertain prices e Capacity and Production planning in face of uncertain future demands and prices e Foundry metal blending in face of uncertain input scrap qualities e Product planning in face of future technology
371. nn nennen nenn 195 WwbSetStringSuppott i aisrui sets cond eieaa ia eie aa aa aa a aaia EEN 195 WDSOIVE aa lae dek DEENEN 196 wbztochaesttecChancetonstrained nennst tnnn nnmnnn eenn 198 WbStochasticFunction EE 200 WHStOChASTICHISLOGrAM aE a E E a a 201 WbotochastiGRe ports EE 202 WDStochasticStageScenarrio ereer E EE R E R ER 203 Ve lete ET LEE 204 5 FUNCTIONS AND OPERATORG RER 205 List of Supported Functions and Operators tnn nn nnt 205 FUNGHONS eene edd ee Eegeregie 205 Operators ic pete ceed At cutest ane sedate Maca et aa seeds Saath aan a A el 205 Distributions Correlations for Stochastic Programming eseseseeesseeerreseerrsserrrssrenssees 206 BE Le EE 207 er 207 Statistical FUNCIONS retia EE 208 1 Erlang s Loss of Probability WDBERLANG BA 208 2 Erlang s Busy Probability WBERLANG C A 208 3 Inverse Exponential Cumulative Distribution WBEXPOINV sssssssssssssssesssresrrnnsens 209 4 Inner Sum Product WBINNERPRODUCT sssssssssssessssesrnrrenssrrrrrrnsnsstrenrtnnsnnsrrrnn rn 209 5 Logistic Cumulative Distribution WBLOGISTIC s sssesssssssrennsnssreerrrnnsnrsrrrrrrnnsees 209 6 Logistic Probability Density Distribution WBLOGIGTICDENS seeeeeeeeeeeeeeeen 210 7 Logistic Inverse Distribution WBLOGISTICINV sssssssssssssssrsnnssssrerrrnnsnesrerrrnnnseeee 210 8 Inverse Multinomial Cumulative Distribution WBMULTINV sssssssssesessssssrrsrrnrnenn 210 9 Standard Normal Linear Loss Function
372. nse upgrade to handle the additional constraints LICCAP2 Adjustable Cell Limit If your model has more adjustable cells than is allowed for your installation the following error message will be displayed on the WB Status tab Error Message ERROR Adjustable Cell Limit Help Reference LICCAP2 The number of adjustable cells in this model number of adjustables exceeds the limit of adjustable limit The model has more adjustable cells than is allowed by your installation You will need to either reduce the size of your model or upgrade to a larger version Suggestions The model exceeds the adjustable cell limit for your installation The capacity limits of your version may be found by running the WB About What sBest command One option is to remove adjustable cells from the model until it satisfies the limit Also if the workbook contains multiple independent models you can separate them into different workbooks in order to meet the limit If eliminating adjustables is not an alternative then you may wish to contact LINDO Systems regarding a license upgrade to handle the additional constraints 424 CHAPTER 8 LICCAP3 Integer Cell Limit If your model has more integer cells than is allowed for your installation the following error message will be displayed on the WB Status tab Error Message Integer Cell Limit Help Reference LICCAP3 The number of integer cells in this model number of integers
373. nstraint argument NonlinOpt_BadStratSteepestEdgeArg Bad StratSteepestEdge argument NonlinOpt_BadStartingPointArg Bad StartingPoint argument NonlinOpt_BadOptimalityToleranceArg Bad OptimalityTolerance argument NonlinOpt_BadItLimitSlowProgArg Bad ItLimitSlowProg argument NonlinOpt_BadDerivativesArg Bad Derivatives argument 192 CHAPTER 4 Example If one wished to set all the nonlinear options the simplest syntax would be wbSetNonlinearOptions True True True True True True False True False 0 0001 200 1 To set one or more options named arguments should be used wbSetNonlinearOptions OptimalityTolerance 0 0001 MACROS THE VBA INTERFACE 193 wbSetStochasticOptions This routine can be used to set the What sBest stochastic solver options seen in the Stochastic Solver dialog box All arguments are optional For additional discussion of the options available through this routine see the section entitled Options Stochastic Solver Syntax wbSetStochasticOptions StochasticSolverMethod StochasticSeed StochasticSamp1Size StochasticSamp Cont StochasticEVWS StochasticEVEM StochasticEVPI StochasticEV MU StochasticRepScenHoriz StochasticSolverMethod StochasticSolverMethod is an i integer indicating the stochastic solver method to employ 0 Solver Decides 1 Free 2 Deterministic Equivalent 3 Nested Benders Decomposition 4 Augment
374. nstrate putting dual value functions in the model In the examples above none of the arguments used the named argument syntax To do so simply list the argument name followed by a colon and equal sign and then the argument To set the range C5 D5 as adjustable with the named argument syntax enter wbAdjust AdjRange C5 D5 AdjChoice Adjustable Using the named argument syntax can make the code easier to read and when calling procedures with multiple arguments allows you to list the arguments in any order you choose 150 CHAPTER 4 Solving Multiple Problems with a Looping Macro When automating a process using macros you may want to run the same macro many times on different data while storing the optimal solution for each data set For example you may have a database filled with information on the return on a group of investments at a range of interest rates What sBest can be used to determine the optimal portfolio in each situation by using a looping macro Using the PMIXMAC_XLS sample file which was copied to the WB subdirectory during installation let s look at how a looping macro might be created Use the Visual Basic Editor to go to the Looping Macro module in your workbook and your screen should look like the following Sab Macroloop This macro will increnent the Profit Unit of Product Z from 45 60 solve the model copy the Total Profit and Quantity Produced of Dim Din Products 1
375. nt Value in a 8 bin graph WBSP_ HIST 8 E28 Scenario Tree The Scenario Tree illustrates the concept of modeling under uncertainty In Stage 0 an initial decision has to be made for selling or keeping the stock In Stage 1 the stock return is revealed depending on the market wealth and as a recourse decision the sell or keep action has to be decided 394 CHAPTER7 From Stage 2 to 4 the same sequence is applied In Stage 5 the stock return is revealed a recourse decision is made as well as the final computation The objective is to maximize the total expected profit at the end of planning horizon Stage 5 H S e Des SP_PUTOPTION xIsx Excel 2 P D xXx SI HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Undo Sys Al x f Scenario Tree v A E CG D E F G H I J K L M N o P Een GES Scenariot Scenario Sconario 3 Scenario d Scenario 5 Sconarin Zeenarie Zeenarie Sconariod Sconaria 10 Sconaria 11 Scenario i Sconaria 13 Scenario 14 Scenario 15 Sconario 16 Scenario i Model Scenario Tree CH al SAMPLE MODELS 395 Optimization The SP_PUTOPTION Worksheet Before Optimization H S o De Sp PUTOPTION alen Excel 2 P D xX HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys Fy Al i E f v SJ e Pr c D E FE G fal 2 Stochastic ramming Version of an American Put Option
376. nt linear ones thus allowing you to use the faster and more robust linear solvers in What sBest We refer to this process as linearization Specify the extent to which What sBest should attempt to linearize models with the Degree drop down box The available options here are Solver Decides None Mathematical and Mathematical Logical Under the None option no linearization occurs With the Mathematical option What sBest linearizes ABS MAX and MIN function references as well as any product of binary variables and at most one continuous variable The Mathematical Logical option is equivalent to the Mathematical option plus it will linearize AND IF INTO MOTO OR SIGN SUMIF VLOOKUP and HLOOKUP functions and all logical operators lt gt and lt gt Under the Solver Decides option What sBest will do maximum linearization if the number of adjustable cells doesn t exceed 12 Otherwise What sBest will not perform any linearization What sBest defaults to using Solver Decides The linearization process may add a considerable number of constraints and variables to the mathematical program generated to optimize your model The number of such constraints and variables added is noted in the WB Status report Delta Coefficient You can specify how closely you want the additional constraints added as part of linearization to be satisfied with the Delta Coefficient text box What sBest defaults
377. nteger cells on a protected sheet Remarks IntSos_BadArgListArg Bad ArgList argument Integer variables can dramatically increase the solution time Example To constrain cell F6 to be a general integer using the range name staff enter whIntegerSos 1 Sheet1 B 1 Sheet1 C 1 C 3 Sheet1 A 1 The cell Al then contains the function WBSOS 1 Sheet B 1 Sheet1 C 1 C 3 wbintegerSolverKBestReport For additional discussion of the functionality provided see the section entitled Options Integer Solver and Usage Guidelines for K Best Solutions which refers to the dialog box that calls this procedure This routine is used to build WB KB_REP function with ranges which are areas of the worksheet that What sBest will see the trade off cells while solving This function will need to be used in conjunction with the option KBest defined via the wbhSetintegerOptions Syntax wbIntegerSolverKBestReport ArgList Refers_to NoErrDialog KBestName Yes ArgList is the range or address of the cell s to be read Refers_to Yes Refers_to is a cell reference to specify in which to write the WBIKB_REP function No Any argument passed here causes all What sBest error NoErrDialog dialog boxes from the wbIntegerSolverKBestReport routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number Useful in an embedded application o
378. nteger to get any possible returned What sBest error number Useful in an embedded application of What sBest MACROS THE VBA INTERFACE 155 Error Codes Description Best_BadBestCellArg Bad BestCell argument Best_BadBestChoiceArg Bad BestChoice argument Best_ProtectedSheetError Unable to set the best cell in a protected sheet Best_CreateStyleError Error creating a Best style Remarks Only one cell can be specified as a best cell Example To set I17 as your objective to minimize enter wbBest I17 Minimize To set F17 as the objective to maximize enter wbBest To reset cell F17 to None enter wbBest F17 Maximize WEP None WBBIN For additional discussion of the functionality provided see the section entitled nteger which refers to the Binary option button that calls this procedure This routine is used to build binary integer ranges named WBBIN The adjustable cells contained in these ranges will be set to either 0 or 1 by the What sBest solver Syntax WBBIN IntName Refers_to Argument Required Description IntName Yes IntName is a string that refers to the range being made integer Refers_to No Refers_to is the range or address of the cells to be specified as integer If omitted the default is the current selection Error Codes Description Int_BadIntNameArg Bad IntName ar
379. numbers of employees and longer time periods make the task more difficult This problem involves scheduling several staff members in an organization that operates in multiple time shifts each day seven days a week The Problem in Words Your business works in three shifts day evening and night For each shift you must meet certain minimum staffing levels Each staff member must be assigned a specific number of shifts and has individual preferences for working the various shifts Moreover because of the nature of the work each employee must have an adequate rest period between shifts in order to perform the job effectively This model demonstrates how you can meet your staffing requirements while satisfying your employees scheduling preferences to the greatest possible degree Background Your specific staffing needs for a particular week are as follows Staff Members Required Mon Tue Wed Thu Fri Sat Sun Day 2 1 1 3 1 1 1 Eve 1 1 0 0 2 1 1 Nite 1 0 0 0 1 1 1 Your staff members Nixon Ford Bush and Reagan must each be assigned to five shifts for the week and have individually selected their preferred shifts on a descending scale of 5 to 1 These rankings appear on the Preferences worksheet of the model In addition to considering your staff s preferences you must abide by two rules in scheduling the shifts Staff members cannot work more than one shift in a single day After working a shift a staff member
380. o 0oN n eech EE ER E sch MI OO GO Ga GENEE EE EE ENEE 4 Oa E ENER EH EN v h sch sch EN EH P CO eene eeeeeeneee ch E sch zech E sch E E CHE CH CH P STAFF NEEDS MET WB Status FIXED2 2 DE PREFERENCE TOTAL Z AA AB AC AD AE AF AG 12 Single 0 Assign ooooococoococoocococoe Som Aen O 368 CHAPTER 7 The maximized preference total in cell AH19 is 150 and the staffing needs established by stage 1 are met To verify that assignments have been made according to seniority and preference go back to screen and observe that Tom in row 7 with a seniority level of 9 has rated shift 8 as his highest preference After solving Tom has indeed been assigned to shift 8 SAMPLE MODELS 369 Pipeline Optimization File name PIPELINE XLSX TYPE LINEAR OPTIMIZATION Application Profile This model is an example of a network problem requiring the movement of resources at minimum cost along different routes with which varying costs are associated With the addition of limits to capacity along the routes it becomes capacitated Oil and gas pipelines truck and air routes may be utilized at their highest cost efficiency by applying the principles demonstrated in this model The Problem in Words As the operator of an oil supply network you must choose among several available pipelines from two wells to three pumping stati
381. o no longer be adjustable If omitted the default value for AdjChoice is Adjust For backwards compatibility with earlier versions of What sBest AdjChoice also accepts the numbers for Adjustable and 2 for Reset NoErrDialog No Any argument passed here causes all What sBest error dialog boxes from the wbAdjust routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What seet error number Useful in an embedded application of What sBest Error Codes Description Adj_BadAdjRangeArg Bad AdjRange argument Adj_BadAdjChoiceArg Bad AdjChoice argument Adj_ProtectedSheetError Unable to set cells as adjustable on a protected sheet Adj_CreateStyleError Error creating an Adjustable style Adj_CheckStyleUnlockedError Error checking that the Adjustable style is unlocked Adj_CheckStyleProtectionError Error checking that the Adjustable style includes protection Remarks An adjustable cell must contain a number or the cell is ignored by the solver The Adjust procedure formats the cell s with a style called Adjustable which carries a blue font color as a visual reminder All adjustable cells will return non negative values unless they are ina WBFREE range Example To set the cells D8 E10 as adjustable enter the macro wbhAdjust D8 E10 or wbAdjust Range Cells 8 4 cells 10 5 154 CHAPTER 4 To reset t
382. oErrDialog CardNumber Yes CardNumber is an integer meaning that at most N of the variables in the set will be allowed to be nonzero ArgList Yes ArgList is a string list of range or cells reference separated by a comma Refers_to Yes Refers_to is the range or address of the cell s to be specified as SOS NoErrDialog Any argument passed here causes all What sBest error dialog boxes from the wbIntegerCard routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number Useful in an embedded application of What sBest IntCard_BadCardNumberArg IntSos_ProtectedSheetError 172 CHAPTER 4 Remarks Integer variables can dramatically increase the solution time Example To constrain cell F6 to be a general integer using the range name staff enter whIntegerCard 3 Sheet 1 B 1 Sheet1 C 1 C 3 Sheet A 1 The cell Al then contains the function WBCARD 3 Sheet1 B 1 Sheet1 C 1 C 3 wbintegerSemic For additional discussion of the functionality provided see the section entitled Integer Semi continuous which refers to the Semi continuous dialog box that calls this procedure This routine is used to build the Semi continuous ranges WBSEMIC Adjustable cells contained in these ranges will be restricted to integral values by the What sBest solver If you wish to delete a SEMIC function using VBA instead
383. ochastic WBSP_DIST 1 Format 441 Error messages amp Warnings Stochastic WBSP_DIST 2 Format 442 Error messages amp Warnings Stochastic WBSP_DIST 3 Format 442 Error messages amp Warnings Stochastic Error 443 Error messages amp Warnings Stochastic WBSP_HIST Format 444 Error messages amp Warnings Stochastic WBSP_RAND Format 444 Error messages amp Warnings Stochastic WBSP_REP Foramt 445 Error messages amp Warnings Stochastic WBSP STSC Format 446 Error messages amp Warnings Stochastic WBSP_VAR Format 446 Error messages amp Warnings Cardinality Cell Format 451 Error messages amp Warnings Semi continuous Cell Format 453 Error messages amp Warnings Special Ordered Sets Cell Format 454 Estimation Model 313 Excel 3 4 145 151 EXLVER 410 EXP 205 Exponential smoothing 308 Exposure 324 Expressions convex 217 linear 213 nonlinear 214 Nonsmooth 218 Smooth 218 Extended Version 134 FALSE 205 feasibility tolerance 52 FIXED1 XLSX 360 FIXED2 XLSX 360 Flow 270 376 Flow Cover 72 Flow Network Modeling 270 FLOWNET XLSX 270 Forecasting Models 304 308 FORMULAI 411 FORMULA2 411 FORMULAS 412 470 INDEX Forward Analytical 64 Forward Differences 64 Free 24 Deleting designation 24 variables 24 FUNCADDIN 413 FUNCMACRO 413 FUNCSERVER 414 Function 147 Functions 205 12 convex 217 linear 213 nonlinear 214 G GCD 72 General and Opera
384. od drop down box Possible choices include Solver Decides Primal Simplex Dual Simplex and Barrier The simplex method moves along the surface of the feasible region toward the optimal solution while the barrier method moves through the interior region The Solver Decides setting currently defaults to the primal simplex method As a rough guideline primal simplex tends to do better on sparse models with fewer rows than columns Dual simplex tends to do well on sparse models with fewer columns than rows The barrier method is most effective on densely structured or very large models The barrier method is an optional feature in What sBest However most versions ship with a 30 day trial license for the barrier solver If your version of What sBest doesn t currently include the barrier option you may add it at any time Please contact LINDO Systems for information If the barrier solver is chosen without a license What sBest will default to using the primal simplex method The default setting for Solver Method is Solver Decides Pricing Select the type of pricing for the dual simplex and primal simplex algorithms in the Dual Pricing and Primal Pricing drop down boxes respectively Pricing is a way of assessing the relative attractiveness of variables for selection in the simplex algorithm 60 CHAPTER 3 Dual Pricing One pricing algorithm for dual simplex is called Partial according to which the dual simplex solver prefers var
385. odel 421 Irreconcilable Constraints 421 Iteration Limit Reached 422 Large Infeasibility 419 Lower Range Cell Format 452 No Adjustable Cells 416 No Best Cell 435 No Constraint Cells 435 No Feasible Solution Found 418 Nonlinear Adjustable Cell Limit 424 Nonlinear Solver Not Licensed 429 Omitted Cell Reference 436 Parsing Cell Formula 432 Pending Expiration of Option Trial 427 Pending License Expiration 426 Quadratic Recognition 437 Runtime Limit Reached 438 Solver Error 439 Solver Interrupt 419 Stochastic Error 440 String Arguments Found 447 String List Error 447 String Result of Formula 448 Unbounded Model 449 Undefined Reference 450 Unsupported Functions 411 Unsupported Lookup Usage 431 Unsupported Name 433 Unsupported Sumif Usage 448 Upper Range Cell Format 454 Error messages amp Warnings Multiple Add in Links 408 Error messages amp Warnings Arithmetic Error 409 Error messages amp Warnings Blank Cell Warning 409 Error messages amp Warnings K Best WBIKB_ REP Format 417 Error messages amp Warnings Indicator Model Cell Reference 417 Error messages amp Warnings License key Dongle Required 428 Error messages amp Warnings Mixed Integer Solver Not Licensed 429 Error messages amp Warnings Stochastic Solver Not Licensed 430 Error messages amp Warnings Conic Solver Not Licensed 430 Error messages amp Warnings Stochastic WBSP_CORR Format 441 Error messages amp Warnings St
386. odels On the other hand setting this parameter too low will result in infeasible models For this particular model a setting of 1 000 works well After solving you ll see the following result The LINEARZ Worksheet After Optimization x ld ko KSC g Jj e INAR Microsoft Excel ain e ES e File Home Insert Page layout Formulas Data Review View Developer Team What sBest 9 e o E ZS Pred Cost Error 123 4 449 128 8 23 0 161 0 11 9 182 5 8 7 204 0 20 4 230 9 36 1 257 8 44 9 322 3 20 3 483 6 449 510 5 20 1 Sq Feet 1500 1600 2200 2600 3000 3500 4000 5200 6200 8700 snl ln elon lel call AB S RRWENNNAAAG Coefficients Max Error 16 42 7567 0 0538 0 0000 0 0000 17 18 19 20 21 4 4 b H WB Status LINEARZ 2 Ha m Ready 23 e 10 Thus our optimal solution minimizes the maximum error at 17 8 using the following formula Total Cost 5 6896 0 0373 Sq Feet 19 5877 Beds 15 0613 Baths 316 CHAPTER 7 Linearization Note that as formulated this model is nonlinear This is the result of the ABS and MAX functions used in computing the error terms and the objective value respectively Both ABS and MAX can create problems for the nonlinear solver in that they aren t continuously differentiable Both functions have kinks in their graphs at various points that the nonlinear solver is unable to see around With a fair amount of effort one c
387. ods will tend to be faster on smaller sparse models Large integer problems can be very difficult to solve and take a great deal of time arriving at a solution To solve an infeasible problem or to shorten the solution time you can try various options on the Integer Solver Options dialog box Setting an Optimality Tolerance can improve run times dramatically if you are happy being within a certain percentage of the optimal solution Some problems solve faster when the Branching Direction is set to Up Setting the Application of the Constraint Cuts to All Nodes may help solve some problems Setting the Probing Levels may also help shorten solution time We recommend setting to a level of three or lower Nonlinear problems are generally difficult to solve Setting a Feasibility Tolerance or Optimality Tolerance may help you to reach a solution Trying different Strategies may also be useful to reaching a solution Many nonlinear problems are made unnecessarily difficult or slow to solve by the presence of nonlinear expressions that could be rewritten in linear form The Linearization option is a tool for automatically rewriting these nonlinear expressions in linear form Linearization can be a great performance boost if all nonlinear formulas in a model can be linearized such that the final model becomes totally linear If linearization can only be applied to a subset of the nonlinear formulas then performance may erode The options described above
388. of deleting it on the spreadsheet you can use Selection Clear This statement clears the selected cell from any of its content Syntax wbIntegerSemic LowerBound UpperBound ArgList Refers_to NoErrDialog LowerBound Yes LowerBound is a number indicating the lower bound in the range UppererBound Yes UpperBound is a number indicating the upper bound in the range ArgList Yes ArgList is a string list of range or cells reference separated by a comma Refers_to Yes Refers_to is the range or address of the cell s to be specified as SEMIC NoErrDialog No Any argument passed here causes all What sBest error dialog boxes from the wbIntegerSemic routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number Useful in an embedded application of What sBest IntSemic_BadLowerBoundArg Bad LowerBound argument MACROS THE VBA INTERFACE 173 IntSemic_BadUpperBoundArg Bad UpperBound argument IntSemic_BadArgListArg Bad ArgList argument IntSemic_BadRefersToArg Bad Refers_to argument IntSemic_ProtectedSheetError Unable to set integer cells on a protected sheet Remarks Integer variables can dramatically increase the solution time Example To constrain cell F6 to be a general integer using the range name staff enter whIntegerSemic 10 20 Sheet1 B 1 Sheet1 C 1 C 3 Sheet1 S A 1 The cell Al then contains the funct
389. of it as the sum of three simpler linear expressions Nonlinear Expressions By definition all expressions that are not linear are nonlinear Nonlinear expressions include relationships in which variables are squared cubed or taken to powers other than one variables that are multiplied by each other and many expressions using nonlinear spreadsheet functions such as JE MAX and MIN Models with nonlinear expressions are intrinsically much more difficult to solve than linear models Unlike linear models a badly formulated nonlinear model may prevent What sBest from finding a solution even though one in fact exists Another problem posed by some nonlinear models is that What sBest may detect a locally optimal solution to the model that appears to be the best whereas a better but also locally optimal solution still exists For more on what you can do to help minimize the occurrence of these undesirable results see the section titled Guidelines for Modeling with What sBest Linearization The presence of any nonlinear expressions in the model will cause the nonlinear solver to be invoked and the model to be classified as nonlinear You can determine whether your model is linear or nonlinear by the classification under Model Type in the solver status window or the status report The nonlinear models take much longer to solve than a linear model with the same number of constraints The process of converting a nonlinear expression to a lin
390. of oil or gas through systems of pipelines The particular shipping example illustrates the use of optimization to provide the least cost distribution for a business that produces a product at many locations transports it to intermediate warehouses and then to final consumption or sales locations Manufacturers utilities retail chains and other distributors are all likely users of shipping optimization systems modeled along similar lines The Problem in Words You work in the shipping department of a manufacturing business and need to minimize shipping costs while meeting demand without exceeding capacity Background In this case two steel mills produce the same product This product must be sent out to three plant locations Each location has a demand for the product that must be met and each steel mill has limited manufacturing capacity Finally shipping costs vary from each steel mill to each plant Shipping Costs Per Unit of Steel From Steel Steel To Mill1 Mill 2 Plant A 200 500 Plant B 300 400 Plant C 500 600 Objective of Optimization The objective is to meet all plant demand without exceeding steel mill capacity at minimum shipping cost 374 CHAPTER7 The Worksheet Let s look at the SHIPPING sample file The SHIPPING Worksheet Before Optimization l is SHIPPING xlsx Microsoft Excel ela Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 2 o El 3 fe SHIPPING COST RED
391. og box at the Chance Constrained page All arguments are required except for the error code but a 0 value can be placed for unnecessary arguments For additional discussion of the options available through this routine see the section entitled Options Stochastic Solver Syntax wbStochasticChanceConstrained FunctionName Percent ObjWeight Refers_to Place_in_cell NoErrDialog FunctionName Yes WBSP_CC_LT FunctionName is a string argument indicating the name of the function to implement either WBSP_CC LT or WBSP _CC GT Percent Yes Percent is an integer between 0 and 1 indicating the wether the probability of the set is satisfied MACROS THE VBA INTERFACE 199 ObjWeight Obcj Weight is a number indicating the amont set on the objective value Refers_to Refers_to is the range or address of the cell to copy the chance constraint function Place_in_cell Place m cell is a cell reference to specify the cell in which to write the WBSP_ function NoErrDialog Any argument passed here causes all What sBest error dialog boxes from the wbStochasticChanceConstrained routine to be suppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number Useful in an embedded application of What sBest Sto_BadFunctionNameArg Sto_BadPlaceInCellArg Examples To set a Chance Constrained information to constraint cells the simplest syn
392. ogistic distribution with input probability C location parameter A and scale parameter B 8 Inverse Multinomial Cumulative Distribution WBMULTINV This function returns the inverse of a multinomial cumulative distribution for a supplied set of probabilities and corresponding values The syntax is WBMULTINV Prob ProbRange ValueRange Prob The probability corresponding to the multinomial distribution The probability must be greater than or equal to 0 and less than or equal to 1 ProbRange The cell range containing the probabilities ProbRange must be a one dimensional range i e a range of cells in either a single row or a single column ValueRange The cell range containing the values that correspond with each probability The ValueRange must be the same size and shape as the ProbRange FUNCTIONS AND OPERATORS 211 For example given the following aias gare WBMULTINV xlsx Microsoft Excel b Home Insert Page Layout Formulas Data Review View Developer Team What sBest YV B1 v L WBMULTINV 0 6 A3 A5 B3 B5 A E D E F G H WBMULTINV 31 2 3 0 2 2 4 0 3 1 e 0 5 3 A then WBMULTINV 0 6 A3 A5 B3 B5 returns 3 This means that the minimum outcome X such that 60 percent of the outcomes are less than or equal to X is X 3 9 Standard Normal Linear Loss Function WBNORMSL This function returns the expected value of max 0 Z X where Z is a standard normal random variable In inventory modeling WBNO
393. olerance is 0 0 Relative Use the Relative text box to set the relative optimality tolerance This is a value r ranging from 0 to 1 indicating to the branch and bound solver that it should only search for integer solutions with objective values at least 100 7 better than the best integer solution found so far The end results of modifying the search procedure in this way are twofold First on the positive side solution times can be improved tremendously Second on the negative side the final solution obtained by What sBest may not be the true optimal solution You will however be guaranteed the solution is within 100 7 of the true optimum on linear integer models Typical values for the relative optimality tolerance would be in the range 01 to 05 In other words you would be happy to get a solution within 1 to 5 of the true optimal value On large integer models the alternative of getting a good solution within a few percentage points of the true optimum after several minutes of runtime as opposed to the true optimum after several days makes the use of this tolerance quite attractive The default value for the relative optimality tolerance is 0 00001 Note Generally speaking increasing the relative optimality tolerance is the change that will most likely improve runtimes on integer models ADDITIONAL COMMANDS 77 Time to Relative If an integer programming model is relatively easy to solve then we would like to have t
394. ollows Linear Solver Options Iw Scale Model Iw Model Reduction Solver Method Solver Decides v Pricing Cancel Dual Pricing Solver Decides v Solver Decides v Help ADDITIONAL COMMANDS 59 This command allows you to set a number of options controlling the function of the linear solver Scale Model Select the Scale Model checkbox to rescale the matrix coefficients so the ratio of the largest to the smallest coefficients is reduced Rescaling reduces the likelihood of roundoff error and thereby promotes numerical stability and accuracy The default setting is to enable scaling Model Reduction Enable the Model Reduction checkbox to have the solver identify and remove extraneous variables and constraints from the formulation before solving In some cases this greatly reduces the size of the model to be solved to the user s benefit In other cases reduction only adds to the solution time without significantly decreasing the size of the model Because Model Reduction can offer significant improvement in performance this is one of the more significant options However it is extremely difficult to predict whether a model will solve better or worse with reduction so the user is advised to try both settings to determine which setting offers better performance The default is to enable reduction Solver Method Indicate the method you would like the linear solver in What sBest to employ using the Solver Meth
395. olver Reset to Default From the dialog boxes posted by these commands you can set the options by simply selecting the options you would like and clicking the OK button If you wish to restore the options to their default values you should use the WB Options Reset to Default command to return all What sBest options to their default values ADDITIONAL COMMANDS 51 Options General The dialog box posted by the Options General command appears as follows General Options Solver Feasibility Tolerance Limits Iteration Limit iterations Runtime Limit seconds Number of Threads RW Display Constraint op IV Auto Select Free Int Omit Ranges Minimize Excel R on Solve Hide Status Window on Solve C Slack m Linearization Degree Solver Decides vv Delta Coefficient Big M Coefficient m Reports Location and Warnings Warnings IV Nonlinearity Present Iw No Best Cell Reference to Blank Cell Iw Unsupported Function IV String Argument Present Status Report Always Created D Beginning Solution Report Never Created D Iw Irreconcilable Constraint Infeasible Constraint Unbounded Variable Iw Support Lookup Functions Edit Links 52 CHAPTER 3 The General Options dialog box contains options that let you control the ways in which What s Best displays processes and saves information All of the options in t
396. olver setting probing to a level it believes will offer the best result ADDITIONAL COMMANDS 71 Constraint Cuts The options contained in the Constraint Cuts box on the Integer Pre Solver dialog box m Constraints Cuts Max Passes Relative Limits e 0 75 Types M CoefficientReduction V Lattice Iw Disaggregation M Lifting IV Flow Cover Iw Plant Location Iv GCD I Obj Integrality MV Gomory Iw Basic JW GUB Cardinality V Knapsack Cover IV Disjunctive can be used to influence the solver s cut generation phase on linear models What sBest s integer programming pre solver performs extensive evaluation of your model in order to add constraint cuts Constraint cuts are used to cut away sections of the feasible region of the continuous model i e the model with integer restrictions dropped that are not contained in the feasible region to the integer model On most integer models this will accomplish two things First solutions to the continuous problem will tend to be more naturally integer Thus the branch and bound solver will have to branch on fewer variables Secondly the bounds derived from intermediate solutions will tend to be tighter allowing the solver to fathom i e drop from consideration branches higher in the branch and bound tree These improvements should dramatically speed solution times on most integer models Max Passes Set the maximum number of passes allowed by the integer pre solver to any non nega
397. om Phone 312 988 9421 General information e mail info lindo com phone 800 441 BEST 800 441 2378 www lindo com From our website www lindo com you can download trial versions of any of our optimization products You can also find a database of sample models and past newsletters to assist you in your modeling efforts Our website also accommodates online ordering and upgrading information 465 REF 450 0 0 1 integer variables 2 44 A ABC steps 9 12 About What sBest 133 ABS 205 Absolute 74 Absolute value function ABS 207 Absolute Violation 67 182 Absolute Width 67 182 Access 145 151 Acknowledgements 2 ACOS 205 ACOSH 205 Active 39 ADDINLINK 408 Additional commands 41 Adjustable button 22 Adjustable cell 9 12 Dual Value for 114 Adjustable command 22 refers to 23 Adjustable dialog box 22 24 Adjustable Best Constraints Steps 9 Advanced Parameters 126 Advanced Dual 110 Advanced Dual 110 Advanced Function Support 126 Advanced Om 124 Advanced Omit 124 Advanced Parameters 129 Advanced Stochastic Support 128 Advanced String Support 127 Advertising 324 Algebraic Reformulation 67 Algorithms 42 Alpha 308 alternate optima 79 American option 390 Index AND function 205 207 Arc 270 ARITHERR 409 ASIN 205 ASINH 205 Asset 292 298 ASSIGN XLSX 353 ATAN 205 ATAN2 205 ATANH 205 Audience 324 AVERAGE 2
398. ome What If trials and round them in the direction that doesn t violate the maximum load constraint If you round the proportion up to 1 00 the weight of the load increases to 15 000 pounds This violates the 10 000 pounds maximum weight constraint Instead round the fraction of item 1 down to zero This drops the value of the load to 7 500 pounds leaving 2 500 pounds of load capacity unused No other item weighs less than 2 500 pounds so the truck can t be filled up further Rounding fractional weights as in the conventional method the truck would carry only item 2 for a load weight of 7 500 pounds and a load value of 24 000 The Binary Integer Method This problem can be converted very simply to give an integer solution one with no fractional weights for an item Use the binary Integer command to specify that the adjustable cells in D6 D11 cannot be anything other than zero or one You could also eliminate the constraints in E6 E11 and the constants in F6 F11 which are now superfluous 382 CHAPTER7 The re optimized solution should look like the following The TRUCK Worksheet in Integer form After Optimization Z ed IM g ie ru ckadsx Microsoft Excel File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ai o El es WBBINbin A B Cc TRUCK LOADING Proportion Proportion Value Weight Loaded Loaded 22 500 7500 24 000 7500 8 000 3000 9 500 3500 11 500 4000
399. on dual values see the section on Dual Values in Chapter 3 Additional Commands SAMPLE MODELS 263 Chance Constrained Blending File name HOGCHANC XLSX TYPE NONLINEAR OPTIMIZATION Application Profile In the previous HOGFEED blending example we showed you a deterministic model the nutrient content of the different grains to be incorporated in the finished feed were known and constant However what if the nutrient content is not so reliable What if the content varies at random This model is nonlinear and perhaps more likely to occur in the real world The Problem In Words You must determine how much of four available grains to include in blended feed in circumstances under which the content of one of the nutrients varies at random to meet nutrient requirements with some degree of certainty Background You ve had several samples of the four grains tested and you find that their content of Nutrient D varies randomly and is normally distributed You want to find a new blend that ensures the minimum requirements for Nutrient D are met at least 95 of the time You ve calculated the mean and variance for each grain the content means are the same as in the original HOGFEED model The equation that calculates Nutrient D now looks like this Mean Nutrient D in the blend Z standard deviation Nutrient D gt 21 For 95 confidence in the content of Nutrient D set Z 1 645 Refer to any elementary text on statis
400. onlinear In a nonlinear problem the Solution Status INFEASIBLE message may not mean that there is no solution that satisfies all constraints It only indicates that none can be found from the starting values you ve entered in the adjustable cells If you know or suspect there is a feasible answer to the problem enter adjustable cell values that yield a feasible or near feasible solution and try solving from that starting point Alternatively using the Global Solver option may help One other possible course to follow is to view the constraints in slack mode rather than Indicator mode This helps you determine which constraints are furthest from being satisfied Then enter educated guesses for the adjustable cells values that cause the constraints to come closer to being satisfied and try solving again from these starting values 32 CHAPTER 2 Explicitly Specifying Convexity to the Solver One of the important considerations for the solver in finding a global optimum is the exploitation of convexity In layman s terms if an optimization problem is convex then a carefully implemented hill climbing search algorithm or valley finding for a minimization problem will find a global optimum More generally if the feasible region is convex then any strict local optimum can justifiably be declared a global optimum Our solver is fairly sophisticated in its ability to identify convex expressions Nevertheless there may be some constra
401. ons and from the pumping stations to four refineries Wells have a monthly supply capacity that must not be exceeded capacities of the pipelines may be limited and costs vary among the pipelines In addition monthly refinery demand must be fully met Background You must decide how many barrels per month to pump along each pipeline At present no pipeline is operating between Well 1 and Pump C between Pump A and Refineries 3 and 4 and between Pump C and Refinery 1 The decision on how much material to send along a given pipeline is governed by the monthly cost per unit on that pipeline and by the necessity of satisfying refinery demand without exceeding monthly well supply ECH 370 CHAPTER 7 Objective of Optimization The objective in this model is to minimize the Total Pumping Cost without exceeding either the monthly output capacity of the wells or the capacity of the pipelines while meeting demand at each refinery The Worksheet Open the PIPELINE sample file and let s have a look at it The PIPELINE Worksheet Before Optimization aas e g ENa Microsont ed TT ao File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ai o Eil Z3 MONTHLY PUMPING VOLUME Pumped From Inflow To Refinery No Well 1 Well 2 Outflow 1 2 3 4 Through Pump A 0 0 0 Pump B 0 0 0 0 0 0 0 0 0 0 0 Pump C 88 Demand 30 57 41 51 lt Not gt Notze Not gt Not gt PUMPING COSTS
402. ook at the sample file called SAMPLEWB The SAMPLEWB Worksheet Before Solving 7 dd GF YTS SAMPLEWeBaxtsx Microsoft Excel kala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o El Ss fe Stratified Sampling Plan Design Stratum 2 L Sample Size 1 00 Lower Bound gt Upper Bound lt lt Population 400000 300000 200000 100000 Cost 1 00 1 00 1 00 1 00 Weight 40 0 30 0 20 0 10 0 Stratum Variance Question 1 5 5 5 5 Question 2 1 2 4 8 Fixed Cost 1 00 Total Cost 5 00 Maximum Variance Question 1 7 4999 Not lt 0 043 Question2 1 799915 Not lt 0 014 4 gt gt SAMPLEWB 27 Hal il D 100 A Determine Adjustable Cells The adjustable cells are B5 E5 the Sample Sizes for each stratum B Define Best The best cell is the minimized cost of sampling in cell B16 The formula here adds a Fixed Cost a nominal 1 00 in this example to the sum of sample sizes times the cost per unit sampled C Specify Constraints There are four types of constraints in the model In B6 E6 a Lower Bound of 001 is placed on the sample sizes This ensures that optimizer errors caused by division by zero will not occur In B7 E7 the sample size is required to be no larger than the population from which it is taken In C18 and C19 the variances on the two measured features are bounded on the upper end so as to force reliable estimates The vari
403. optimal answers from the solver In this case we ve emulated the F function using two adjustable cells and one constraint For each of the scenarios we ve added an adjustable cell in columns G and H Then we use a constraint to force the adjustable cell in column G to be equal to the amount the scenario return is Over the target return or zero if the return is less than the target The adjustable cell in column H is likewise required to be equal to the amount the scenario return is Under the target return or zero if the return is greater than the target The constraints in cells 14 115 force the difference between the adjustable cells G4 H15 to equal the difference between the return for this scenario F4 F15 and the Target Return C19 SAMPLE MODELS 301 For example for scenario 1 the constraint in cell 14 reads VWB G4 H4 F4 C 18 If Target Return C18 is 115 and the scenario return F4 is 120 the constraint forces G4 H4 to be equal to 5 As adjustable cells G4 and H4 are implicitly nonnegative Since the objective is to minimize a function of these adjustable cells they re forced to the smallest values that satisfy all constraints Thus G4 will be forced to 5 and H4 will be forced to 0 Similarly if the scenario return F4 is 110 then the constraint forces G4 H4 to return 5 G4 is forced to 0 and H4 to 5 If you experiment with the asset allocations in cells G4 H15 you can confirm that the forcing constr
404. or by decreasing the Feasibility Tolerance in the General Options dialog or by unchecking the Scale option in the Linear Option dialog box Suggestions What sBest calculates the amount by which all constraints are violated after the solver returns a solution In general this value will be quite small when a feasible or optimal solution is returned In some cases the total violations or infeasibilities may be found to be excessive When the total infeasibilities exceeds 0 01 What sBest will display this error Under these conditions you should check the solution carefully You may be able to resolve this error by decreasing the Feasibility Tolerance in the General Options dialog or by unchecking the Scale option in the Linear Option dialog box INTERRUPT Solver Interrupt If the Hold Interrupt button is pressed before completion of the solution process the user can hold the process and continue it some point later or stop the process via the following dialog box What sBest Solver Interrupt Click on Interrupt to halt the solver or Continue to resume solving Interrupt Continue By clicking OK the following warning message is displayed on the WB Status tab in the returned workbook Warning Message RAK KKK EE EE EE EE EE EE EE E EE EEN INTERRUPTED 8 KEE E EE EE EE EE EE EE EE EE EN WARNING Solver Interrupt Help Reference INTERRUPT The solver was interrupted before finding the final so
405. ork within a budget to acquire finite amounts of ore coke alloy metals and power Orders must be delivered on time and up to specifications or you risk losing business Such limits to doing business are referred to as constraints in the language of optimization modeling With What s Best you can use the operators gt greater than or equal to lt less than or equal to or equal to to express your particular constraints What sBest allows you to enter constraints using the four following methods 1 The Constraints dialog box 2 The three constraint toolbar buttons 3 Manually entering constraint functions as cell formulas 4 Using VBA to automatically enter constraint functions as cell formulas The first two methods only allow the entry of cell references The dialog box method offers an error checking interface for out of range and other errors The last two methods allow you the flexibility of entering complex expressions as well as cell references To learn how to use VBA to enter constraints see the section titled wb Constraint Let s consider the following constraints a resource limitation constraint Advertising expenditures must be no more than lt 10 000 and a performance requirement constraint Advertising exposures must be at least gt 100 Home Insert Page Layout Formulas Data Review V c6 X f WB B6 lt D6 Advertising Projection EXPENDITURE BUDGET d z lt 10 0
406. ormation on using Stochastic Solution values refer to section Options Stochastic Solver 446 CHAPTER 8 SPSTSC Stochastic WBSP_STSC Format Using the stochastic feature the user has to specify a table of scenario per stage The WBSP_STSC function is used to select this two column table where stage is in the first column and scenario on the second column If the argument to this function is not correctly specified the following error message will be displayed on the WB Status tab Error Message Stochastic WBSP_STSC Format Help Reference SPSTSC A WBSP_STSC cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSP_STSC cells where cells must refer to a two column range Also review the value of the arguments in the distribution function additional message Suggestions There is an incorrectly formatted Stochastic Scenario cell in the model Such cell must use the format WBSP_STSC cells where cells is a reference to a two column range Also review the value of the arguments in the distribution function some of them could be out of range For more information on using Stochastic Solution values refer to section Options Stochastic Solver SPVAR Stochastic WBSP_VAR Format Using the stochastic feature the user has to associate a stage information to a variable cell The WBSP_VAR function is used to specify the timing inform
407. ot gt Mon 0 Not gt Recommended FTEs Tue Not gt Scheduled FTEs Wed Not gt Staff FTEs Thu Not gt Pool FTEs Fri Not gt Sat Not gt Total Allocated FTE s ooooco Sun Mon Tue Wed Thu Fri Sat Not gt Not gt COSTS PER DAY Not gt Not gt Staff FTEs 120 Not gt Pool Days 160 Not gt Not gt TOTAL COSTS COOC EN _ 2 3 4 5 6 7 8 9 10 11 12 13 14 15 WI 11 18 19 20 21 22 HAH FIXEDI 23 al il Ready amp BA 10 362 CHAPTER 7 The second screen P1 AG20 consists of possible individual schedules R5 AE16 work patterns and the adjustable cells P5 P16 The FIXED1 Worksheet screen 2 Before Solving q EE lt ag ZX W 3 e Gr FIXED1 xlsx Microsoft Excel Home Insert Page layout Formulas Data Review View Developer Team What sBest V 2 o EN 8 Al X f P Q R s TtT u v w x Y Z AAlAB AC AD AE AF AG AH Number Schedule Available Schedule Patterns Total Assigned Number Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Days OO rJOom P GAbh A E 10 11 12 qgoooocoocoocoo OO wh et sch sch sch sch OO sch a EH CH h sch sch sch EH EH 4 sch sch sch OQO ad ad sch wh sch wh E sch E sch EN EH EH wh et wh sch sch sch Oe EN EH EH wh sch EN ER EH EH wh sch sch sch SPS We SE SSS 1 1 1 1 1 1 1 1 0 1 0 0 CO EH h ch E E E E ch a ch a E E wh ER wh wh sch wh sch wh Oo ooo sch sch sch sch
408. otal Profit A3 generated Once you arrive at a reasonable solution jot down its total profit SAMPLE MODELS 333 Now that you ve experimented on your own you re ready to solve the model The PRODMIX Worksheet After Optimization Zx a ie PRODMIXxlsx Microsoft Excel 77 bala File Home Insert Page layout Formulas Data Review View Developer Team What sBest YV e o El X G PRODUCT MIX p 1 r 2 L 3 r 4 r 5 r 6 6 Profit Unit 30 45 24 26 24 30 H 8 Quantity 120 0 220 160 20 50 D Produced Product Resource Requirements Plastic Rubber Glass Paint The best possible solution to this problem is a total profit of 15 020 Note how effectively What sBest used the available raw materials and how quickly this optimal solution was calculated Note also how many of each product What sBest tells you to produce and that the solution manufactures none of the product with the highest profit contribution This nonintuitive result which you d have difficulty finding through what if is a good indication of the power of What sBest 334 CHAPTER 7 The Building Block Method File name BLOCK XLSX TYPE LINEAR OPTIMIZATION Application Profile This example uses the full power of your spreadsheet software to develop larger applications using smaller ones as building blocks In this way comprehensive models can be created that can simulta neously cover many different aspec
409. ould linearize this model by adding a number of additional variables and constraints However the linearization option in What sBest can do this for you automatically For illustration we ran this model twice once with linearization off and once with it on using the two Linearization Degree settings of None and Maximum The adjustable cells were reset to 0 for each run Here are some comparative results Linearization Off On Adjustables 4 4 Constraints 0 61 Integers Bin 0 20 Variables 25 76 Nonlinears 20 0 Solution Time sec 1 lt l As you can see the model is considerably larger with linearization enabled because it has internally increased the number of variables from 25 to 76 integers from 0 to 20 and constraints from 0 to 61 The crucial observation however is that the number of nonlinears goes from 20 to 0 Thus the linearization completely removes all the nonlinearities from the model This allows What sBest to invoke its faster and more accurate linear solver which reduces total solution time down to less than 1 second In conclusion if your model has nonlinearities that can all be handled by the What sBest linearizer solution times can be reduced dramatically by engaging the linearization option For more information on setting the linearization options see Selecting Options For more information on the linearization process see Overview of Mathematical Modeling For a list of the functions that can
410. ower 0 1 30 lt 50 0 20 1E 30 Hard Drive 1 2 120 lt 120 250 60 40 WB Status xvz 4 OKE i Average 1 11111E 29 Count 9 Sum 1E 30 o 90 ADDITIONAL COMMANDS 119 The ranges for the Standard computer tower stock constraint are 60 upper and 40 lower That is the dual value will stay at 50 as the number in stock varies from 20 60 40 through 120 60 60 If the right hand side of the equation is increased to the limit of 120 and the model is re solved the profit increases to 36 000 33 000 50 60 as shown in the following EE E EE 2 WE XYZ COMPUTER CORPORATION PRODUCTION PLAN Product Standard Deluxe PROFIT Quantity to Produce 120 0 Profit per Unit 300 500 Product Component Requirements Components Quantity Required Total Number Standard Deluxe Usage In Stock 1 0 120 lt 0 1 0 lt 1 2 120 lt Standard Tower 19 E 21 22 23 24 44 gt PI 120 CHAPTER 3 Increasing the right hand side of this constraint beyond 120 exceeds the upper range for the original dual value of 50 and a dual value of 0 is now in effect Since the dual value is 0 changing cell G15 to 121 and re solving the model does not increase the profit beyond 36 000 as shown in the following xH s g0 geg XYZ xlsx Microsoft Excel uo el File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o Eil ss fe WBDUAL FS15 0
411. pear as in the following was GOST XYZ xlsx Microsoft Excel Sm x Home Insert Page Layout Formulas Data Review View Developer Team What sBest V e o El ES H15 X fe WBDUAL F 15 50 v A B C D E F G dk 1 XYZ COMPUTER CORPORATION PRODUCTION PLAN e 2 3 Product Standard Deluxe 4 PROFIT 5 Quantity to Produce 60 30 6 33 000 8 Profit per Unit 300 500 9 M 10 Product Component Requirements 11 12 Components Quantity Required Total Number 13 Standard Deluxe Usage In Stock 14 Standard Tower 1 0 60 lt 60 50 Deluxe Tower 0 1 30 lt 50 0 Hard Drive 1 2 120 lt 120 2501 E 18 19 20 21 v It 4b M WB Status XYZ 2I all ll Ready 73 Average 100 Count 3 Sum 300 Flog 100 The dual value of the constraint function WB E15 lt G15 is shown in cell H15 as 50 Note You must re solve your model to allow What sBest to update any new dual cells This means the value of the best cell would improve by 50 for each unit increase in the right hand side of the constraint equation In other words changing the cell G15 to 61 and re solving the model would return a new solution with a maximum profit of 33 050 assuming a valid range on the dual value of at least one This is also the maximum price at which you should be willing to purchase an additional Standard computer tower Note In What sBest we use the convention of having dual values on constraints return the rate of i
412. pecify Constraints The constraints in cells D5 D11 and D13 D19 require that the employees scheduled C5 C11 and C13 C19 for each day of the scheduling period be greater than or equal to staffing needs for that day E5 E11 and E13 E19 With the ABC s in place go ahead and solve the model The FIXED1 Worksheet screen 1 After Solving No Pool aggre e Te eae EE cia File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V o X H l STAFF SCHEDULING Fixed Shift Scheduled Recommended TOTAL FTEs AND POOL DAYS Sun 6 Mon 10 gt Tue 8 Wed 12 gt Thu 10 gt Fri Sat gt Recommended FTEs Scheduled FTEs Staff FTEs Pool FTEs o o o oO CO o On Total Allocated FTE s Sun Mon Tue gt Wed gt Thu gt Fri gt Sat gt COSTS PER DAY Staff FTEs 120 Pool Days 160 TOTAL COSTS 14 400 o o o oO CO o On 364 CHAPTER 7 The FIXED1 Worksheet screen 2 After Solving No Pool was e eoe FIXED1 xlsx Microsoft Excel kala Home Insert Page layout Formulas Data Review View Developer Team What sBest Y e o E ZS Al X fe x MNO B Q RI S T U V W X Y Z AAJAB AC AD AE AF AG AH 2 Number Schedule Available Schedule Patterns Total 3 Assigned Number Su Mo Tu We Th Fr Sa Su Mo Tu Weih Fr Sa Days 4 0 5 0 4 8 e 2 4 Oe EO Eo oe Oe 6 2 248 E DE OK 2 ee eee W Geh 7 4 72 O27 2 Oe PT ET a a se
413. per Team What sBest 9 Qe o El 3 Al M fe STANDARD MARKOWITZ PORTFOLIO PROBLEM v B Cc D E E G H l J K D MARKOWITZ PORTFOLIO PROBLEM Percentage Upper Covariance Matrix Invested Bound Asset 1 Asset 2 Asset 3 Asset 1 0 1 lt 75 0 3 0 1 0 0 5 Asset 2 0 2 lt 75 0 1 0 2 0 0 4 Asset 3 0 3 lt 75 0 0 5 0 4 1 0 Invested 0 6 Hot 100 0 Desired Portfolio Return Return 0 1 Not gt 15 0 Variance WE m gt Bon en GE A Determine Adjustable Cells The adjustable cells are B6 B8 the Percentages Invested in each of the three stocks B Define Best The best solution is the one that minimizes the risk of the entire portfolio In the Markowitz model a portfolio s variance is used as the measure of risk Using the variance gives a relatively greater penalty to outcomes that are far from the mean The variance of a portfolio is Zeimen where x is the percentage invested in Asset i CO for i j is the covariance between Assets i and j y for i j is the variance of Asset i 290 CHAPTER 7 This is computed by means of the following formula in cell B16 G6 B6 2 G7 B6 B7 G8 B6 B8 H H6 B7 B6 H7 B7 2 H8 B7 B8 16 B6 B8 17 B7 B8 18 B8 2 C Specify Constraints There are three types of constraints in the Markowitz model The first in C6 C8 requires that no percentage invested in any single stock exceed the Upper Bound for each stock of 75 D6 D8 For exam
414. ple C6 has WB B6 lt D6 The second in C15 is WB B15 gt D15 This requires that the combined return on the three Assets B15 be greater than or equal to the desired return in cell D15 15 The third in C10 is WB B10 D10 This requires the sum of the percentages invested in each stock B10 add up to 100 D10 Now let s solve the model After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning This warning can be shut off from the General Options dialog box Your solved model now appears as follows The MARKOWIT Model After Solving Gleis MARKOWT xis Microsoft Excel kalak File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o El Es G STANDARD MARKOWITZ PORTFOLIO PROBLEM Percentage Upper Covariance Matrix Invested Bound Asset 1 Asset 2 Asset 3 Asset1 18 3 75 0 3 0 1 0 0 5 Asset2 24 8 75 0 1 0 2 0 0 4 Asset3 56 9 75 0 0 5 0 4 1 0 Wi 2 3 4 5 6 7 8 a 10 Invested 100 0 100 0 1 Desired Portfolio Return Return 15 0 gt 15 0 Variance 042 MARKOWIT 23 al eo 100 COU SAMPLE MODELS 291 What sbeetl returns a minimized variance of 0 42 An interesting exercise is to solve this model for different levels of Desired Return in cell D15 recording the portfolio variance at each step A graph of the resulting data illustrating the tradeoff bet
415. plication Profile In Staff Scheduling problems the goal is to meet specified manpower requirements at minimum cost In general the schedule must meet certain conditions such as those imposed by regulations or union contracts including minimum shift length number of work breaks or maximum overtime hours These models have applications in the scheduling of airline flight crews hospital and office staffs and restaurant personnel to name just a few The Problem in Words You are running a business with daily staff needs on varying work loads each day of the week Background The daily staff needs range from 110 to 190 people as shown below Staff Scheduling Needs by Day of Week 150 100 50 Tue Wed Tu Fi ge a Sun In addition there s a labor requirement Employees must work a five consecutive day workweek followed by two days off Thus the allowable shifts are Monday through Friday Tuesday through Saturday Wednesday through Sunday etc Each employee earns 200 per week Objective of Optimization The objective is to cover staff needs with five day shifts at minimum weekly payroll cost 350 CHAPTER 7 The Worksheet Let s look at the STAFF worksheet included in the sample files Look it over for a minute and examine its layout and formulas to see how it has been designed The STAFF Worksheet Before Optimization x No VS ile I STAFF xtsx Microsoft Excel T LS a Home Insert Page Layout Formul
416. port to give you the error or warning message This message describes the problem the solver encountered and offers suggestions for correcting it The user may change the error and warning situations under which the status report is automatically opened at the bottom of the General Options dialog box ABCs 37 The status report generated by solving the completed sample model XYZ_XLS is shown below H o c a D WW XYZ xlsx Excel D ox HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys Al v fx What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w A B Cc D E 1 What sBest i3 0 d 0 Sep 30 2014 Lib 9 0 1889 103 64 bit Status Re 2 3 DATE GENERATED Oct 14 2014 09 27 AM 4 5 6 MODEL INFORMATION 7 8 CLASSIFICATION DATA Current Capacity Limits Bi es 10 Total Cells 20 11 Numerics 1 12 Adjustables 2 Unlimited 13 Continuous 2 14 Free 0 15 Integers Binaries 070 Unlimited 16 Constants 1 17 Formulas 4 18 Strings a 19 Constraints 3 Unlimited 2N Honlinaarse n Inlimitad WB Status WB Solution XYZ Ka al The status report is organized as follows First final values for the fields appearing in the solver status window are presented At its conclusion the status report appends critically important information such as the solution status The fields in the report and the significance of the returned values are as follows Classificatio
417. pound capacity However the items currently scheduled for shipment will exceed the capacity of the truck so you have to make a yes no decision as to whether each item gets shipped Each item has an associated dollar value and weight as shown below Dollar Value and Weight for Each Item Item Value Weight 1 22 500 7 500 Ibs 2 24 000 7 500 Ibs 3 8 000 3 000 lbs 4 9 500 3 500 lbs 5 11 500 4 000 lbs 6 9 750 3 500 Ibs Objective of Optimization The objective of optimization is to maximize the total value of the items loaded onto the truck without exceeding the truck s weight capacity 380 CHAPTER 7 The Worksheet Let s look at the TRUCK sample file The six items scheduled for shipment A6 A11 along with their corresponding dollar Values B6 B11 and Weights C6 C11 appear in the worksheet TRUCK Worksheet Before Optimization by Conventional Method x Mo p nie MMR Microsoft fen geng Gialin File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o El ss TRUCK LOADING Maximum Proportion Proportion Value Weight Loaded Loaded 22 500 7500 lt 24 000 7500 lt 8 000 3000 lt 9 500 3500 lt 11 500 4000 lt 9 750 3500 lt Total Value Total Weight Maximum __ of Load of Load Load Weight 0 0 10000 d e E M 4 gt H TRUCK 27 al ill OG om G A Determine Adjustable Cells The adjustable cells are the Proportio
418. ppressed Instead the error number is delivered in this return argument Pass an integer to use any possible returned What sBest error number Useful in an embedded application of What sBest Sto_BadArgListArg Bad ArgList argument Sto_BadPlaceInCellArg Bad PlaceInCell argument Sto_ProtectedSheetRepError Bad ProtectedSheetRep argument Examples To set several reporting cells so to display the stochastic report the simplest syntax would be wbStochasticReport Sheet1 B 1 B 3 Sheet1 C 1 A1 0 wbStochasticStageScenario This routine can be used to set the stochastic stage scenario table seen in the Stochastic Support dialog box All arguments are required except for the error code For additional discussion of the options available through this routine see the section entitled Options Stochastic Solver Syntax wbStochasticStageScenario CellRangel Place_in_cell RangeChoice NoErrDialog CellRangel Yes CellRangel is a cell reference for indicating the range of the table Place_in_cell Yes Place_in_ cell is a cell reference to specify the cell in which to write the WBSP_STSC function 204 CHAPTER 4 RangeChoice RangeChoice is a string SET to enter the function or NONE to delete the selected cell NoErrDialog Any argument passed here causes all What sBest error dialog boxes from the wbStochasticFunction routine to be suppressed Instead the error number is delivered in this retur
419. protected must reside on one or more worksheets that are separate from the rest of the model To demonstrate how to conceal and protect a model from the user we will modify the Product Mix model First we rename the Prodmix sheet as Model Second we will create two new worksheets that have all the information that the user needs one called Jnputs and the other called Outputs When we are done the Model sheet will be entirely hidden and protected from the user It will contain data and formulas that are considered proprietary We now populate the Inputs and Outputs sheets as follows First we copy all of the data from A5 G6 on the Model sheet to the Inputs sheet We now set the Profit Unit for each of the products to unlocked cells on this Inputs sheet We can then protect the Inputs sheet with the Tools Protect Sheet command and enter a password Turning to the Outputs sheet we copy and change the Quantity to Produce for each of the products to formulas that reference the Model sheet We can then protect the Outputs sheet from the user so nothing can be changed First select the Quantity to Produce cells and choose Format Cells On the Protection tab select Hidden leave the cells Locked so that the user can not see the formulas in these cells Then choose Tools Protection Protect Sheet and enter a password On the Model sheet we change the Profit Unit for each of the products to formulas that reference the nputs sheet The l
420. prove performance you may wish to use options such as Tolerance and or Hurdle Known IP Such options can significantly decrease the solution time on some integer problems For details on these options see the section entitled Options Integer Solver Integers Special Ordered Set The Integers Special Ordered Set command allows you to support Special Ordered Sets SOS variables of type 1 2 and 3 and Cardinality sets of variable via the following dialog box Special Ordered Set Cardinality xs Special Ordered Set Cardinality Type 1 WBSOS1 WBCARD Type 2 WBSOS2 C Type 3 WBSOS3 Select any cells multiple selection holding ae Lx SAS List of selected cells select and change by Add or Remove Cancel Add Remove Place the function WBSOS1 in cell Special Ordered Set The properties of the three SOS types are via the WBSOSx function SOS Type Property WBSOS1 At most one variable belonging to an SOS1 set will be gt 0 46 CHAPTER 3 At most two variables in an SOS2 set can be gt 0 If two variables are nonzero then the variables will be adjacent to one another SOS2 sets are particularly useful for implementing piecewise linear functions in models Exactly one variable from a given SOS3 set will be equal to 1 All remaining variables will be equal to 0 The syntax for the WBSOSx declarations is as follows written in the selected cell of the spreadsh
421. r Messages amp Warnings is a list of messages that may be encountered in building and solving a model Most of these messages are returned in the WB Status report The Appendix section gives additional information on the installation process If you encounter an error message that is not discussed here please contact LINDO Systems FAQ Frequently Asked Questions Frequent Questions and General Operating Problems Content The solution returned from What sBest is not optimal i e there is a solution that yields a better value in the best cell and satisfies all constraints An Excel error appears claiming that a workbook cannot be opened under High Security Level An Excel error appears referring to multiple copies of WBA XLA WBA XLAM When I try to close Excel an error appears stating This workbook is currently referenced by another workbook and cannot be closed The What sBest menu does not load There are Excel error codes of REF in What sBest cells What are the system requirements to install What sBest How do I install What sBest add in on my computer Where are the What sBest add in files installed on my computer What can I do if I receive an error message Can I protect my workbook from viewing How large can my model be How do I fix the Error Opening File error message How do I fix the Error in Auto_add 5 Invalid procedure or call argument error message How do I fix the Er
422. r download If you currently have the most recent version then you will be returned to the main What sBest environment If a newer build of the software is available you will be presented with the following dialog box 140 CHAPTER 3 eh There is a new version available x A What sBest A checkmark next to the command in the WB menu indicates that the command is still enabled You will need to download the new version of the software from the Website at the address indicated You can disable this option by checking off the command item Upon completion of downloading you will be prompted to begin installation of the new update Close Excel and double click on the file to open the install wizard which guides you through the setup process to update What sBest For your convenience your license key will be automatically transferred to the new version during installation Keeping your software up to date helps ensure that you are using the most recent version of the software and that compatibility and operational problems are kept to a minimum ADDITIONAL COMMANDS 141 Language This feature allows the user to select the language of his choice without reinstalling the add in bala a SP Language English F English Chinese French services Japanese After selecting the language the user can revert to the previous setting because the language words will stay displayed in the native language Make sure th
423. r message Sub or Function not defined then What sBest needs to be set as an available reference To do this choose Tools References from the Visual Basic Editor and check WBA_XLA in the list Now you should be able to run the procedure without error The procedure BuildXYZ shown above is very simple It sets C5 D5 to be adjustable cells makes the Total Profit in G6 the cell to maximize and constrains Total Usage E15 E17 to be less than the number in stock G15 G17 When these steps have been performed the macro code solves the model and displays the results To make this example more readable the ranges passed to the What sBest procedures are text references Alternately the ranges could also have been passed as objects to allow the developer to work with row and column numbers instead of the text The above code presented with object references would look like this Make Quantities to Produce C5 D5 Adjustable wbAdjust Range Cells 5 3 Cells 5 4 Make Total Profit G6 the best cell to Maximize wbhBest Cells 6 7 Maximize Constrain Total Usage E15 E17 to be less than Number in Stock G15 G17 wbConstraint Range Cells 15 5 Cells 17 5 lt _ Range Cells 15 7 Cells 17 7 Range Cells 15 6 Cells 17 6 The two other procedures in the ABC e module MaxDeluxe and MaxDeluxe2 simply change the XYZ model slightly and solve it again The Dual module contains a couple of subroutines that demo
424. r value What sBest will replace value with the actual lower range value the next time you run the solver For more information on using range values refer to section Advanced Dual TROUBLESHOOTING 453 WBSEMICFORM Semi continuous Cell Format If requested What sBest can specify Semi continuous sets Range values tell you over what range a particular set is valid The WBSEMIC function is used to request Semi continuous ranges If the arguments to this function are not correctly specified the following error message will be displayed on the WB Status tab Error Message x P RPROR Semi continuous Cell Format Help Reference WBSEMICFORM A Semi continuous cell is incorrectly formatted Correct the formula and the validity of the arguments in the cell below The format should be WBSEMIC lower upper cells where min and max are constant numbers and cells must refer to adjustable cells cell address Suggestions There is an incorrectly formatted WBSEMIC function in the model A WBSEMIC function cell must use the format WBSEMIC lower upper cells where lower and upper are numbers and cells is a reference to the cells you want the semic continuous on The cell reference should be to an adjustable cell For more information on range values refer to section Jnteger Semi continuous 454 CHAPTER 8 WBSOSFORM Special Ordered Sets Cell Format If requested What sBest can specify
425. rSemic 172 whbIntegerSolverKBestReport 174 whbIntegerSos 173 WBLOFORM 452 WBLOGISTIC 209 WBLOGISTICDENS 210 WBLOGISTICINV 210 WBLOWER Formula 110 WBMULTINV 210 WBNORMSL 211 WBOMIT 175 WBPOSD 28 wbResetOptionsToDefault 176 WBSEMICFORM 453 wbSetFunctionSupport 176 wbSetGeneralOptions 177 wbSetGlobalOptions 181 wbSetIntegerOptions 183 wbSetIntegerPreSolverOptions 186 wbSetLinearOptions 189 wbSetNonlinearOptions 190 wbSetStochasticOptions 193 wbSetStochasticSupport 195 wbSetStringSupport 195 whbSolve 196 WBSOSFORM 454 WBSP_MEAN 101 WbStochasticChanceConstrained 198 WbStochasticFunction 200 201 INDEX 475 wbStochasticReport 202 wbStochasticStageScenario 203 WBTRIAINYV 211 WBUNIFINV 212 wbUpdateLinks 204 WBUPFORM 454 WBUPPER Formula 110 WBxxx 41 WEIBULL 205 What If projections 11 18 Working while Solving 19 Worst Bound 67 78 X XYZ production problem adjustable cell ranges 12 after optimization 18 best cell 13 what s best if 18 XYZ XLS 10 XYZVBA XLSM 147
426. raint contains no slack then What sBest will return an equal sign before the indicator Oe lt If an indicator is not satisfied at all What sBest will return a Not before the indicator i e Not Slack mode displays the slack value of each constraint The slack value of a constraint tells you how close you are to satisfying the constraint A positive slack is the amount by which the constraint is overly satisfied A zero slack value means the constraint is exactly satisfied A negative slack is the amount by which the constraint is violated Computing the slack of a constraint involves simply subtracting one side of the constraint from the other side The default setting is indicator mode Auto Select Free Int Omit Ranges Check this option if you want the Free Integer or Omit ranges selected as you scroll through any list of What sBest defined named range names these range names begin with WB With this option checked on the range corresponding to a particular name is selected when you click on that name on the list This enables you to easily identify the range corresponding to a particular name The default setting is on Minimize Excele on Solve Check this option if you would like Excel to be minimized while the What sBest solver is running The default setting is off Number of Threads This feature will tell the What sBest solver to run on multiple threads so to allocate calculation tasks on dif
427. re f x b however the feasible region to the relaxation f x lt b or f x gt b is convex ABCs 33 Solve Once the ABC s Adjustable Best and Constraint cells have been specified you are ready to solve your model Choosing the Solve command prompts the What sBest solver to begin examining and solving your model During the time that the solver is computing it displays the Solver Status window which appears as shown below Classification Statistic et LINDO Systems Inc S Copyright 2014 64 bit Category Current Maximum What sBest 13 0 0 2 Oct 24 2014 Numerics i Lib 9 0 1905 120 Extended License Adiustables M Solver Status Integers Bin Model Type ig Formulas State Tries Constraints Nonlinears peste Coefficients Objective GE Obj Direction Extended Solver Activity Extracting Data Solver Type ji Reading File Best Obj SEN Obj Bound p Elapsed Runtime Steps SCH 00 00 01 Active SS Hold Irtemupt Help The solver status window remains present for the duration of the solution process and is updated periodically Once the solver completes its run it returns to the workbook to install a new solution and inserts a new worksheet entitled WB Status This new worksheet is referred to as the status report The status report is an easily
428. re should be exercised in applying omit ranges Please refer to the section entitled Usage Guidelines for Omit OMIT Names in Workbook and Refers to What sBest uses range names to specify the cell range to be omitted The target cell range is indicated in the Refers to box What sBest automatically fills the Refers to box with the range of the currently selected cells If this is not the range of cells you want omitted you can type the correct range in or select the button on the right edge of the text box to bring up a cursor for cell selection Next enter any word of your choice in the OMIT Names in Workbook box and click on the Add button The name you entered should then appear in the box below with a WBOMIT prefix If you decide later you would like to remove the omit restriction simply go to the Omit dialog box select the name of the omit range to remove from the list of names and click on the Delete button ADDITIONAL COMMANDS 125 Usage Guidelines for Omit What To Omit You may use the Advanced Omit command to remove parts of your workbook from What sBest s consideration thereby decreasing the time to reach a solution If you can identify cells with a numeric value or equations that are extraneous to the problem being solved then you can place them in an omit range For example some cells in the spreadsheet may be used for evaluation and reporting and are not used in finding the solution If these cells contain unsuppo
429. reformulation may not be possible If your model contains inherently nonlinear expressions you may choose to turn off this nonlinearity warning by clearing the Nonlinearity Present checkbox on the General Options dialog box NOADJ No Adjustable Cells Adjustable cells represent activities that are under the solver s direct control In other words these cells have been identified as ones that are allowed to be changed by the solver during the optimization process If there are no adjustable cells in the model the following error message is displayed on the WB Status tab Error Message No Adjustable Cells Help Reference NOADJ No cells have been specified as adjustable You must use the Adjustable command to specify the cells you want What sBest to adjust to find the solution Adjustable cells must contain numbers Adjustable cells that are blank or contain formulas or text will be ignored by the solver Suggestions You will need to add at least one adjustable cell to the model See section The ABC s Three Steps to What sBest for information on how to mark cells as being adjustable Adjustable cells are easy to find in that they are displayed in a blue font and have the Adjustable style applied to them When identifying your adjustable cells be sure to place a numeric value any will do in each adjustable cell If an adjustable cell does not contain a numeric value What sBest will not attempt to change its value TROUB
430. rices of appropriate dimensions i 0 m 1 bi and ci are vectors of constants di are constants x x0 x2 xn 1 is an n vector of decision variables 2 is one of the relational operators lt or gt Without the integrality restrictions SOCPs are nonlinear convex problems that include linear and convex quadratically constrained quadratic programs as special cases Several decision problems in engineering design and control can be formulated as SOCP What sBest solves this class of problems using the so called conic optimizer which uses an interior point algorithm To solve a convex problem using What sBest it may be advantageous to cast the problem e g a QCQP as a SOCP and use the conic optimizer To motivate the second order cone problems and common forms of quadratic cones consider the following two constraints x2 y zM lt 0 z gt 0 Geometrically the feasible region defined by these two constraints is an ice cream cone with the point of the cone at 0 0 0 The feasible region for the constraint x2 y2 z 2 lt 0 by itself is not convex The feasible region consists of two ice cream cones one right side up the other upside down and with their pointy ends touching The constraint z gt 0 eliminates the upside down cone and leaves the quadratic cone illustrated in Figure 1 Second order cone problems are essentially a generalization of linear models defined over polyhedral cones to ones defined
431. rincipal Thus in the current year your client will receive an interest payment of 1 00 or 10 units 10 rate of interest as calculated in cell 110 E10 D10 100 Next year and the year after he will continue to receive interest payments of 1 00 J10 and K10 In three years when the bond matures he will receive another interest payment of 1 00 and additionally a repayment of the principal of 10 units for a total of 11 00 as calculated in cell L10 E10 1 D10 100 282 CHAPTER7 You re now ready to solve the model and find the best possible solution to this problem el eee The BONDS Worksheet Part 1 After Optimization xlsx Microsoft Exc B een File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ai o X Amount Covered Le Cash Flow Need WB Status 1 2 Year 0 17 00 gt 17 00 r 0 996 0 997 0 923 0 987 0 993 1 061 0 883 1 102 0 889 Year 1 62 00 gt 62 00 a 10 5 45 0 10 5 0 0 10 75 10 7 11 2 0 0 11 8 45 6 12 0 0 10 0 0 12 6 0 0 0 00 10 2 56 3 50 02 TOTAL COST FIN Year 2 Year 3 Year 4 23 00 56 74 62 00 gt r gt F gt 23 00 35 00 62 00 SAMPLE MODELS 283 What sBest returns a total cost of 150 04 million with only one cash surplus in Year 3 of 21 74 million The Income Stream for each bond also appears in its optimized form The BONDS Worksheet Par
432. rio by scenario report of the wealth and the allocation to Stocks and Bonds each period by placing the expression WBSP_REP F9 G9 H9 Wealth1 G10 H10 Wealth2 G11 H11 D12 D14 D15 D16 into cell J25 Similarly the cell J26 contains the function for the histogram over 10 bins as WBSP_HIST 10 D12 240 CHAPTER 6 The SP_ INVESTMENTCOLLEGE Worksheet After Optimization H 6 amp SPLINVESTMENTCOLLEGE xlsx Excel 2 B a x HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys v Al X fe Investment Planning for Going to College After v A B c D E F G H J fa 1 investm nt Planning for Going to College After 3 Periods C 2 Two investment options each stage Stocks and Bonds Ref Birge amp Louveaux 3 80 Goal for wealth at beginning of period 4 4 4 Penalty unit for wealth under goal Step 2 Time stage specificatio 5 4 Utility of wealth unit over goal Random variables 6 Step 1 Core model 7 Growth factor Beginning Total Investin 8 Stage Stocks Bonds Wealth invested Stocks Bonds 9 0 D 55 0000 41 4793 13 5207 10 1 1 25 1 14 67 26272 67 2627 65 0946 2 1681 11 2 1 06 1 127 71 428577 71 4286 0 0000 71 4286 Step 3 Distribution specificatio 12 3 1 25 1 147 81 42857 13 14 Under goal 0 15 Over qoal 1 428571 gt 0 16 Net utility 1 428571 To be maximized 17 18 Step 4 Sampling specifications 19 20 21 22 23 v WB Status WB _S
433. rk patterns selected in stage 1 The Worksheet This model is also in 2 screens of the worksheet FIXED2 Screen 1 contains space for up to 12 individual employee names B5 B16 the employee seniority performance index D5 D16 and space for work pattern preferences F5 Q16 Screen 2 contains the adjustable cells employee names and their assignments and a preference subtotal for each employee You must now copy the optimal work patterns selected information from cells P5 P16 of the Stage 1 model after optimization and enter into cells U4 AF4 For this example we ve used the optimal scheduling generated without using Pool FTE s 366 CHAPTER 7 After the data from the first stage is entered the model looks like this The FIXED2 Worksheet screen 2 Before Optimization X a 3 e g uy FIXED2 xlsx Microsoft Excel elle Home Insert Page Layout Formulas Data Review View Developer Team What sBest e o gH X Al PoEGu RS i UMW AV Z AA AB AC AD AE AF AG AH AS E 2 Schedule Staffed LLOYD DIANE TOM JOANNE DAN JIM SUSAN JOY JOHN MPLOYEE ASSIGNMENTS TO SCHEDULES 10 ab gt N 12 Single Pref 0 Assign Sub lt lt lt lt lt lt lt lt lt lt lt oooooooocoecoecoeoeco m 2 0 0 0 0 0 0 0 0 0 0 0 0 0 KK E eooooocoocoocoocoooCOoON amp KG o a KEE KG 1 0 0 0 0 0 0 0 0 0 0 0 0 0 oooocoocccecoce oooocococococococea Toovo
434. rksheet model and find the best answer to your problem 21 22 CHAPTER 2 Adjustable The dialog box posted by the Adjustable command appears as follows l Adjustable r This command allows you to set properties of selected cells in your workbook Specifically it is used to identify to What sBest the cells that may be adjusted by the solver in it s search for a solution that optimizes the objective cell while satisfying all constraints Enter the range of cells whose properties you wish to set in the Refers To field the current selection of cells is already entered Next select the property you wish to apply to the cells from the drop down list at the top of the dialog box You have the following options 1 Make Adjustable 2 Remove Adjustable 3 Make Adjustable amp Free or Remove Free See below for more detail on these options Clicking OK will apply the change in properties Make Adjustable Select Make Adjustable to specify the range indicated in the Refers To text box as adjustable cells Before What sBest can solve a problem it must know what cells it can change in its search for the optimal solution These are the adjustable cells By default What s Best assumes the adjustable cells can be set to any non negative value Adjustable cells also called decision variables usually represent quantities or activities over which you have direct control Traditionally mathematicians refer to them as
435. robability functions e WBERLANG BO Erlang s loss probability for a service system with X servers and an arriving load of A no queue allowed e WBERLANG CO Erlang s busy probability for a service system with X servers and an arriving load of A with infinite queue allowed PREFACE xv UI Additional Functionalities e Redesign of a splash window informing the user of any remnant of other spreadsheet modeling interface on the same model so asking to integrate or remove such hidden names e Redesign of the Locate feature to look for any Adjustable Best Constraint Violated Dual WBCALC WBOMIT names in the workbook e Add a feature to generate a K Best report via a WB _KBest tab e Correction of compatibilities when the user develops its own macro that calls the What sBest add in and invokes other workbooks e Adjust error and warning messages when using solvers and debuggers clarifying relevance of non default options e Correction to support models being designed on non English version of Excel with mixing languages e New set of arguments for the VBA functions wbIntegerSolverKBestReport wbSetIntegerOptions wbSetNonlinearOptions with adjusted error codes e Correction in the order of the WBTRIAINV function arguments Other Valuable Features UI Convert Model Format The solver will assist you to convert a model made via competing spreadsheet modeling interfaces to a What sBest format It will extract
436. ror in returning solution in cell error message When using Function Support the system seems to hang with the message Server Busy What Excel file format should be used What 32 bit or 64 bit format should be installed Error in Managing Temporary Files E E E E E E E E eff o o 399 400 CHAPTER 8 The solution returned from What sBest is not optimal i e there is a solution that yields a better value in the best cell and satisfies all constraints Problem The model may be incorrectly formulated or with a nonlinear model the returned solution may be a local optimum rather than a global optimum Suggestions The following actions may help you in checking your formulation and or improving the solution returned by What sBest Use the Warnings feature to enable all warning messages set via Options General and re solve the model Check the returned status report for any indication of a problem A warning you consider trivial may be a sign of a more serious underlying problem Look at all of the constraints in the model to ensure that each was formulated properly all cell references are correct and their signs lt gt and are correct Ifyou are using the Omit feature carefully check the contents of each omitted range For information on the Omit feature see the section entitled Advanced Omit e Ifyou know ofa better solution than the one returned by What sBest inpu
437. rted spreadsheet functions placing them in an omit range will eliminate the error message caused by the equations If they contain equations that depend upon adjustable cells placing them in an omit range can shorten the time required for solving What Not To Omit What sBest will ignore the values and equations of every cell within an omit range Therefore it is very important that information pertinent to the problem is not included in an omit range For example you should be especially careful not to include Adjustable cells Any adjustable cell within an omit range will not be adjusted during the solution process Constraint cells Any constraint cells included in an omit range will be ignored during the solution process Cell Precedent to Equations Outside Omit Range An equation outside of any omit range that references a cell within an omit range will cause the solution to be aborted with an error message and the unsolved model will be returned 126 CHAPTER 3 Advanced Function Support This feature allows you to build models using not only Microsoft Excel built in functions but also user defined functions The user defined functions can be VBA macros add in file XLA macros calling a user add in file XLA XLAM or a library file XLL This feature is useful if the user has to develop his own function and wants these functions to be integrated in the optimization model The function support and a
438. rue 2 2 To set one or more options named arguments should be used wobSetLinearOptions Reduction True wbSetNonlinearOptions This routine is used to set the What sBest nonlinear solver options seen in the Nonlinear Solver Options dialog box All arguments are optional For additional discussion of the options available through this routine see the section entitled Options Nonlinear Solver Syntax wbSetNonlinearOptions StratCrashInitial StratUseLINDOCrash StratSLPDirection StratSLPSolver StratQuadraticRecognition StratPresolve StratSelectiveConstraint StratSteepestEdge StartingPoint OptimalityTolerance ItLimitSlowProg Derivatives Argument Required Default Description StratCrashInitial No 0 False StratCrashInitial is a True False flag indicating whether or not to use this strategy StratUseLINDOCrash No 0 False StratUseLINDOCrash is a True False flag indicating whether or not to use this strategy StratSLPDirection No 1 True StratSLPDirection is a True False flag indicating whether or not to use this strategy StratSLPSolver No 0 False StratSLPSolver is a True False flag indicating whether or not to use this strategy StratQuadraticRecognition No 1 True StratQuadraticRecognition is a True False flag indicating whether or not to use this strategy StratPresolve No 1 True StratPresolve is a True False flag indicating whether or no
439. rview To get up and running quickly first close all programs and simply run setup exe from the Windows desktop or from the CD and follow the prompts in the dialog boxes that follow The setup program offers Default and Specified installation The Default installation option analyzes your system for the critical information required to successfully install What sBest When you select Default as the installation type in the initial dialog box the add in file is copied into a directory entitled Library within the main Excel directory The Specified installation option is available for situations that require more information from the user and for users who prefer controlling the details of installation See the section entitled nstallation for more information Default installation is recommended for most environments However we recommend you select Specified installation under the following situations You have more than one copy release of Excel installed on your system Excel is installed on a network server rather than a local drive Your system runs on a non English version of Windows If you are updating from an earlier release the location that you specify for the program files may affect how your existing models are interpreted Carefully read the information displayed during installation as well as the Location of the Add In Files and Update Links section As the last step in installing What sBest Excel will op
440. s General Global Solver Functions currently supported are 1 Standard smooth functions x y x y x y log x exp x sqrt x sin x cos x 2 Continuous non smooth abs x max x y min x y 3 Smooth not quite continuous x y xy tan x floor x 4 Logical and relational operators if x y z gt lt AND OR NOT 5 Probability distributions psn z Normal Distribution psl z Normal Linear Loss 208 CHAPTER 5 Statistical Functions What sBest supplies six built in statistical functions These functions can be used within your What sBest models as if they were native supported functions in your spreadsheet e g SUM SUMPRODUCT ABS etc You should precede the spreadsheet function name with For example enter the inverse triangular cumulative distribution distribution as WBTRIAINV 1 3 2 0 7 1 Erlang s Loss of Probability WBERLANG_B This is Erlang s loss probability for a service system with X servers and an arriving load of A no queue allowed The result of WBERLANG B A X can be interpreted as either the fraction of time all servers are busy or the fraction of customers lost due to all servers being busy when they arrive It is extended to non integer values of X by linear interpolation The arriving load A is the expected number of customers arriving per unit of time multiplied by the expected time to process one customer WBERLANG_B Load Num_Servers Load mus
441. s The user may choose alternate features e Uncheck the Global Solver to run the Nonlinear solver Instead of a global solution the solver may find a local optima Uncheck the Function Support Unsupported functions will be read as a constant numeric cell without any further processing Define a WBCALCxxx or WBOMITxxx range depending if the value of the cell should be part of the model to solve SOLVERR Solver Error Mathematical programming problems are inherently difficult to solve and as a result the What sBest solver may encounter an error from which it is unable to recover This should not be a common occurrence but should the solver encounter such an error What sBest will display the following error message on the WB Status tab Error Message Solver Error Help Reference SOLVERR The solver encountered an error from which it was unable to recover A brief description of the error follows error description Suggestions Solver errors should be an uncommon occurrence and you may need to contact LINDO Systems to resolve the error Short of that here are some suggestions Ifthe error appears to be numerical in nature and your model is nonlinear you may want to try restarting from a different point This will tend to force the solver to take a different path to the solution and hopefully avoid the error condition Rescale the model so that the ratio of largest to smallest coefficients is reduced
442. s and that production capacity at each of the five potential plants is not exceeded SAMPLE MODELS 347 First since demand in B16 G16 of the Amount Shipped worksheet must be met the constraints in B15 G15 of the same worksheet require the sum of amount shipped to each demand city Atlanta Boston etc to be greater than or equal to the demand for that city The second constraint is that the amount shipped from each Supply City Baltimore Cheyenne etc must not exceed its supply capacity To enforce this constraint the constraints in H9 H13 of the Amount Shipped worksheet require that the sum of materials shipped from each Supply City is less than or equal to the Monthly Supply Capacity for that city 19 113 of the Amount Shipped worksheet Let s look at the formula in H9 of the Amount Shipped worksheet WB SUM B9 G9 lt 19 Shipping Costs 19 The total amount shipped from Baltimore SUM B9 G9 can be no more than 19 Shipping Costs I9 Baltimore s capacity Since Shipping Costs I9 is either 1 or 0 depending on whether or not a plant is open in Baltimore its use in the formula returns a nonzero value only if the plant is opened Now let s solve the model The Shipping Costs Worksheet After Optimization DIN s g0 E ANT OCs Microsoft Excel bala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 2 o El X F PLANT LOCATION MODEL Shipping Costs Per Ton Mont
443. s function takes in two parameters i the set of possible values of the random variable set vertically ii the cell address of the random variable Step 4 scenario information Specify the scenario information by using the function WBSP_STSC This function requires a two column table as an argument 1 Column 1 for the number of stages in ascending order 2 Column 2 for the respective number of scenarios In this problem the number of stages is 1 and the number of scenarios is 4 Step 5 reporting cells histogram Use the function WBSP_REP and eventually the WBSP_HIST to specify the cells that you wish to report This Reporting function takes in one parameter that is the address of the cell that we wish to report in the final solution The Histogram function will need the number of bins to display the appropriate table which can be calculated automatically Here we are reporting the area allocated to each crop and the yields for the various crops and the histogram for the objective cell Scenario Tree The Scenario Tree illustrates the concept of modeling under uncertainty e In Stage 0 the allocated area has to be decided for each crop to grow In Stage 1 the crop yield is revealed depending on the weather and as a recourse decision the e quantity to produce sell and purchase have to be decided e The objective is to maximize the total expected profit at the end of planning horizon Stage 1 SAMPLE MODELS _ 387
444. s makes possible for other sheets to keep their cells reference from this report for displaying a specific data 100 CHAPTER 3 Create Histogram Using the Function WBSP_HIST The general format is WBSP_HIST number_of_bins cells_to_be_reported e g WBSP_HIST 0 Sheet1 B 1 meaning the solver decides of the number of bins and cell B1 Sheet will appear in the Stochastic Histogram Report After solution a new ob WD Histogram will be created It will have four columns reporting the Bin Lows Bin Highs Mid Points and Bin Counts Select the checkbox to tell What sBest you would like a stochastic histogram created when the model is solved The next time you solve What sBest will generate a worksheet called WB _ Histogram containing a listing of the data and the histogram graph for the Bin Counts against the Mid Points values Click on the WB Histogram tab to see the stochastic histogram report Select button This button will open a new window To create the list of reporting cells specify the cell or cell range in the Select any cell to report field and the number of bins Once this is done pressing the Add button causes the selected cells to appear in the List of selected cells box You can decide to remove any selected cells by simply going to the list box select the cell reference to remove from the list of names and click on the Remove button The WBSP_HIST function will be placed in the current selection of the field
445. s the formula SUMPRODUCT D3 D10 F3 F10 objective cell to maximize Cell G12 is the capacity constraint WB F12 lt H12 Say our friend s ratings of the candidate picnic items is given in the data section above and the rating is different than yours 84 CHAPTER 3 If we solve the model as is thus solely maximizing our preferences we get the following solution The KNAPSACK_KBEST Worksheet After Solving H Q D mW Knapsack_KBest xlsx Excel 7 B D XxX HOME INSERT PAGELAYO FORMULAS DATA REVIEW VIEW DEVELOPER Team What sBest Lindo Sys D Al zi fe A B E D E F G H J 1 eem 2 Weight Rating Include 3 Brats 3 1 0 WBIKB_REP 4 Brownies 3 1 0 5 Beer 3 1 0 6 Ant Repel 7 1 0 7 Blanket 4 6 0 8 Frisbee 1 6 1 9 Salad 5 10 1 10 Watermelon 7 9 1 11 Knapsack Capacity 12 13 lt 15 13 Favorites in Knapsack ES 14 15 This model uses the K Best feature via the Integer Solver 16 17 18 IS WB Status WB Solution WB _KBest Knapsack Ka RI JI ADDITIONAL COMMANDS 85 As indicated by the adjustable cells a few of our favorite items are included in the optimal basket However we are wondering if there isn t another combination of items that our friend might like almost as much that includes most of our favorite items To investigate this question we set the Desired Number parameter of the K Best Solutions box to 5 via the Options Integ
446. s the length of time the solver has been running in hours minutes and seconds Note Variables or Optimizables is defined as the total number of adjustable cells constraint cells and cells containing formulas dependent on adjustable cells that are used by the objective function 36 CHAPTER 2 Getting the Best Results You can obtain the results of your call to solve the model by either examining the values displayed in the spreadsheet or by looking at the status report WB Status and or the solution report WB Solution In some cases such as when you have a pretty good estimate of what the objective should be you might feel satisfied after inspecting the best cell However even under such ideal conditions it is a good idea to confirm that your model solved successfully by examining the status report The status report provides detailed feedback about your model and the solution outcome If you wish a more detailed view of your model you may request the solution report as well The solution report provides a detailed analysis of the adjustable best and constraint cells showing the initial and final values as well as the locations of the cells The generation of the status report and solution report is controlled by settings at the bottom of the General Options dialog box If an error or warning situation was encountered that prevented the solver from running to completion then by default the solver opens up the status re
447. s will always be locally optimal if a solution is found It is a property of nonlinear optimization models that they may have several solutions that are locally optimal Such locally optimal solutions to nonlinear optimization models cannot be assumed to be 216 CHAPTER 6 globally optimal The following example illustrates this property and explains how you might explore the various local optima Consider the following model Cell B3 has been specified as an adjustable cell B4 has been specified to be minimized and contains the equation B3 SZM 3 1416 B3 and B5 contains the constraint B4 lt 6 The following graph shows a plot of B4 the expression to be minimized for values of B3 between 0 and 6 You can see that if you re searching for a minimum there are local optima at B3 values of 0 1 564 3 529 and 5 518 in the valleys If you use the global solver it will find a global optimum for this problem at B3 5 518 since that is the last valley before 6 Graph of B3 SIN 3 1416 B3 Imagine the graph as a series of hills You re searching in the dark for the minimum or lowest elevation If you start your search at B3 3 every step to the left takes you uphill and every step right takes you downhill Therefore you move to the right in your search for the lowest point You ll continue to move right as long as this direction leads to lower ground When you reach B3 3 529 you will notice a small flat area s
448. same directory LINDOWBHELP CHM Finally sample workbooks will be installed in C WB The Specified installation differs from the Default installation in that it lets you choose the specific location for the What sBest add in files The 64 bit files are identified with the 64 inside the file name What can I do if I receive an error message What sBest displays two kinds of error messages those generated by Excel and those generated by What sBest itself Errors from Excel eg Illegal Operation or Runtime Error typically result from operational problems in the loading and running of What sBest You should check that your model is pointing to the right What sBest add in file and that there is no loss of links To do this check the Tools Add ins list and Browse to find What sBest If you are developing macros with the Visual Basic Editor and using What sBest functions verify that the Tools References command is referring to the correct WBA XLA file In Excel 2007 go to the OfficeButton ExcelOptions Add Ins Go to browse to the correct location What sBest generated errors e g Error building the model are typically encountered when building and solving a model Check to see that all adjustable best and constraint cells are correctly specified Also if you have moved your model from one computer to another try running the General Options command and clicking the Update Links button You may
449. se it to find the media mix that will maximize the number of effective exposures subject to a set of constraints the ad budget minimum and maximum media availabilities minimum desired exposure rates etc A great advantage of What sBest is that new plans can be generated quickly to show the significance of changes made in problem specifications The Problem in Words You re a media buyer for an advertising agency You need to minimize the cost while satisfying minimum exposure needs Background There are six target markets Groups 1 through 6 and each requires a specified number of media exposures There are five different media sources the Times Mirror Tribune Herald and Post over which the advertising dollars are to be allocated Each of the media sources offers various combinations of exposures per dollar spent for each of the different target groups Objective of Optimization The objective is to determine how much of each of the media sources should be purchased to meet the exposure requirements at lowest cost SAMPLE MODELS 325 The Worksheet Let s open the MEDIA sample file and look at its structure and formulas The MEDIA Worksheet Before Solving DIN 2 e g rf MEDIA xlsx Microsoft Excel ell File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o El Ss f OPTIMAL MEDIA BUYING E E G H BDIA BUYING Exposure per Dollar by Market and Medium Thousands Target
450. seccueaeeeeeeeeetsnnaees 126 FUNCHON SUPPOR EE 126 Advanced Statistical Funchons cece KEEA EAEE KETERAK EAA E EERE AEAEE 127 AdvanGed Strimg SUPPOR moriar aaa deca EAE IAS 127 String SUPPOMt EE 127 Maximum String Length 128 Advanced Convert Model Format 0 ccccccceeeeeeeeeee sence ee enneeeeeeeeeeeeeeeeeteeeeeseeeene 128 Advanced Parameters sarosa aeaii eiaa a iei ariaa aei ENA 129 Ree LEE teal a 132 Help amp About What sBestl ecccccccceceeeceeenccececeeeeeeeceaeaeceeeeesaceaaaeeeeeeeeeegeeneaeeeeeeeeeeeeeenea 133 Toolbar Ee e 135 License Key Emmer geed edicts deeded 136 Registon asiaani aad added dE eee 138 Khecktlodatez geed itis ae eed lees ne Me ee a 139 LANGUAGE EE EEN 141 WHAT SBEST MACROS THE VBA INTERFACE cccccssseeceseseeeeeseeeeenseeneeseeseneees 143 Usage Guidelines for Macros in VBA ececeeceeeeeeeeeeeeeeeeeneeeeeeeeeeeeeseeeeeeeseneaeeesenaeeeteneaees 143 Introduction to the VBA Interface of What ebest 143 Object BONSE EE 143 Macros RECOrd Of aa deene E E 144 Calling Procedures fcc sircet deer O deeg deed e EA 144 Error messages you might encounter learning VBAL 145 Beyond VAN eege ciel deere atin its a el Minn en Eege AER 145 Embedding What sBest in a Visual Basic Visual Studio Droe 145 Concealing and Protecting a Model from the User 146 Tutorial on the VBA Merata ena Ea EEA A EEE 147 Building and Solving a Basic Model 147 Solving Multiple Problems
451. set of possible discrete values for the scenarios set vertically ii the cell address of the random parameter The random demand in cell B19 will take the values entered in the range 19 S22 with equal probabilities WBSP_DIST_DISCRETE_SV S 19 S 22 B19 Step 4 scenario information Specify the number of scenarios per stage by using the function WBSP_STSC This function requires a two column table as an argument 1 Column 1 for the number of stages in ascending order 2 Column 2 for the respective number of scenarios In this problem there are 5 stages with 2 scenarios each set in the range J28 K32 WBSP_STSC J28 K32 It happens the discrete table for the distribution has only 4 possible values so the random parameters will select 2 among the 4 outcomes with replacement The option Sampling on Continuous Only needs to be turned off to take advantage of the sampling feature Step 5 reporting cells Use the function WBSP_REP to specify the cells that should appear in the Stochastic report This function takes a series of arguments that are the address of the cells that should be reported in the final solution WBSP_REP C19 C23 D18 D23 W1th0 WIth Wi W1th3 W1th4 W1thS Here the stochastic report will display the outcomes of scenarios for all the random cells the price of stocks for any periods the decision to sell and the ending wealth to maximize Use the function WBSP_ HIST to generate a histogram of the Prese
452. set via a single cell reference or a number The default setting for Seed is 1031 Common Size per Stage This is the default number of scenarios to generate per stage Possible values are positive integers The logical states will behave as follow Sampling on Continuous Only Checked Function WBSP_STSC Use of Function Argument for Continuous and the Use of Function WBSP_STSCOQ Defined Table Size for Discrete Distributions Argument Defined The default setting for Common Sample Size is 2 Sampling on Continuous Distribution Only In case of a model with both distributions continuous and discrete this flag enables the sampling technique only on the continuous distribution leaving the discrete distribution with its own set of data Sampling can be applied with the spreadsheet function WBSP_STSC The default setting is on meaning sampling is applied on continuous distributions 108 CHAPTER 3 Use Simulation Format By checking this option the model will be processed for simulation Based on a stochastic model the user can set up the random parameters and their associated distributions at a stage 0 eventually any additional formulation and What sBest will calculate the values of the reporting cells There is no need of defining an adjustable constraint or objective cells This feature will be useful for knowing the behavior of some cells along the scenarios and to display their histograms The default
453. setting is False unchecked ADDITIONAL COMMANDS 109 Options Reset to Default This command resets all workbook options to their default values Such options can be seen in the Insert Name Define or Name Manager menu as WBxxx names This command does not restore options defined in the Advanced Parameter window to default values See the section entitled Options and Solvers for more information about workbook options Upon first use the Reset to Default command displays the following dialog box Reset to Default Warning ks Reset the options will remove the WBxxx names in the workbook These names belong to What sBest and were created via the Options dialog boxes Deleting hidden names will only remove names in the workbook that are not visible or listed via the Name Manager of Excel Deleting all names and options will actually remove any names from the workbook These names could have been defined by What sBest the user Excel or other applications saving names in this workbook file Removing these visible or invisible names will clean up the file and the user has to redefine the useful names 110 CHAPTER 3 Advanced Dual The dialog box posted by the Advanced Dual command appears as follows Dual exe For Cell Range Report on Type Report Information in B 1 ml Ge The Dual command allows for reporting of dual values for the chosen cells or range of cells If
454. sh flow BONDS XLSX Lockbox Location Locating postal lockboxes to minimize float while still serving all customers LOCKBOX XLSX Markowitz Portfolio Problem Selecting assets to meet a desired return at minimum variance MARKOWIT XLSX Portfolio with Transaction Costs Adjusting a portfolio of assets in such a way that desired return after broker s fees and other transaction costs is met with minimum variance PORTCOST XLSX 255 256 CHAPTER 7 Minimizing Downside Risk Purchasing and maintaining a portfolio of assets so as to minimize the risk of losing value DNRISK XLSX Portolio Scenario Model Demonstrating the differences among minimizing three different measures of risk PORTSCEN XLSX Forecasting Models Seasonal Sales Factoring Determining the effect of seasonal factors on historical sales to improve forecasting SEASON XLSX Exponential Smoothing Two models illustrating one technique for using historical data to predict future sales SIMXPO XLSX SMOOTH XLSX Linearization Option and Construction Cost Estimation Models Linearization Option and Construction Cost Estimation This model demonstrates the performance gains resulting from using the What sBest linearization option and illustrates a case of estimating construction costs LINEARZ XLSX Marketing Models Stratified Sampling Determining the least costly polling sample likely to give reliable results S
455. sheet then the CCP part The six steps are Step 1 Define a core or deterministic model as a regular deterministic What sBest model You can plug regular numbers in a random cell to check results Step 2 Specify staging information about the sequence of decisions and random events This information is stored directly on the spreadsheet using special What sBest functions These functions and formats are Decision variable and their stages are identified by WBSP_VAR stage cell_list where stage is 0 and Random variables and their stage are identified by WBSP_RAND stage cell_list where stage is 1 Step 3 Distribution information about random cells is stored in MATHEMATICAL MODELING 245 WBSP_DIST_distribution table cell_list where distribution specifies the distribution e g NORMAL Step 4 Sample size for the 1 stage is stored in WBSP_STSC table Step 5 Cells to be reported are listed in WBSP_REP cell_list or WBSP_HIST bins cell_list Step Chance Constrained Cells to be reported are listed in WBSP_CC _LT percent weight constraint cells for Less Than or WBSP_CC_GT percent weight constraint cells for Greater Than One function will define one set of Chance Constraint You may type these functions in directly or you may use the Options Stochastic Solver drop down menu in What sBest to guide you through the steps We illustrate the formulation of an SP CCP model in What sBe
456. sheet or via the set of dialog boxes Step 1 core model 1 Data and Formulas Specify the quantity required plantation cost selling price and cost price for all the four crops Also specify the total area of the farm Enter the formulas associated with the plantation and purchase cost and amount from selling 2 Adjustable Cells For each crop the adjustable cells correspond to the following a Area Allocated b Quantity Harvested c Quantity Purchased 3 Objective Function The objective function is the profit given by Profit Amount obtained from Selling the Excess Crop Planting Cost Purchase Cost 4 Constraint Cells a For each crop c the quantity of crop purchased plus the product of the yield and the area allocated to that crop is equal to the quantity sold and required i e Quantity c Harvested Purchased Quantity Sold Required where Quantity Harvested Area Allocated Random Yield per Acre b The sum of the areas allocated to all the crops should be less than or equal to the total area of the farm i e sum area c lt total area SAMPLE MODELS 385 5 Random Parameters Finally the Yield per Acre cells will be read as random parameters Step 2 stochastic information for stage Initial Decision Variables Specify the Area Allocated to each crop as an initial variable This is done by using the function WBSP_VAR This function requires two parameters i stag
457. so have the greater variability so if we are concerned about achieving our goal of 80 000 then Bonds might seem more attractive with their lower variability in return MATHEMATICAL MODELING 237 The SP_ INVESTMENTCOLLEGE Worksheet Before Optimization part 1 H 6 amp sz SPLINVESTMENTCOLLEGE xlsx Excel 2 Bi xXx HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys v Vd Al ka ee fe Investment Planning for Going to College After v A B c D LS SIS ER _ 1 J fa 4 investm nt Planning for Going to College After 3 Periods 2 Two investment options each stage Stocks and Bonds Ref Birge amp Louveaux 3 80 Goal for wealth at beginning of period 4 4 4 Penalty unit for wealth under goal Step 2 Time stage specificatio 5 4 Utility of wealth unit over goal Random variables 6 Step 1 Core model 7 Growth factor Beginning Total Investin 8 Stage Stocks Bonds Wealth invested Stocks Bonds 9 0 55 Not 0 0000 0 0000 0 0000 10 1 1 25 1 147 o 0 0000 0 0000 0 0000 11 2 1 25 1 147 or 0 0000 0 0000 0 0000 Step 3 Distribution specificatio 12 3 1 25 1 147 0 13 14 Under goal 0 15 Over qoal 80 Not 0 16 Net utility 0 To be maximized 17 18 Step 4 Sampling specifications 19 20 21 22 23 v Model 4 D 238 CHAPTER 6 The SP_INVESTMENTCOLLEGE Worksheet Before Optimization part 2 ld Di SPLINVESTMENTCOLLEGE xlsx Excel a amp D xX liam
458. ssinesnrassrenneainnentnnnnsnnnaddtnaneananneneannt 53 Minimize Excel On Solve cececcececceceeeeeeeceaceeceeeeeeececaaeaeeeeeeecesecaeeeeeeeeeseesenueeeeeeeeeees 53 Hide Status Window ON Golve ns nnnt tenn nn nnne e enn 54 BE le TEEN 54 BIER 54 Big Meter eelere ee cts ee ee ean eee ee aie 54 Status REPO EE 55 eieiei EEN 55 Beginningior e DEE 56 WV ARMIN GS eelere Be feat candies Ee 57 Update nger ee A acter a ean ceeded dal Saat Sevens has dates anda 57 Delete Reports dionn a dE eege TEE Edge 58 pions Enea SOW wx yes deed deed deed dE dee det 58 Scale TE EE 59 Model REGUCHON iczte m a EES at ree aan alee 59 SolveriMethod deed sate acta aed de Dee Ad ot cae aan eaves 59 PHENO ssc tdortitersate eth tcaad e a esc iba tagin a felt eeec startin a 59 Options JNonlinear Solve eneiniad aaa 61 Crash Initial Solution Use LINDO Crash 61 SEP Direction araen ain en a e E 62 e Be EE 62 Quadratic RECOGNITION 0 0 0 eee e teeter ee etne ee ee tees eet aeee a ea eraa 62 Eeselen ed Ee EE Eed ett 62 Selective Constraint Evaluation ccccccceeeceeceeceeeeeeeseccneaeceeeeeeesecsacaeeeeeeeeesensanaeeeeess 62 Steepest EE 63 Slarting Pointe EE 63 Optimality Tolerance EE 63 Iteration Limit for Slow Progress assssssssssessssesssnnessnnsstrnnestnnnestnnnnnnnnnntnnanntnnnaannnnaenannaaa 64 RV EE 64 Options Global Soe sanien a a r a A a A eae aa 65 Global SoN eege eech eva ih cesta eneen Sheen era ores
459. ssion as in the following Graph of F A1 gt 0 A12 A12 100 200 180 160 140 120 80 60 40 20 NMM st O O KwK DO MH 220 CHAPTER 6 In simplified terms What sBest searches along the plot of the expression to find a maximum or minimum point representing an optimal solution Breaks and sharp bends on the plots of non smooth functions pose challenges to the solver not posed by smooth continuous functions It is a good practice to avoid formulating your problem with non smooth functions Solution Outcomes The solution and analysis of the outcome of the solution process is presented in the status report worksheet The status report worksheet is inserted following the completion of the solution process unless you have disabled the status report regarding disabling reports see the Reports Location and Warnings box on the General Options dialog box posted by the Options General command The status report is opened by clicking the WB Status tab among your Excel worksheets Unless you have imposed a limit on the number of iterations in the solution search or have interrupted the solver by pressing the Hold Interrupt button on the What sBest solver status window the message provided in the field Solution Status in the status report should be one of those listed below Case 1 Optimization Models If a cell has been specified to be maximized or minimized there are several possible outcomes of an attempt to solve the mo
460. st toolbar also makes tool tips available To learn the function of a particular toolbar button just move the cursor over the button for a second and a statement of the button s function will appear FA at 2 Should you wish to remove the What sBest toolbar you would use View Toolbars Customize command select the What sBest toolbar and press the Delete button You would then have to reinstall What sBest in order to restore the toolbar In Excel versions 2007 2013 What sBest just shows an additional tab in the Ribbon Bar layout with an easier access to the dialog boxes and the shortcuts r mm mmm e DIE Ka o 0s Bookl Microsoft Excel alak Home Insert Page Layout Formulas Data Review View Developer Team What sBest a ei og SS O K Make Adjustable A JW Minimize lt Less Than or Integers 7 Locate GB License SP Language English H BS Remove Adjustable A Maximize gt Greater Than Options hHep Register Adjustable Best Constraints Solve Equal To Advanced 7 fD About amp Check Update Model Definition Settings Solvers Information Services 136 CHAPTER 3 License Key Entry The dialog box posted by the License command appears as follows If you have a What sBest R license key please paste Crt V or type it in below If you enter the key by typing please be sure to include all hyphens If you don t have a What sBest R license key you can press the Demo button to run
461. st with perhaps the simplest SP CCP model possible the Feeder Mix problem model SP_FEEDERMIXCCP XLSX This model has just 1 stage In stage 0 half stage we must decide how much X1 X4 At the beginning of stage 1 Protein is revealed At the end of stage 1 we minimize the Objective This model is an excerpt of the blending model HOGCHANC_XLSX explained in the Chance Constrained Blending example 246 CHAPTER 6 The SP_FEEDERMIXCCP Worksheet before Optimization H S e DO SP_FeederMixCCP xlsx Excel a D xX HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys Ol Al sei f Product Feed Mix Problem v Jl A B E D E F G H J K L 1 Product Feed Mix Problem with Chance Constraints 2 Van de Panne and Popp presented a CCP formulation of feed mixer problem Obj 29 89 3 The variables are defined at stage 0 the randoms at stage 1 gt 4 5 1 Core model 2 Stage info 6 X1 x2 x3 x4 Total 7 0 0 0 o7 0 0000 WBSP_VAR 8 OBJ 2455 26 75 39 40 5 9 FAT 23 5 6 11 1 13 0 Not gt 5 10 PROTEIN 12 11 9 41 8 52 1 0 Not gt 21 WBSP_RAND 11 UNITY 1 1 1 1 0 Not 1 12 13 3 Probability info 4 Sampling info 14 The protein coefficients are random Normal WBSP_STSC 15 Means 12 119 418 52 1 1 32 16 Std Dev 0 53 0 44 45 0 79 17 WBSP_DIST_NORMAL 18 WBSP_DIST_NORMAL 5 Reporting cells 19 WBSP_DIST_NORMAL WBSP_REP 20 WBSP_DIST_NOR
462. staff members and forces this sum to be greater than or equal to at least as great as the number of people required for that shift The model uses an equality constraint for each staff member to force the number of shifts assigned each week to equal the number he s expected to work The formula in cell L3 of the Constraints worksheet for example VB ASSIGNMENTS B3 SUM ASSIGNMENTS D3 J3 forces this equality for Reagan Assigning him to more than 5 shifts causes the constraint to return Not Finally the model must assure that after working one shift a staff member isn t assigned to either of the following two shifts and that each staff member is assigned to only one shift per day This is accomplished by summing the assignment variables 0 s and 1 s for each set of three consecutive shifts and forcing that total to be less than or equal to one If for instance a staff member were assigned to two shifts out of a consecutive block of three the constraint would be violated Examine the formula in D3 and D4 of the Constraints worksheet WB SUM ASSIGNMENTS D3 D5 lt 1 and WB ASSIGNMENTS D4 ASSIGNMENTS D5 ASSIGNMENTS E3 lt 1 which excludes Reagan from working more than one of the three Monday shifts or more than one of three shifts beginning with Monday Evening respectively SAMPLE MODELS 359 You re now ready to solve the problem Model Worksheet in ASSIGN After Optimization Kd gt O PS Age
463. stalled with Excel 64 bit on a 64 bit operating system Otherwise install the 32 bit version of What sBest The Installation topic in the Appendix section shows additional settings to verify in Excel for running an add in Error in Managing Temporary Files There is a topic named TEMPFILE for the Error Managing Temporary Files message in this section What sBest needs to create temporary files for building data listing and returning solutions or reports Such message implies a non access to the folder or its files network location without mapping a drive a file format XLSX without the Microsoft NET Framework library in the system a wrong 32 or 64 bit installation or missing user s privileges The user may just try a sample file in the C WB folder Being able to run a XLS file but not a a XLSX means your system is missing the NET Framework in which situation you can run a Windows Update to download it Also you can verify the access rights then moving the model file in this same C WB location This simple location will be accessed by What sBest In some situations you can map your network location via the Windows Explorer then open the file from there Finally another instance of Excel may still be running as a back task then your model file handler will still be on hold This eventually happens if you run a large file via a macro loop in VBA code 406 CHAPTER 8 Error Messages amp Warnings If
464. t IntPreSolvOpt_BadFlowCoverCutsArg Bad Flow Cover Cuts argument IntPreSolvOpt_BadGCDCutsArg Bad GCD Cuts argument IntPreSolvOpt_BadGomoryCutsArg Bad Gomory Cuts argument IntPreSolvOpt_BadGUBCutsArg Bad GUB Cuts argument IntPreSolvOpt_BadKnapsackCoverCutsArg Bad Knapsack Cover Cuts argument IntPreSolvOpt_BadLatticeCutsArg Bad Lattice Cuts argument IntPreSolvOpt_BadLiftingCutsArg Bad Lifting Cuts argument IntPreSolvOpt_BadPlantLocationCutsArg Bad Plant Location Cuts argument IntPreSolvOpt_BadObjIntegralityCutsArg Bad Objective Integrality Cuts argument IntPreSolvOpt_BadBasicCutsArg Bad Basic Cuts argument IntPreSolvOpt_BadCardinalityCutsArg Bad Cardinality Cuts argument IntPreSolvOpt_BadDisjunctiveCutsArg Bad Disjunctive Cuts argument MACROS THE VBA INTERFACE 189 Example If one wished to set all the options the following would work wbSetIntegerPreSolverOptions 2 1 6 20 3 False False True True False True True False False True True False True Tru To set individual options here setting the ProbingLevel to 4 named arguments should be used wbSetIntegerPreSolverOptions ProbingLevel 4 wbSetLinearOptions This routine is used to set the What sBest linear solver options which can be seen in the Linear Solver Options dialog box All arguments are optional For additional discuss
465. t gt Upper bound lt 4 gt SIMXPO 2 al Mm ISS wm A Determine Adjustable Cells The adjustable cells are the Predicted sales in C5 C11 and the Alpha smoothing term in C14 Note that Period 1 in cell C4 is fixed at 10 since there is no previous period on which to base a prediction B Define Best The best cell is the minimized Sum of Squared Errors differences between Sales and Predicted in cells E4 E11 in E13 C Specify Constraints The constraints in D5 D11 reproduce the basic model for exponential smoothing see preceding page for each Predicted period In C15 C16 the Alpha term is bounded by 001 and 999 310 CHAPTER 7 Now you are ready to solve the model After solving the WB Status worksheet will open in order to show you the Nonlinearity present warning This warning can be disabled from the General Options dialog box Your solved model now appears as follows The SIMXPO Worksheet After Solving maS e CS TIET age Microsoft Ec o File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o El s amp s Ba ac onential Smoothing Sales Predicted 10 10 000 14 10 000 12 12 601 19 12 210 14 16 626 21 14 918 19 18 874 26 18 956 Alpha Lower bound Upper bound M 4 WB Status SAMPLE MODELS 311 Following is another sample file called SMOOTH which uses the same principles to analyze a much larger set o
466. t see WBA XLA in the drop down list then you must check in the What sBest add in via the Excel menu s or Ribbon s Tools Add ins or re install the What sBest add in After you ve selected WBA_XLA in the Object Browser you should see WBUsers among the Classes listed This class is your primary source of What sBest procedures As you select this class the right window should display all of the Members procedures available to you from that class Macro Recorder Excel s Macro Recorder can be a very valuable tool for creating macros of tasks in Excel Unfortunately it generally does not work well in conjunction with Excel add ins such as What sBest The Macro Recorder of Excel 97 and later versions is unable to record the What sBest add in commands so we recommend you do not try to use it to generate VBA code You can use Excel s Object Browser described above to more quickly and accurately write your VBA code Calling Procedures Visual Basic for applications is quite liberal in the syntax it allows when calling procedures For the sake of simplicity the calling procedures used for illustration below will stick to one or two conventions depending upon whether or not named arguments are used For example to call the procedure to set cells D8 E10 as adjustable without named arguments would be wb Adjust D8 E10 The same procedure call with named arguments would be wbAdjust AdjRange D8 E10 Not
467. t 2 After Optimization Glas ENDS Microsoft Excel cs i Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 ei o Eil S amp S 44 82 0 00 9 90 0 00 45 30 0 00 0 00 0 00 50 02 Investment Bond Issue Year of Maturity 1 2 3 Year 0 4 7250 0 0000 1 1529 0 0000 5 3834 0 0000 0 0000 0 0000 5 7387 Year 1 49 7250 0 0000 1 1529 0 0000 5 3834 0 0000 0 0000 0 0000 5 7387 Income Stream Year 2 Year 3 Year 4 284 CHAPTER 7 Lockbox Location File name LOCKBOX XLSX TYPE LINEAR OPTIMIZATION The Problem in Words As a corporate cash manager or officer of a bank whose clients must deal with the problem of optimizing collections from customers located at large distances from your home office you must decide where to locate postal lockboxes so that customers deposits can be credited with a minimum of expense caused by mail delay or float time while minimizing operating costs associated with the locations In addition each customer must be assigned to exactly one location Background Your customers located in Seattle Los Angeles Houston Philadelphia and Miami whose deposits must be credited with a minimum of float time may be assigned to potential lockbox locations in New York Atlanta Cincinnati Denver or St Louis It may also be more cost efficient to assign them to the home office Objective of Optimization Each
468. t Excel am D Galnm Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 CA o ER f E F G PRODUCT MIX 5 Product 1 7 y 4 p 66 6 Profit Unit 30 45 24 26 24 30 T 8 Quantity 0 0 0 0 0 0 9 Produced 10 11 Product Resource Requirements Total Start 12 Usage Inv 13 14 Steel 800 15 Wood 1160 16 Plastic 1780 17 Rubber 1050 18 Glass 1360 19 Paint 1240 20 21 22 44 gt gt PRODMIX 2 Ready 73 A Determine Adjustable Cells The adjustable cells in this model B8 G8 contain the Quantity Produced for each product B Define Best The best solution is the one that results in the maximum Total Profit A3 Take a moment to examine the formula in this cell SUMPRODUCT B6 G6 B8 G8 That is interpreted as Profit Unit of Product 1 Quantity Produced of Product 1 Profit Unit of Product 2 Quantity Produced of Product 2 and so on You want to find a combination of values B8 G8 that will yield the highest Total Profit A3 Note The SUMPRODUCT method of expression eliminates the need for lengthy formulas while simplifying later addition of other products Inserting rows not appending within the ranges allows you to enlarge them without rewriting the Total Cost formula In writing small models you may find it easier to write such formulas without SUMPRODUCT In large models or ones you intend to enlarge it s probably best to use SUMPRODUCT 332 CHAPTER 7
469. t be a non negative real number Num_Servers must be a strictly positive integer 2 Erlang s Busy Probability WBERLANG_C This is Erlang s busy probability for a service system with X servers and an arriving load of A with infinite queue allowed The result of WBERLANG _C A X can be interpreted as either the fraction of time all servers are busy or the fraction of customers that must wait in the queue It is extended to non integer values of X by linear interpolation The arriving load A is the expected number of customers arriving per unit of time multiplied by the expected time to process one customer WBERLANG_C Load Num_Servers Load must be a non negative real number Num_Servers must be a strictly positive integer FUNCTIONS AND OPERATORS 209 3 Inverse Exponential Cumulative Distribution WBEXPOINV This function returns the inverse of an exponential cumulative distribution for a supplied mean and standard deviation The syntax is WBEXPOINV Prob Mean The probability corresponding to the exponential distribution The probability must be greater than or equal to 0 and less than or equal to l The arithmetic mean of the distribution The mean must be greater than or equal to zero For example WBEXPOINV 5 1 returns 0 69315 This means that for an exponential distribution with mean 1 0 50 percent of the outcomes are less than or equal to 0 69315 4 Inner Sum Product WBINNERPRODUCT This
470. t contain any symbols Suggestions This error occurs when temporary work files used by What sBest could not be accessed Go to the folder where your model workbook is located and remove the files listed above You should then be able to solve your model UNBOUNDED Unbounded Model If without violating any constraints the value of the cell to be maximized can be increased to infinity or the value of the minimized best cell can be decreased to negative infinity then the problem is said to be unbounded In this case the following error message will be displayed on the WB Status tab Error Message Unbounded Model Help Reference UNBOUNDED The value of the cell to be maximized minimized can be increased decreased without limit and without violating a constraint The problem may be incorrectly formulated Be sure that the best cell has been correctly specified and all equations and constraints have been correctly formulated Refer to Help at Solution Status Unbounded Suggestions 450 CHAPTER 8 Check the formulation to ensure that the adjustable cells the best cell and the constraint cells have been properly specified and no constraints have been left out The returned worksheet will display a large positive or negative number in the best cell and may have large numbers in one or more adjustable cells This information can give you an indication of where formulation errors lie An incorrectly specified best cell or cons
471. t of functions WBTRIAINV Inverse Triangular Cumulative Distribution WBTRIAINV Low High Mode Prob See the part Statistical Functions for additional information Advanced String Support This feature allows you to build models using strings as arguments e g in functions such as IF VLOOKUP and SUMIF String support related settings are entered using the following dialog box String Support Xs String Support Maximum String Length mp za String Support By checking this option string arguments will be supported in the model Otherwise What sBest will treat strings as arguments with a numeric value of zero String support may make the model bigger so it may need more resources to be solved The default setting is False unchecked which means string arguments will be read as a 0 value number 128 CHAPTER 3 Maximum String Length This length can be set between and 255 By making this setting small you reduce the memory required by the string support feature however making the max string length too small may truncate two different strings such as New_York and New_Jersey make them appear to be identical and lead to incorrect results The maximum string length default value is 20 characters Note Ifthe String Support option is set to FALSE then the Maximum String Length setting will be disregarded String operations are allowed only in vari
472. t sBest menu does not load Problem The add in is not set to load or there is a conflict such that it is unable to load Suggestions In Excel to set the What sBest add in to load choose Tools Add ins from the Excel menu and select What sBest from the list of add ins If What sBest is not in the list press the Browse button to locate the What sBest add in file WBA XLA or WBA XLAM so it can be loaded The default location for it is the Library subdirectory below the Exce directory If it is not there it will probably be found in the WB subdirectory If you have a laptop machine and are running Excel it is possible that the files required to support add ins have not been installed If the WB menu item does not appear on the menu after trying to set the What sBest add in to load run the installation program for Excel and choose the Typical installation option when prompted There are Excel error codes of REF in What sBest cells Problem The What sBest add in provides special functions to Excel giving it the ability to express constraints and dual cells As it does with all add in functions Excel internally stores the location of the add in program files whenever you use one of the What sBest add in functions in a model As a result if you create a model with What sBest add in functions and later open it using a copy of Excel that has the What sBest program files installed in a different location then
473. t the new adjustable cell values and check that all the constraints are satisfied and the best cell has improved Ifthe model contains nonlinear relationships check the model statistics in the status report consider re solving the model with different starting values for the adjustable cells Also check the scaling and consider tightening the bounds on your adjustable cells The section entitled Guidelines for Modeling with What sBest in Overview of Mathematical Modeling may be helpful in building better nonlinear models An Excel error appears claiming that a workbook cannot be opened under High Security Level Problem This error occurs when Excel tries to open the What sBest add in What sBest makes use of Excel macros to implement the WB constraint function Suggestions The safest option is to put Excel into Medium security mode To do this run the Tools Macro Security command in Excel and set the Security Level to Medium The problem with this approach is that you will be prompted by Excel each time it loads as to whether or not you wish to allow the What sBest add in to be loaded An alternative is to run the Tools Macro Security command select the Trusted Sources tab then check the Trust all installed add ins and templates button An Excel error appears referring to multiple copies of WBA XLA WBA XLAM Problem You have a toolbar left from a previous version of What sBest which must be delete
474. t to reduce variability or risk by spreading your investment over the three stocks Background From the historical data you have calculated an expected return the variance of the return rate and the covariance of the return between the different assets Variance is a measure of the fluctuation in the return the higher the variance the riskier the investment The covariance is a measure of the correlation of return fluctuations of one stock with the fluctuations of another High covariance indicates that an increase in one stock s return is likely to correspond to an increase in the other A low covariance means the return rates are relatively independent and a negative covariance means that an increase in one stock s return is likely to correspond to a decrease in the other You have a target return of 15 What percentages of your funds should you invest in each of the three assets to achieve this target and minimize the variance or risk of the portfolio As an additional safety feature you decide to invest no more than 75 in any single asset Objective of Optimization The objective is to determine the percent to invest in each asset while minimizing risk of the entire portfolio SAMPLE MODELS 289 The Worksheet Let s look at the MARKOWIT sample file as supplied The MARKOW IT Model Before Solving DIN 2 e g Le MARKOWIT xlsx Microsoft Excel File Home Insert Page Layout Formulas Data Review View Develo
475. t to use this strategy StratSelectiveConstraint No 1 True StratSelectiveConstraint is a True False flag indicating whether or not to use this strategy MACROS THE VBA INTERFACE 191 StratSteepestEdge 0 False StratSteepestEdge is a True False flag indicating whether or not to use this strategy StartingPoint 0 False StartingPoint is a True False flag indicating whether or not to use this feature OptimalityTolerance 0 0000001 OptimalityTolerance is a positive number indicating the optimality tolerance ItLimitSlowProg 100 ItLimitSlowProg is an integer greater than 2 indicating the iteration limit for slow progress Derivatives 0 Solver Decides Derivatives can take 5 values 0 for Solver Decides 1 for Backward Analytical 2 for Forward Analytical 3 for Central Differences 4 for Forward Differences Error Codes Description NonlinOpt_BadStratCrashInitialArg Bad StratCrashInitial argument NonlinOpt_BadStratUseLINDOCrashArg Bad StratUseLINDOCrash argument NonlinOpt_BadStratSLPDirectionArg Bad StratSLPDirection argument NonlinOpt_BadStratSLPSolverArg Bad StratSLPSolver argument NonlinOpt_BadStratQuadraticRecognitionArg Bad StratQuadraticRecognition argument NonlinOpt_BadStratPresolveArg Bad StratPresolve argument NonlinOpt_BadStratSelectiveConstraintArg Bad StratSelectiveCo
476. tax would be wbStochasticChanceConstrained WBSP_CC_LT 0 8 0 A2 B3 D4 0 200 CHAPTER 4 wbStochasticFunction This routine can be used to set the stochastic support functions seen in the Stochastic Support dialog box All arguments are required except for the error code but a 0 value can be placed for unnecessary arguments For additional discussion of the options available through this routine see the section entitled Options Stochastic Solver Syntax wbStochasticFunction FunctionName Stage CellRangel CellRange2 CellRange3 Refers_to Place_in_cell NoErrDialog Required Default Description FunctionName Yes WBSP FunctionName is a string argument indicating the name of the function to implement Argument Yes Stage is an integer between 1 and 255 indicating the stage the cell belongs to CellRangel Yes CellRangel is a cell reference for indicating the value of the first argument used for distributions CellRange2 Yes CellRange2 is a cell reference for indicating the value of the first argument used for distributions CellRange3 Yes CellRange3 is a cell reference for indicating the value of the first argument used for distributions Refers_to Yes Refers_to is the range or address of the cell to copy the stochastic function Place_in_cell Yes Place_in cell is a cell reference to specify the cell in which to write the WBSP_ function NoErrDialog Any argument pass
477. ter than the Hurdle value Any user supplied Hurdle value comes into play when What sBest is searching for an initial integer solution At this point the solver can ignore branches in the search tree with objective values worse than the Hurdle value because a better solution exists i e the Hurdle on some alternate branch Depending on the problem a good Hurdle value can greatly reduce solution time However if you set a Hurdle value better than the optimal integer solution What sBest will return an infeasible error message because no feasible answer can satisfy the bound you have set Once What sBest finds an initial integer solution the Hurdle tolerance no longer has an effect At this point the relative optimality tolerance comes into play Hurdle differs from the relative optimality tolerance If you use Hurdle by itself and an integer answer is found it will yield the true optimal integer solution For example if you re confident the best integer answer is at least 95 for a maximization problem just enter 95 as the value in the Hurdle field What sBest won t consider any branch that doesn t yield an answer of at least 95 If in fact the best integer answer is only 93 you will eventually get the message Solution Status No Feasible Solution Found The default value for Hurdle is None 78 CHAPTER 3 Note When entering a hurdle value be sure that a solution exists that is at least as good or better than your hur
478. ters Step 3 Distribution of Distribution Bea 17 of Sell decisions and give stage possible returns on stock table 18 WBSP_VAR 19 WBSP_RAND WBSP_DIST_DISCRETE_SV 20 WBSP_RAND WBSP_DIST_DISCRETE_SV 21 WBSP_RAND WBSP_DIST_DISCRETE_SV 22 WBSP_RAND WBSP_DIST_DISCRETE_SV 23 WBSP_RAND WBSP_DIST_DISCRETE_SV 24 25 Step 4 Sample sizes 26 WBSP_STSC Step 5 Reporting cells 27 i Reporting Cells 28 WBSP_REP 29 WBSP_HIST Generate a histogram of the PV 30 31 32 33 34 35 LJ 36 X Model Scenario Tree W L_ Jb SAMPLE MODELS 397 The SP_PUTOPTION Worksheet After Optimization H S E D Zo SP_PUTOPTIONAxIsx Excel 2 amp D xX HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys Al vj fx What sBest 13 0 0 0 Sep 30 2014 Lib 9 0 1889 103 64 bit w i A B C D E F a 1 What sBest 13 0 d 0 Sep 30 2014 Lib 9 0 1889 103 64 bit Stochasti 2 ima 3 DATE GENERATED Oct 14 2014 10 01 AM SCH 5 6 STOCHASTIC INFORMATION 7 8 CLASSIFICATION DATA Current Capacity Limits 9 i ee 10 Adjustables 20480 Unlimited 11 Integers Binaries 0 Unlimited 12 Constraints 27650 Unlimited 13 Nonlinears 10240 Unlimited 14 RANDOMNS 5 15 STAGES 6 16 NODES 1365 17 SCENARIOS 1024 18 19 Expected Value EV 3 45E 00 2n l Exznactad Valua of Parfert Tnfnormation I FUNC EYL 1 GGEAnn Is D WB Status WBIStochastic WB _Histogram
479. ters with multicore processors The extensions are of two types concurrent solvers and parallel solvers A concurrent solver runs two or more different algorithms simultaneously on the same problem As soon as one solver finishes all solvers are stopped Concurrent solvers tend to give higher utilization of multiple cores but may not give reproducible results e g if there are alternate optima A parallel solver repeatedly splits the task of solving a problem into two or more subtasks and then allocates these subtasks over multiple cores A parallel solver will generally give reproducible results but may not achieve 100 utilization of all available cores The What sBest development team wishes you the Best in all your optimization endeavors Copyright 2014 LINDO Systems Inc 1 Getting Started with What sBest What is What sBest What sBest makes available to your Excel spreadsheet program a highly developed solver capable of performing linear and nonlinear optimization on the most difficult of problems What sBest gives you access to this solver from within Excel and may either be run directly or called from within Visual Basic People in business finance science math and many other fields use What sBest every day to model and solve problems in production financial planning personnel scheduling resource allocation portfolio management stock cutting inventory control It s a long list to wh
480. than or equal to total demand for period 1 B6 The second group of constraints D27 F39 is that supply sources not be used beyond their capacity is in cells D27 F39 In cell D27 for instance is the formula WB D6 lt D 20 D6 the amount purchased from Source 1 in Period 1 is required to be less than or equal to D20 the supply capacity per period Now let s solve the model i The Inventory Worksheet After Solving l CF Ble INVENT as Microsoft Excel File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o El X INVENTORY PLANNING MODEL S Time Period Demand Met 100 180 220 150 100 200 250 300 260 250 240 210 140 0 1 2 E 4 5 6 T 8 9 lt lt lt lt lt lt lt SS SS E G Purchase From Source Ending 1 140 180 180 180 180 180 180 180 180 180 180 180 140 3 Inventory 0 40 40 0 30 110 126 92 N w een E EI Seenen enen en en e H Cost Per Period 14 080 18 080 18 000 18 060 18 220 22 104 22 036 21 868 25 920 25 694 24 564 21 210 14 000 Time Period al D Saw 10 ST What sBest has arrived at a minimized Total Cost of 263 836 H21 This simple model is intended to demonstrate the basic principles in modeling inventory Add fixed ordering and shipping costs for each source etc for a model more reflective of the real world
481. the function WBPOSD in cell D1 enter wbConstraintPOSD A1l C3 D1 or wbConstraintPOSD Range Cells 1 1 Cells 3 3 Cells 1 4 wbDeleteReports This routine is called by the Delete Reports button on the General Options dialog box posted by the Options General command This routine is used to delete any What sBest report worksheets WB Status and WB Solution in the current workbook Syntax wbDeleteReports The wbDeleteReports procedure has no arguments Error Codes Value Description Rep_DeleteReportsError Error deleting one of the reports wbDeleteWBMenu This routine is used to delete the WB menu item from Excel s menu Syntax whDeleteWBMenu The whDeleteWBMenu procedure has no arguments Remarks This procedure together with the whAddWBMenu procedure allows a developer to remove and add the WB menu as desired MACROS THE VBA INTERFACE 159 wbDualValue For additional discussion of the functionality provided see the section entitled Advanced Dual which refers to the dialog box interface that calls this procedure This routine is used to build the dual formulas All arguments are optional Syntax wbDualValue DualCells DualLoc DualChoice Argument Required Description DualCells No DualCells is the range or cell that dual value information is desired for If omitted the default is the offset of one cell to the left of the current selection
482. this may result in feasible models being reported as infeasible Relative Specify the relative amount of violation from integrality that is acceptable in the Relative text box Specifically if Z is the closest integer value to X X will be considered an integer if X 1I lt Relative Integrality Tolerance xI ADDITIONAL COMMANDS 75 The default value for the relative integrality tolerance is 000008 Although one might be tempted to set this tolerance to 0 this may result in feasible models being reported as infeasible LP Solver When solving a mixed linear integer programming model the branch and bound solver solves a linear programming LP model at each node of the solution tree You may choose between the primal simplex dual simplex or barrier assuming the barrier option was purchased with your license solver for handling these linear programs The two options in the LP Solver box Warm Start and Cold Start control this choice of LP solver based on whether there is a starting basis warm start or no starting basis cold start Warm Start Use the Warm Start option to control the linear solver that is used by the branch and bound solver at each node of the solution tree when a starting basis is present to use as an initial starting point The Cold Start option discussed below determines the solver to use when a previous solution does not exist The available options are Solver Decides What sBest chooses th
483. tics for a discussion of Z values Objective of Optimization The objective is to determine how much of each grain you should buy at today s prices to meet their nutritional requirements at lowest cost 264 CHAPTER 7 The Worksheet Let s look at the HOGCHANC worksheet as supplied in your sample files The HOGCHANC Worksheet Before Optimization 7 Gleis HOGCHANCsx Microsoft Excel kala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 2 o El 3 SWINE amp ROSES Hog Farm Nutrients Per Unit Weight of Grain Nutrients Minimum Dual Item 1 2 3 4 Supplied Reqd Value Nutrient A 22 3 4 T2 1 5 0 0 Not gt 24 1 00 Nutrient B 14 11 0 0 0 8 0 0 Not gt 0 7 1 00 Nutrient C 23 56 11 1 13 0 0 Not gt 5 0 1 00 Nutrient D Mean Value 12 0 11 9 41 8 52 1 0 0 Not gt 21 0 1 00 Variance 0 3 2 2 20 5 33 2 Sear an eN h Weight Units Unity to Purchase 0 0 0 0 0 0 0 0 Not Dual Value 1 00 1 00 1 00 1 00 4 4 gt M HOGCHANC 22 al i Ready 7 G GI 100 A Determine Adjustable Cells The cells What sBest is free to manipulate in this model are the Weight Unit Percentages to Purchase for each grain C18 F18 B Define Best The optimal solution to this problem is the one that meets needs at lowest cost If you examine the formula in the Total Cost cell J18 SUMPRODUCT C18 F18 C15 F15 you see that every change in price or purchase quanti
484. ties has a direct bearing on cost What sBest of course is only free to change the purchase quantities in C18 F18 C Specify Constraints The limitation to this problem is that the final mix must contain the minimum required levels of nutrients for Swine amp Rose s hogs This limitation is enforced by creating a constraint cell for each nutrient H7 H9 H11 Each constraint will return the Not gt indicator until the Minimum Required 17 19 111 for that nutrient is met in the Nutrients Supplied column G7 G9 G11 SAMPLE MODELS 265 Now let s solve the problem with What sBest The HOGCHANC Worksheet After Solving X a 9 C B UF HOGCHANC xlsx Microsoft Excel Home Insert Page Layout Formulas Data Review View Developer Team What sBest VY ai o EN Ys SWINE amp ROSES Hog Farm Nutrients Per Unit Weight of Grain Nutrients Minimum Dual 1 3 4 Supplied Reqd Value 7 Nutrient A 22 3 7 2 1 5 3 7 gt 24 0 00 8 Nutrient B 1 4 ji 0 0 08 0 9 gt 0 7 0 00 9 Nutrient C 23 x 11 1 1 3 5 0 gt 5 0 0 97 10 Nutrient D 11 Mean Value 12 0 418 52 1 21 0 gt 21 0 1 59 Variance 0 3 2 2 20 5 33 2 Weight Units Unity Total E to Purchase 63 4 0 0 31 3 53 Cost 52 26 Dual Value 0 00 11 62 0 00 0 00 4 4 gt M WB Status HOGCHANC 27 al m Ready amp BSA 10 This What sBest solution costs 52 26 per bushel It s more expensive than the HOG
485. tion Check to be sure that all adjustable cells in the model are still required Also if the workbook contains multiple independent models you can separate them into different workbooks in order to meet the limit If eliminating integer cells is not an alternative then you may wish to contact LINDO Systems regarding a license upgrade to handle the additional constraints LICCAP4 Nonlinear Adjustable Cell Limit If your model has more nonlinear cells than is allowed for your installation the following error message will be displayed on the WB Status tab Error Message Nonlinear Adjustable Cell Limit Help Reference LICCAP4 TROUBLESHOOTING 425 The number of nonlinear adjustable cells in this model number of nonlinears exceeds the limit ot nonlinear adjustable cell limit The model has more nonlinear adjustable cells than is allowed by your installation You will need to either reduce the size of your model or upgrade to a larger version Suggestions The model exceeds the nonlinear adjustable cell limit for your installation The capacity limits of your version may be found by running the WB About What sBest command An adjustable cell is considered nonlinear if it appears in a nonlinear manner in one or more cell formulas in your workbook As an example suppose that cells A and B1 are both adjustable cells Furthermore suppose that we have the following formula somewhere in the workbook SIN A J 3 B1 The SI
486. tion B27 B31 is multiplied by the cell indicating whether a lockbox has been assigned B7 B11 a zero or a one then by the amount of cash flow from the given customer location H7 H11 The sum of these products is then multiplied by 1 000 to compensate for the fact that monthly cash flow figures are abbreviated by three digits and by the Daily Cost of Capital in cell C18 Fixed costs are calculated simply by multiplying the cost per month for each proposed lockbox cell B14 in the case of NYC by the cell indicating whether the location has been opened B13 These costs per location are added to produce subtotals in cells H15 and H17 The sum of the subtotals Total Operating Costs appears in H19 the objective cell C Specify Constraints The constraints are of two types First cells B40 G44 prevent a customer from being assigned to a location where no lockbox has been opened For instance move the cursor to cell B40 and observe the formula there WB B 13 gt B7 It requires that B13 a 1 or 0 depending on whether or not the New York lockbox is opened be greater than or equal to B7 a 1 or 0 depending on whether or not the Seattle customer is assigned to the New York Lockbox The value in B7 cannot be greater than that in B13 If the Seattle customer is assigned to a lockbox located in New York the location must be open or else the constraint in cell B40 will be unsatisfied The constraints in cells H40 H44 ensure that each cus
487. tion there is no necessary call for sampling because it takes the discrete values directly from the discrete table Otherwise sampling will be applied on the discrete distribution too In case of a model with both distributions continuous and discrete so the user may want to apply sampling only on the continuous with the option Sampling on Continuous Distribution Only via the Stochastic Solver options box Select Range Select the a two column range where the column is for the Stage in ascending order and the second column for the number of scenarios associated to the stage Place function in cell Specify the cell in which to write the WBSP_STSC function Set button Place the function in the spreadsheet None button Delete the selected cell ADDITIONAL COMMANDS 97 Page Reports Stochastic Support es 5 Select the cells to appear in the Stochastic Report MV Create Report Using the Function WBSP_REP Select V Create Histogram Using the Function WBSP_HIST Select Report Information Expected Value of Wait and See Model s Objective Expected Value of Policy Based On Mean Outcome V Expected Value of Perfect Information Expected Value of Modeling Uncertainty Print Scenarios Horizontally in Report Use Preview Window for Scenario Selection EE Optimization Method Seed for Random Generator Common Size per Stage Jh Sampling on Continuous Distribution Only e ret
488. tion the model into blocks You may currently select from two graph partitioning algorithms named simply GP1 and GP2 with the default setting being GP1 Usage Guidelines for K Best Solutions As an example you are packing a basket for a picnic you will be taking with a friend You ve constructed a list of items you would like to carry with you on the picnic Each item has a weight associated with it and your knapsack is limited to carrying no more than 15 pounds You have also come up with a 1 to 10 rating for each item which indicates how strongly your friend wants to include the particular item in the knapsack for the picnic The information are listed in the model below KNAPSACK_ KBEST xlsx The KNAPSACK_KBEST Worksheet Before Solving H OD m Knapsack_KBest xlsx Excel Fx HOME INSERT PAGELAYO FORMULAS DATA REVIEW VIEW DEVELOPER Team What sBest Lindo Sys Al 8 f v A B c D E F G H J a 1 C I 2 Weight Rating Include 3 Brats 3 1 D WBIKB_REP 4 Brownies 3 1 D gt Beer 3 1 D 6 Ant Repel 7 1 0 Ef Blanket 4 6 0 8 Frisbee 1 6 0 9 Salad 5 10 0 10 Watermelon d 9 0 11 Knapsack Capacity 12 o lt 15 13 Favorites in Knapsack o 14 15 This model uses the K Best feature via the Integer Solver 16 17 18 READY CALCULATE 3 ADDITIONAL COMMANDS 83 Where Cell F12 has the formula SUMPRODUCT C3 C10 WBBINf where WBBINf is the range for the adjustable binary cells in column F Cell E13 ha
489. tional Problems 399 General integer variables 2 44 General Modeling Guidelines 222 General Options Dialog Box 51 Global 134 Global Distance 67 Global optima 220 Global Solver 66 Global Solver Options Dialog Box 65 Global Width 67 Goal seeking 221 Gomory 72 GUB 72 Help 133 Heuristics Level 69 Hidden cell 23 146 Hide model 146 HIDSNAME 415 Histogram 231 HLOOKUP 205 207 431 HOGCHANC XLSX 263 HOGFEED XLS 258 Hold Interrupt 419 Hurdle 77 IF function 205 207 IKBREP 417 INDICMOD 417 Industrial Version 134 Infeasibility 39 INFEASIBLE 221 418 INFLARG 419 Ingredients 258 Initial Values 223 Installation 4 455 63 INT 205 Integer command refers to 44 Integer names in workbook 44 Integer Pre Solver Options Dialog Box 68 Integer problems 224 binary 2 44 general 2 44 Solution method in 73 Integer Solver Options Dialog Box 73 Integers 134 Integers Integer Binary 43 Integers Semi continuous 48 Integers Special Ordered Set 45 Integrality 74 Interactive environment 7 INTERRUPT 419 Invalid Outside Procedure 408 INVENT XLSX 327 Inventory 308 327 330 Invest 292 295 Investment 298 INVMOD 421 IRRECONST 421 Iteration Limit for Slow Progress 64 ITRLIM 422 K K Best Solutions 82 Knapsack 379 Knapsack Cover 72 Kuhn Tucker 220 Language 141 Lattice 72 Left hand side 27 LHS 27 LICCAP1 422 LICCAP2 423 LICCAP3 424 LICCAP4
490. tiple local optima The following example shows a convex function of a single variable Graph of 4 A1 3 2 5 40000 35000 30000 25000 20000 15000 10000 5000 0 So Oo oS L Fe 300 250 200 150 100 100 150 200 250 300 A geometric definition of convexity states that a function is convex if for any two points on or above the function a straight line connecting the two points lies entirely on or above the function As illustrated in the preceding graph a strictly convex function with no constraints has a single minimum That is water drizzled on it will collect in a single puddle at the global minimum Therefore minimizing a smooth convex function with no constraints will yield the global optimum regardless of the initial value of the adjustable cells However if the function is not convex there may be more than one local optimum In this case the returned answer may be locally optimal but not globally optimal 218 CHAPTER 6 Determining the convexity of a multiple variable problem is no easy task Mathematicians call a function convex if the matrix of second derivatives is positive definite or has all positive Eigen values A function is called concave if the matrix of second derivatives is negative definite A function can be concave in one section and convex in another The following function is strictly concave A Strictly Concave Function Graph of A12 300 250
491. tive These tolerances allow you to tradeoff solution time vs solution quality Ideally we d always want the solver to find the best solution to a model Unfortunately integer programming problems are very complex and the extra computation required to find an optimum solution can be prohibitive On larger integer models the alternative of getting a solution within a few percentage points of the true optimum after several minutes of runtime as opposed to the true optimum after several days makes the use of these tolerances quite attractive Absolute Use the Absolute text box to set the absolute optimality tolerance This is a positive value r indicating to the branch and bound solver that it should only search for integer solutions with objective values at least r units better than the best integer solution found so far In many integer programming models there are huge numbers of branches with roughly equivalent potential This tolerance helps keep the branch and bound solver from being distracted by branches that can t offer a solution significantly better than the incumbent solution In general you shouldn t have to set this tolerance Occasionally particularly on poorly formulated models you might need to increase this tolerance slightly to improve performance In most cases you should experiment with the relative optimality tolerance discussed below in order to improve performance The default value for the Absolute optimality t
492. tive integer value with the Max Passes text box The integer pre solver makes iterative passes through a model determining appropriate constraint cuts to append to the formulation In general the benefit of each successive pass declines At some point additional passes will only add to the total solution time Thus What sBest imposes a limit on the maximum number of passes The default limit is 200 passes 72 CHAPTER 3 Relative Limit Set the relative constraint cut limit by changing it to any desired fractional value with the Relative Limits text box Most integer programming models benefit from the addition of some constraint cuts However at some point additional cuts take more time to generate than they save in solution time For this reason What sBest imposes a relative limit on the number of constraint cuts that are generated The default limit is set to 0 5 times the number of true constraints in the original formulation Types Enable or disable any of the different strategies What sBest uses for generating constraint cuts with the checkboxes in the Types box It is beyond the scope of this help file to go into the details of the various strategies Interested readers may refer to any good text on integer programming What s Best defaults to enabling all cut generation strategies Coefficient Reduction Disaggregation Flow Cover GCD Gomory GUB Knapsack Cover Lattice Lifting Plant Location Objective Integrality Bas
493. tive value the amount to sell For more information see the Adjustable command above ABCs 25 Best The dialog box posted by the Best command appears as follows D This command is used to specify the cell in your model to maximize or minimize Select the objective sense you wish to apply from the drop down box on the left of the dialog box Possible options are 1 Minimize 2 Maximize 3 None Then enter the cell you wish to set in the text box on the right of the dialog box What sBest defaults to entering the current selection Clicking OK will define the best cell Objective SENE ar ra Minimize or Maximize WK L Select Minimize or Maximize to specify whether your objective is to determine the smallest or largest value for the best cell respectively These choices may also be made using the Minimize Je and Maximize toolbar buttons For optimization models you must define a best cell equation solving and goal seeking models do not require a best cell as discussed below The best cell sometimes called the objective of optimization is the cell whose value is to be minimized or maximized during optimization The best cell must be an adjustable cell or a formula depending upon an adjustable cell defining exactly what it is you want to optimize 26 CHAPTER 2 The two most common objectives of optimization models are to minimize cost or maximize profit but you can choose to maximi
494. to a Delta Coefficient coefficient of 0 000001 Big M Coefficient Specify the Big M value to use during linearization with this text box When What sBest linearizes a model it will add forcing constraints to the mathematical program generated to optimize your model These forcing constraints are of the form ADDITIONAL COMMANDS 55 ft Adjustable Cells M ey where M is the Big M Coefficient and y is a 0 1 variable The idea being that if some activity in the adjustable cells is occurring the forcing constraint will drive y to take on the value of 1 Given this if we set the Big M value to be too small we may end up with an infeasible model Therefore the astute reader might then conclude that it would be smart to make Big M quite large thereby minimizing the chance of an infeasible model Unfortunately setting Big M to a large number can lead to numerical roundoff problems in the solver resulting in infeasible or sub optimal solutions So getting a good value for the Big M Coefficient may take some experimenting The default value for Big M is 100 000 Status Report Use the Status Report option to specify under what conditions if any you would like a status report created when a model is solved The available options here are Always Created Never Created Only on Error Warning If you select Always Created What sBest will insert a status report worksheet entitled WB Status into the current workbook every time you solv
495. to show how What sBest provides you with the best possible answer A Determine Adjustable Cells In this example we first want What sBest to adjust the value for Quantities to Produce for both models of computer in cells C5 D5 What sBest requires that numbers be placed in all adjustable cells You may simply enter zeroes in these cells although any number will suffice Next specify that cells C5 and D5 are adjustable by selecting both cells and either 1 choose Adjustable from the WB menu and click OK or Kx Kx 2 use the Make Adjustable toolbar button or to Remove Adjustable If you use the WB menu to access the Adjustable dialog box you ll notice that the Adjustable dialog box has C 5 D 5 the current selection entered in the Refers To text box In the drop down box the default setting Make Adjustable is already selected so you need only click OK What sBest identifies an adjustable cell by applying an Adjustable style distinguished by a default font color of blue as a visual reminder and unlocked cell status as follows The Adjustable Cells in XYZ KW s e g Ols XYZ xlsx Microsoft Excel Home Insert Page Layout Formulas Data Review View Develop A D WEE E F XYZ COMPUTER CORPORATION PRODUCTION PLA Product Standard Deluxe PF Quantity to Produce 0 al Profit per Unit 300 500 10 Product Component Requirements 11 12 Components Quantity Required Total N GETTING STARTED
496. tochastic WB _Histogram Model f p The solver writes a series of solution in the created tab WB Stochastic and WB Histogram with the expected value and displays the first default scenario or a selected scenario on the spreadsheet MATHEMATICAL MODELING 241 The scenario by scenario report is generated on the WB Stochastic tab H 85 Os SP_INVESTMENTCOLLEGE xlsx Excel 2 P D xXx HOME INSERT PAGELA FORMUL DATA REVIEW VIEW DEVELO Team What sB Lindo Sys 126 fe Model D11 v F G H J K L D 26 Hodel D10 Model G10 Model H10 Model D11 Model G11 Model H11 Model D12 Mo 27 WEALTH1 STOCKINVEST1 BONDINVEST1 WEALTH2 STOCKINVEST2 BONDINVEST2 WEALTH3 UN 28 STAGE 1 STAGE 1 STAGE 1 STAGE 2 STAGE 2 STAGE 2 STAGE 3 29 30 67 26272 65 094582 2 168138 428571 0 71 428571 81 428571 31 67 26272 65 094582 2 168138 428571 Deet 80 32 67 26272 65 094582 2 168138 833305 83 839905 104 79988 33 67 26272 65 094582 2 168138 839905 83 839905 88 870299 Sm 59 11124 36 743215 22 368029 80 25 59 11124 36 743215 22 368029 67 84 36 59 11124 36 743215 22 368029 i 71 428571 81 428571 37 59 11124 36 743215 22 368029 428571 71 428571 80 38 39 An WB Status WEB Stochastic WB _Histogram Model 4 b AVERAGE 48 44950783 COUNT 33 SUM 1162 788188 E E t 90 The scenario report we obtain is show above Our expected utility at the end of the three periods is 1 514085 This means that ther
497. tomer is assigned to a lockbox by requiring that the sum of lockbox assignments for a given customer be at least 1 SAMPLE MODELS 287 With all constraints in place we re ready to solve the model n The LOCKBOX Worksheet After Optimization O emgeet Fe em X a 3 e g UF LOCKBOX xlsx Microsoft Excel kolak Home Insert Page Layout Formulas Data Review View Developer Team What sBest V e o E ZS 13 14 15 16 7 18 19 20 21 fe CHOSEN LOCKBOX LOCATIONS amp CUSTOMER F G H L J K E Monthly Proposed Lockbox Locations Cash Home Flow lew York Atlanta Cincinnal Denver Seattle Office 000 5000 5000 Houston 5000 Philadelphia 5000 Miami 5000 Open 1 1 0 1 0 0 Cost Month 1 300 975 1 000 1 100 S0 Fixed Costs 1 300 975 0 1 100 s0 S0 3 375 Variable Costs 1 350 1 350 SD 5 400 so s0 8 100 Daily Cost of Capital 0 027 TOTAL OPERATING COST E SA AVERAGE MAIL DELAY BETWEEN LOCATIONS 37 38 39 40 41 42 Customer Home Locations lew York Atlanta Cincinnai Denver Seattle Office Box Seattle gt gt aber mer pe spar be Los Angeles gt gt pe gt gt gt gt Houston gt gt gt gt gt gt gt 4 4 gt WB Status LOCKBOX 4 ia m Ready Bam 80 g After optimization What sBest has returned a minimized cost of 11 475 in cell H19 and the optimal solution recommends that lockboxes be opened in New York Atl
498. tory produces sheet metal in various widths that you cut from 100 inch widths In order to meet customer demand you must produce rolls of these widths and footage Width Total Footage 35 1 020 25 3 000 18 967 15 1 450 For each roll of 100 metal you select one of four cut patterns Pattern A B C D Rolls 35 35 25 35 cut into 25 35 25 257 widths 18 15 25 15 of 18 15 29 15 340 CHAPTER 7 Schematically the patterns look like this if TU Fre r 35 25 18 18 4 Pattern A Edge Waste bh mg 35 35 15 15 Pattern B 25 25 25 25 Pattern C 35 25 45 15 Pattern D 10 Edge Waste Each length of 100 metal must be cut into one of these patterns but how many feet should be cut using each pattern Objective of Optimization Your objective is to minimize the total waste cost the sum of edge waste and end waste How many feet of each pattern should you cut in order to meet customer demand at the lowest cost SAMPLE MODELS 341 The Worksheet Let s examine the CUTSTOCK sample file and see how the edge waste and end waste are calculated The CUTSTOCK Worksheet Before Optimization 7 mas e oF IS cutstockxtsx Microsoft Excel Sm x File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 e o El Ss E Widths To Cut in Inches E F G H Feet Cut Edge Waste In Pattern Ins H 0 00 0 0 00 0 0 00 0 0 00 0 Cut 0 0 Need 145
499. traint i e Maximizing a cell that should be minimized or incorrectly specifying a greater than or equal to constraint as a less than or equal to constraint may be causing the problem UNDEFREF Undefined Reference If What sBest encounters formulas with REF type Excel errors the following error message will be displayed on the WB Status tab Error Message Undefined Reference Help Reference UNDEFREF An invalid cell reference or an invalid output value was found in the formula of the cell listed below You must correct any illegal references to continue Running the Update Links command from the WB Options General menu may correct the error cell address Suggestions This error can occur if a cell referenced by another cell in the worksheet is deleted or replaced by moving another cell over it This error can also occur when a file is opened that contains functions created on a system in which the What sBest program files were in a different location The latter problem can be corrected using the Update Links button on the General Options dialog box posted by the Options General command If this is not the result of links needing to be updated the references in the specified cells need to be corrected to eliminate all REF errors TROUBLESHOOTING 451 WBCARDFORM Cardinality Cell Format If requested What sBest can specify Cardinality sets Range values tell you over what range a particular set is valid
500. traints golterLimit No None golterLimit is an integer indicating how many tries to allow in solving the model goRuntimeLimit No None goRuntimeLimit is an integer indicating the maximum number of seconds to be used in solving the model goNumber ThreadsLimit No 1 goNumberThreadsLimit is an integer specifying the number of threads between 1 and 32 goThreadChoice No 0 goThreadChoice is an integer specifying the choice for the threads 0 Solver Decides 1 Parallel Preferred 178 CHAPTER 4 2 Parallel Only 3 Concurrent Preferred 4 Concurrent Only golndSlack 1 Indicator golndSlack is an integer indicating what form to display constraints in 1 Indicator 2 Slack goAutoSelectFreeIntOmit No 1 True goAutoSelectFreelInt is a True False flag indicating whether to automatically select Free Integer or Omit range names goMinimizeExcel 0 False goMinimizeExcel is a True False flag indicating whether to minimize Excel during the solution process goHideStatusWindow 0 False goHideStatus Window is a True False flag indicating whether to minimize the status window during the solution process goLinearizationDegree 0 Solver Decides goLinearizationDegree is an integer indicating the degree of linearization to use 0 Solver Decides 1 None 2 Mathematical 3 Mathematical Logical goLinearizationDelta 0
501. ts in this problem are simply that the production of sheet metal in each of the four widths must meet the amount demanded The requirements for 15 18 25 and 35 inch sheet metal appear in B10 E10 The actual footage of each width resulting from the selected Cut patterns is tallied using formulas in B9 E9 B11 E11 contain constraints forcing these requirements to be met The formula for 15 End Waste in B11 for example is WB B9 gt B10 This ensures that actual footage B9 is at least equal to the required amount B10 Now you re ready to solve the model The CUTSTOCK Worksheet After Optimization D Xli d 3 Cut Need amp e e 8 a CUTSTOCK xlsx Microsoft Excel fe Widths To Cut in Inches E Feet Cut Pattern 483 50 0 00 447 88 725 00 1450 967 3000 1450 967 3000 e e End Waste In Inches 0 0 0 0 G H Edge Waste In Ins 4 0 0 10 10 875 Stock Width Inches 100 End Waste Cost Per Inch Ft 0 75 Total End Waste Cost 4 948 Total Edge Waste Cost 13 776 Edge Waste Cost Total Waste Cost 18 724 Per Inch Ft 1 50 4 4 gt h WB Status CUTSTOCK lt 3 Ready The solution to the CUTSTOCK model is a Total Waste Cost of 18 724 13 776 Edge Waste E18 and 4 948 End Waste E17 Rounding may give a slightly different answer Here s a schematic of the solution Note If multiple raw material types were avai
502. ts of a business situation The Problem in Words You run three plants Each plant is capable of producing six products from six raw materials You also operate two steel mills that can ship steel as a raw material to any of your plants You want to know the amount of steel each mill should ship to each plant and the number of products each plant should produce to maximize your total profit Background The PRODMIX shown earlier and SHIPPING shown later worksheets are combined in the BLOCK problem which involves maximizing the profit from several manufacturing plants while minimizing the cost of shipping raw materials from multiple sites The cost of shipping one unit of steel from each of the mills to each of the plants is shown in the table below Shipping Costs Per Unit of Steel From Steel Steel To Mill1 Mill2 Plant A 2 5 Plant B 3 4 Plant C 5 6 Mill I has a maximum total capacity of 1200 units and Mill 2 has a maximum total capacity of 1800 units Each plant has an 800 unit minimum requirement of steel for the period that has been specified by each plant manager The actual starting inventory of steel at each plant is determined by the total number of units shipped to that plant from the two steel mills The starting inventories of the other five raw materials at each plant are listed below Resource Units on Hand Wood 1160 Plastic 1780 Rubber 1050 Glass 1360 Paint 1240 The profit contribution and product resource r
503. ty No 0 000008 Relativelntegrality is a fractional value indicating the relative amount of violation from integrality that is acceptable for the integer variables WarmStartLP No 0 Solver WarmStartLP is an integer value Decides indicating the linear solver to use during branch and bound when a starting basis is present 0 Solver Decides 1 Barrier 2 Primal 3 Dual ColdStartLP No 0 Solver ColdStartLP is an integer value 184 CHAPTER 4 Decides indicating the linear solver to use during branch and bound when a starting basis is not present 0 Solver Decides 1 Barrier 2 Primal 3 Dual AbsoluteOptimality AbsoluteOptimality is a positive value r indicating to the branch and bound solver that it should only search for integer solutions with objective values at least r units better than the best integer solution found so far RelativeOptimality 0 00001 RelativeOptimality is a value r ranging from 0 to 1 indicating to the branch and bound solver that it should only search for integer solutions with objective values at least 100 7 better than the best integer solution found so far TimeToRelativeOptimality 100 TimeToRelativeOptimality is the number of seconds before the branch and bound solver resorts to using the RelativeOptimality tolerance HurdleTolerance None HurdleTolerance is a value of a known integer solution What sBest
504. ual value changes is called the upper range 118 CHAPTER 3 Constraint Ranges For example building on the XYZ example an upper and lower range can be determined for the dual values of the stock constraints These ranges are put into the model by highlighting the cells you would like the range to appear in selecting Advanced Dual specifically selecting the constraint cells F15 F17 to display in For Cell Range choosing Upper Range or Lower Range whichever is appropriate and clicking OK Note The default value entered in the For Cell Range is G15 G17 which is not the range of the constraint cells You must make the correction to F15 F17 in order to obtain the true range values In the illustration below we used cells 115 117 and J15 J17 for the upper and lower ranges respectively and then re solved Again we could have placed the dual value cells in any convenient location in the workbook DIE LAKE 8 XYZ xlsx Microsoft Excel bala File Home Insert Page Layout Formulas Data Review View Developer Team What sBest V ei o Eil Ys H15 v fe WBDUAL F 15 50 B Cc D E F G XYZ COMPUTER CORPORATION PRODUCTION PLAN Product Standard Deluxe PROFIT Quantity to Produce 60 30 Profit per Unit 300 500 OOoNnN oan kWh Product Component Requirements Components Quantity Required Total Number Dual Lower Upper Standard Deluxe Usage In Stock Value Range Range Standard Tower 1 0 60 lt 60 50 40 60 Deluxe T
505. ula for the Total Cost cell SUM F4 F 12 This formula sums the amount invested in each bond issued for each of the nine bonds offered C Specify Constraints The constraints in this problem B18 F18 require that the total cash inflows in B17 F17 Ge from the interest and or principal income each year remain greater than or equal to cash outflows needed per period in B19 F19 SAMPLE MODELS 281 The cells B17 F17 Amount Covered contains formulas that add the cash received from bond interest payments as well as the repaid principal when applicable for each year This Income Stream is detailed in cells 14 M12 and appears as follows F The BONDS Worksheet Part 2 Before Optimization x WH I g Ae MM BONDS xisx Microsoft Excel oE File Home Insert PageLayout Formulas Data Review View Developer Team What sBest V ei o El X Al F Investment Bond Issue 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 G Year 0 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 Year 1 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 Income Stream Year 2 Year 3 Wa m gt fi Eam 100 C Y Oe For instance suppose that in the beginning of year 0 your client invests in 10 units of a 10 percent 3 year U S Treasury bond see the bond listed in C10 F10 A 10 0 would then be inserted in cell E10 Each unit represents a 1000 face value or p
506. un time error message box In many instances this runtime error message provides you with a What sBest error code a number over 30000 However in some cases you may only receive a Run time error 5 Invalid Procedure Call or Argument message box like the one shown below Whether you receive a What sBest error code or an Excel error code you must take steps to 1 correct the source of this error and 2 insert error handling into your code to anticipate any further errors Error handling is placed in your VBA code by adding a suitable On Error statement before any calls to What sBest routines and inserting some appropriate error handling code Including error handling in your code will prevent Excel runtime error messages like that shown above For an example of such code see the section entitled wbhError and Error Codes in chapter VBA Interface If you don t correct the source of the error fail to insert error handling and you again run the routine that produced the error then Excel will generate the following cryptic error message Microsoft Visual Basic 3l i Run time error 91 Object variable or With block variable not set This message signifies that Excel has an unhandled error left over from the previous run and cannot display the new error that was just generated You must now try to correct the source of the error but this time you do not have the benefit of a What sBest error code If you can t manage to
507. undefined arithmetic operation in the cell listed below One example of an undefined arithmetic operation would be division by zero but there are many others Check the cell below to determine the source of the error You must either rewrite the formula or constrain the adjustable cells to avoid the error cell address Suggestions Examples of undefined arithmetic operations are division by zero multiplying by a text string and evaluating to a number larger than 1030 If the cells are unrelated to solving the model include them ma WBOMIT range or delete them Otherwise change the initial values of the adjustable cells to move away from the undefined region Also consider rewriting the model in such a way that all formulas are defined over the entire domain of the adjustable cells BLKCELL Blank Cell Warning If your model has references to blank cells the following warning message will be displayed on the WB Status tab Warning Message Blank Cell Warning Help Reference BLKCELL Blank cells have been referenced in formulas During the solution process their values have been taken to be zero This warning can be turned off via the WB Options General menu See cell list below cell addresses listed at bottom of tab Suggestions You should verify that the blank cells being referenced were actually intended to be blank If the model looks correct then you may choose to disable this warning message using the WB Options General
508. understood analysis of the model and solution It provides a hard copy of the information appearing in the solver status window The section entitled Getting the Best Results discusses the information contained in the status report in further detail You may use the nterruptSolver button on the solver status window to interrupt the solver while it is solving If you do you can not expect any useful information to be returned unless you have an integer problem In the case of an integer problem the best solution to the point of interruption is returned For linear problems and non linear problems the returned values will not be useful 34 CHAPTER 2 The definitions of the information in the What sBest solver status box are shown below Model Type This shows one of six categories your model falls into Integer Quadratic Integer Nonlinear Integer Linear Quadratic Nonlinear Linear For further information on these categories see the section entitled Linear vs Nonlinear Expressions and Linearization in Overview of Mathematical Modeling State This shows the state of the current solution Possible states include Globally Optimal Infeasible Unbounded Feasible Infeasible or Unbounded Near Optimal Locally Optimal Locally Infeasible Cutoff Numerical Error Undetermined Unknown Error See Overview of Mathematical Modeling for more information on these states Tries This shows the current number of tries or iterations used in solv
509. urity TrustedSources menu Then save the model and restart Excel 414 CHAPTER 8 Suggestions In Excel 2002 there is an additional security setting that the user needs to set for allowing the server to access a user defined macro Select Trust Access to Visual Basic Project via the Tools Options Security MacroSecurity TrustedSources menu Then save the model and restart Excel In Excel 2007 adjust the security setting from the Excel Options then click on Advanced TrustCenter TrustCenterSettings Enable macros and grant the same access in the Macro Settings tab In case your add in has been digitally signed you will need to enable this add in to run your model In some situations a time delay may occur after enabling the add in Refer to the What sBest sample file Shipping MacroFunctions xlsm for an example of valid user defined function usage FUNCSERVER Failed to Access the Server If the What sBest solver was unable to access Excel to calculate the user s defined functions the following error message will be displayed on the pop up window Error Message Failed to Access the Server Help Reference FUNCSERVER The solver needs to access Excel to run the users defined functions Make sure only one Excel application is running version 2002 or later via the Task Manager Also verify that the application is not already busy with any macro virus scan Suggestions The solver could not
510. use this message For more on this subject see the Solve topic FORMULA3 External Reference If there are external links to other workbooks that can t be resolved the following error message will be displayed on the WB Status tab Error Message External Reference Help Reference FORMULA3 A link to an external workbook in the cell below could not be resolved Check the validity of the link or remove the external link cell address Suggestions An external reference was found that could not be imported You should check to see if the link is valid and if it can be resolved Array formulas can also generate this error in that they may only reference native data contained in the primary workbook If any of your array formulas have external links you will need to import the external data into the native workbook TROUBLESHOOTING 413 FUNCADDIN Failed to Access the Add in If the What sBest solver was unable to locate an add in that is needed to calculate the user s defined functions the following error message will be displayed on the pop up window Error Message Failed to Access the Add in Help Reference FUNCADDIN The workbook is referring to an add in that is not at the specified location add in location This is needed to run the user s defined functions from Excel Reset any call to this add in then save the model and restart Excel Suggestions Clear any Excel call of this add in via the
511. ust be greater than or equal to Low Probability Low High For example WBUNIFINV 4 1 2 returns 1 4 This means that for a uniform distribution on the interval 1 2 40 percent of the outcomes are less than or equal to 1 4 6 Overview of Mathematical Modeling Introduction The relationships in your model influence the computation time the solution methods used by What sBest and the type of solution returned This overview very briefly explains some of the different types of expressions entailed and explores how the expression type affects the solution search An understanding of these basic principles is not required to use What s Beet but it can go a long way in helping you to use the software more effectively In the section entitled Linear vs Nonlinear Expressions and Linearization we consider the two expression types linear and nonlinear and how they influence the solution process The section entitled The Solution Process Determining optima introduces some of the issues in finding optima These issues include local versus global optima and the distinction between smooth continuous and non smooth non continuous functions The type of outcomes generated by What sBest is discussed in the section entitled Solution Outcomes Finally some suggestions for modeling are offered in the last section Guidelines for Modeling with What sBest and Guidelines for Stochastic Modeling Linear vs Nonlinear Expressions an
512. variables Some examples might be the number of televisions to produce the amount of money to be spent on advertising the number of shares to purchase of a particular stock ABCs 23 the location of your next service facility Inappropriate adjustable cells would be things you have no control over such as the total demand for televisions the price of advertising to be purchased the risk of a particular stock the local building restrictions o Cells containing equations are also inappropriate as adjustable cells What sBest cannot rewrite an equation although the value returned by an equation will change if the equation depends upon any adjustable cells What sBest will not alter the contents of cells specified as adjustable that contain equations text or blanks In other words the cells must be numeric Therefore be sure to enter a numeric value in each of your adjustable cells Note When the adjustable quality is applied to a cell What sBest assigns a predefined Adjustable style to the cell This style is automatically made available to each of your What sBest models and can be customized e g font color as you wish x Remove Adjustable Select Remove Adjustable to return an adjustable cell to its fixed non adjustable state By default a cell is fixed until it has been specified as adjustable When you instruct What s Best to remove a cell s adjustable status the Adjustable style is r
513. ve Workbook Names WBINTstaff Delete This statement removes the WBINT range name thereby returning the adjustable cells contained in the former range to normal status 170 CHAPTER 4 wbinteger For additional discussion of the functionality provided see the section entitled nteger which refers to the nteger dialog box that calls this procedure This routine is used to build the integer ranges WBBIN and WBINT Adjustable cells contained in these ranges will be restricted to integral values by the What sBest solver If you wish to delete an integer range name using VBA instead of the Delete button on the Integer dialog box you can use Active Workbook Names WBBINmyRange Delete This statement removes the integer range name thereby returning the adjustable cells contained in the former range to normal status Syntax wbInteger IntName Refers_to IntChoice Argument Required Description IntName No IntName is a string that refers to the range being made integer Refers_to No Refers_to is the range or address of the cell s to be specified as integer If omitted the default value is the current selection IntChoice No IntChoice is a string to indicate if the cells should be binary or general integer IntChoice accepts BIN or BINARY for binary 0 1 and INT or GENERAL for general integer If omitted the default is binary For backwards compatibility with earlier versions of What sBest IntChoice also
514. ving along this route Limit the maximum amount that can be moved along this route You also know the rates and limits for each route or arc in the network Objective of Optimization The objective is to ship all the uniforms to the ntake Centers at minimum cost while satisfying demand at each center SAMPLE MODELS 377 The Worksheet Let s look at the sample file TRAFFIC The TRAFFIC Worksheet Before Solving aS SC STAC A Microsoft Excel nnn regex File Home Insert Page Layout Formulas Data Review View Developer Team What sBest 9 CA CH es D E TRAFFIC FLOW Unit 1 Unit 2 Unit 3 Unit 4 Total Supply Warehouse 1 100 0 100 0 100 0 100 0 400 Not 1100 Warehouse 2 100 0 100 0 100 0 100 0 400 Not 700 Warehouse 3 100 0 100 0 100 0 100 0 400 Not 1300 Total 300 300 300 300 Not Not Not Not Demand 900 1200 600 400 RATE Warehouse 1 39 14 14 Warehouse 2 27 9 9 Warehouse 3 24 14 13 LIMIT 30 Warehouse 2 3375 1029 1371 1029 31 Warehouse 3 2743 1680 2040 1560 32 33 Epsilon 0 01 Total Cost 34 M 4 gt gt TRAFFIC 2 A Determine Adjustable Cells The adjustable cells are the amounts shipped along each arc from Warehouse to Intake Center in B5 E7 B Define Best The best solution in C36 is the minimized sum of all time penalties C Specify Constraints There are three groups of constraints in the model In G5 G7 the Total shipped from each Warehous
515. ween risk and return is called the efficient frontier 292 CHAPTER 7 Portfolio with Transaction Costs File name PORTCOST XLSX TYPE NONLINEAR OPTIMIZATION Application Profile As the expected return and variances of each asset change the optimal portfolio is almost certain to change Adjusting your investments with every change may cheer up your broker but the commissions or transaction costs will slowly erode the value of your portfolio Typically there s a cost associated with each sale or purchase Using this model you need to take these transaction costs into account in calculating how to adjust your portfolio The Problem in Words According to your estimates your current holdings will yield a 12 2 return You are interested in adjusting your portfolio to lower the variance yet achieve a return of at least 9 5 Background Your portfolio currently consists of 50 of Asset 1 30 of Asset 2 and 20 of Asset 3 You pay a transaction fee at the beginning of the period that is a percentage of the amount bought or sold The transaction fee is 1 0 for Asset 1 1 5 for Asset 2 and 2 0 for Asset 3 You have estimated the expected return and the covariance terms for each asset Objective of Optimization The objective is to determine the percent to invest in each asset while minimizing the risk of the entire portfolio SAMPLE MODELS 293 The Worksheet Let s look at the PORTCOST sample file The PORTCO
516. wers Working While Solving This simple model solves very quickly While larger models are solving you may want to do other work as you wait for your solution If you want to work in Excel while your model is being solved then just minimize the model being solved and open another copy of Excel or whatever application you wish to you use Simply leave the minimized Excel icon on the taskbar at the bottom of the screen and your model will continue to solve in the background The Next Step The ABC s Basic Functions and Advanced Functions sections explain the What sBest commands in depth To learn more about the principles of optimization modeling see Overview of Mathematical Modeling If you d like to move on to more sophisticated problems see Sample Models 2 ABC s The Basics of What sBest This chapter describes how to use the three basic commands that are used in building almost every model for What sBest We ll refer to them as the ABC s Adjustable Best Constraints These three commands are the first commands at the top of the main WB menu item on the Excel menu In addition to the menu commands you may use the corresponding toolbar buttons on the What sBest toolbar The sections below include in depth discussion of the use of these commands Adjustable EZ KE Best Je L Constraints lt gt After you have created your model by setting up the ABC s you can Solve your wo
517. without the need to pass it on to the full blown integer solver ADDITIONAL COMMANDS 69 The integer pre solver options available to the user are listed below Heuristics Level Use the Heuristics Level drop down box to control the level of integer programming heuristics These heuristics use the continuous solution at each node in the branch and bound tree to attempt to quickly find a good integer solution If an integer solution better than the incumbent is found then it is used to fix or tighten global and local variable bounds There are four options available None Low Medium and High The None option disables heuristics The remaining three options allow you to set the level of the amount of heuristics performed to a low medium or high level What sBest defaults to performing a high level of heuristics Heuristics Cutoff Criterion The Heuristic Cutoff Criterion is used to control the criterion for terminating heuristics Choices here are Solver Decides Time and Iterations Under the Time setting What sBest terminates heuristics after a certain amount of elapsed time The Iterations option terminates heuristics after a certain number of iterations In general the Time setting results in the fastest performance However due to shifting computational loads on a machine solution paths may change under the Time setting from one solve to the next potentially resulting in non reproducible solutions If reproducibility of a
518. word CALL in front of procedure calls where you use parenthesis or remove the parenthesis Beyond VBA VB Model developers may prefer the ability to provide the user with a more elaborate polished interface than can be provided using Excel workbooks running Visual Basic macros Developers can create such applications using the full featured development environments of Visual Basic or Microsoft Access that run What sBest with Excel running in the background The Access or VB application can easily prepare the data for the optimization model insert it into an Excel workbook and run What sBest so that Excel is completely hidden from the user The development of the application can progress in natural stages The optimization model can first be prototyped and tested in Excel Once the structure of the model is decided upon Visual Basic code can be written to automate the process of creating the model within Excel Finally the code can be incorporated into an Access or Visual Basic project in which the What sBest model is built based upon a data set provided by the application Embedding What sBest in a Visual Basico Visual Studios Project We again return to the XYZ Tutorial problem to look at how it could be incorporated into a Visual Basic VB program Assuming that Visual Basic is installed on the computer extract the WB_VB project from the WB_VB zip file of the WB directory Start the Visual Basic or
519. x a number of raw components into a minimum cost final blend that has specified amounts of certain ingredients In the case of hogfeed the issue is vital How can raw feedstocks be combined to produce a high nutrition hogfeed at lowest cost For someone with several thousand hungry hogs the quality of this answer can easily spell the difference between profit and loss Since feedstock prices are typically volatile the complexity of the question and the daily importance of reliable solutions is even more apparent Blending problems are also of interest well beyond the field of animal husbandry Examples include finding the least costly mix of ores that will produce an alloy with specified characteristics or deciding on the most efficient combination of advertising media purchases to reach target audience percentages in multiple demographic groups The Problem in Words You are the manager of the Swine amp Roses S amp R Hogfarm and your hogfeed must meet certain minimum requirements for four nutrients 4 B C and D to assure fast growth and large robust animals SAMPLE MODELS 259 Background The nutrients are found in four different grains Each grain contains a different combination with a price that fluctuates with market conditions The nutrient content by grain is shown in the following graph Nutrient Content By Grain 0 0 ke Objective of Optimization The objective is to determine how
520. xample of an irreconcilable constraint would be WB 0 gt 1 Clearly no matter what values are chosen for the adjustable cells 0 will never be greater than 1 What sBest will provide you with a list of the irreconcilable cell formulas You will need to either delete them or correct them so that they are functions of the adjustable cells To correct them check the cell formulas for errors and be sure that all the adjustable cells have been specified 422 CHAPTER 8 ITRLIM Iteration Limit Reached By default What sBest does not put a limit on the number of solver iterations However by using the Iteration Limit option on the General Options dialog box posted by the Options General command the user may limit the number of iterations When the program has executed the number of iterations you specified without finding a solution the following warning message will be displayed on the WB Status tab Warning Message KKKKKKKKEKKKKKKKKKKKKKAKKKKK a INTERRUPTED gi EE EE a a EE KEE a a EE EE a EE EE WARNING Iteration Limit Reached Help Reference ITRLIM The limit for the maximum number of iterations was reached before the final solution could be found Check the solution carefully it may be sub optimal or infeasible The iteration limit is set via the WB Options General menu Suggestions The iteration limit is set through the WB Options General menu In some cases the solver may be able to return the
521. xpired License KOy orrara rE EE EEEE ETE 427 LICKEY4 Pending Expiration of Option Tal 427 LICKEY5 License Key Dongle Required 0 c ccceceeeceeeeeeeeeeeeeeeeeeeeeeeeeeseeeaeeesenaeeeeeeaees 428 LICOPT1 Global Solver Not Uicensed cece cccccccceeeccssceeecesseeeeeeeuessesuueeseesaaaueeeeaaaees 428 LICOPT2 Nonlinear Solver Not Licensed ccc ccccceeeccsseeeeeseeesesseeeseesaaeeeeaeaees 429 LICOPTS3 Barrier Solver Not Licensed 0 ee cecc cece eecccsceeecessaeeeceeeeecsesuueeseeuaaaaeeeeaneeas 429 LICOPT4 Mixed Integer Solver Not Licensed 0 0000 eee ceeeeeeeeeeeeeeeeeeneeeeeeaeeeeeenaeeeeeeaees 429 LICOPT5 Stochastic Solver Not Licensed occ ccc ceeececseeeeseeeeeseeseueeeeeeaaaaeeeeauaaas 430 LICOPT6 Conic Solver Not Licensed ccccc ccc ccccccce ee cccsceeecessaeeeseeeeeseesuueesessaaaeeeeeanaeas 430 LOOKUP Unsupported Lookup Usage 431 MEMORY Insufficient Memory 0 cc ceeeeeeceee sence r EREE RE 431 MODERR Parsing Cell Fomula scine a e Ea a EER E AET ER 432 NAME Unsupported Name cccccceeeeceeececeeeeeeeeeceaeceeeeeeeseceeaeceeeeeeesecsnaeeeeeeesenensaees 433 NLINCELL Nonlinearities Presentan a a a draad 433 NOADJ No Adjustable Cell 434 NOBEST NO Best Cell man a a a a a a See 435 NOCONST No Constraint Cells nenne a a e a aeaaeai 435 NUMERICAL Numerical Error 436 OMITTED Omitted Cell Reference enana aa iiaa aeri adi 436 QUAPREC Quadratic Recognition
522. xt box Next select the Binary WBBIN or General WBINT radio button in the Integer Type box Once this is done pressing the Add button causes What sBest to assign a WBBIN or WBINT range name to the selected cells which will appear in the list on the nteger dialog box If you decide later you would like to remove the integer restriction simply select the Integer command click on the name of the integer range to remove and press the Delete button It is important to remember that integer restrictions can increase solution times as discussed in the section entitled Runtime Concerns 44 CHAPTER 3 Integer Names in Workbook What sBest uses range names to specify which cells in a model should be integers You can choose any combination of letters for your range name When the range name is created What sBest adds WBBIN or WBINT to the front of the name to represent respectively binary integers and general integers For instance if you used the name Quantity in the Integer Names in Workbook textbox for a general integer a range name WBINTQuantity would be assigned to the selected cells and appear in the list on the Znteger dialog box Refers to Specify the range of cells that are to be made integer in this text box What sBest will automatically fill the Refers to text box in with the range of the currently selected cells If this is not the range of cells you want you can type the correct range in or select the butto
523. y One What sBest proceeds to search by row following by column until it finds the first such cell If there are more cells of the same type across the worksheet or workbook then the following dialog box appears Locate Next or Exit beten Jeng For example if the current cell is Al you are searching for adjustable cells one by one and A2 and B1 are both adjustable cells the next cell selected will be B1 Finally select whether you want What sBest to search across the Entire Workbook or This Worksheet in the Across drop down box If no cells of the type you requested are found in the worksheet or workbook then What sBest lets you know ADDITIONAL COMMANDS 133 Help amp About What sBest The dialog box posted by the About What sBest command appears as follows What sBest 13 0 0 1 Oct 21 2014 Copyright 2014 LINDO Systems Inc Library 9 0 1905 120 Extended License Capacity Unlimited Unlimited Unlimited Unlimited Unlimited r Conic Global Integer Stochastic Location of the add n file WBA XLAM C Program Files Microsoft Office 15 Root Office 15 Library L Location of the license file LNDWB130 LIC C Program Files Microsoft Office 15 Root Office 15 Library L 134 CHAPTER 3 The About What sBest dialog box provides information about which version of What sBest you are running and its capacity according to the license key you possess If you
524. y Required Total Number Standard Deluxe Usage In Stock 15 Standard Tower 1 0 20 lt 60 16 Deluxe Tower 0 1 15 lt 50 17 Hard Drive 1 2 50 lt 50 18 19 20 21 22 23 24 M 4 gt H WB Status Average 15 Count 2 Sum 15 ADDITIONAL COMMANDS 123 Note that since the dual value formulas now refer to a non adjustable cell What sBest ignores these cells and they are not changed If the quantity of Deluxe computers to produce is decreased to 3 and the model is re solved the profit increases to 15 300 15 000 100 3 and the number of Standard to produce increases to 56 as shown in the following This might occur if there are three obsolete Deluxe models and they are taken apart for the common parts used in the Standard model x H 5 e Sle 8 XYZ xlsx Microsoft Excel bala Home Insert Page Layout Formulas Data Review View Developer Team What sBest YV ei o El es D4 f constant B c Wim E F c XYZ COMPUTER CORPORATION PRODUCTION PLAN Product Standard Deluxe constant Dual Val PROFIT Quantity to Produce 56 2l 15 300 Low Rng Upp Rng Profit per Unit 300 500 Product Component Requirements Components Quantity Required Total Number Standard Deluxe Usage In Stock Standard Tower 1 0 567 lt 60 Deluxe Tower 0 3 lt 50 Hard Drive 1 2 50 lt 50 M 4 H WB Status i e IKIE w Ready E Average 3 Count 2 Sum 3 Em
525. you are requesting dual values for a range of cells then the range in Report Information in should be identical in dimension to the range in For Cell Range What sBest provides three dual value options in the Report on Type box The first Dual Value lets you define the dual value of a cell or range of cells The formula will be WBDUAL cell number The other two Upper Range and Lower Range let you define the upper and lower ranges for dual values The formulas are WBUPPER cell number and WBLOWER cell number The study of these values and their effect on the solution of the model is called sensitivity analysis Please refer to the section Usage Guidelines for Dual Values for a tutorial and information on how to use this option effectively ADDITIONAL COMMANDS 111 For Cell Range This is the target range of cells you wish dual reporting on What sBest will automatically fill this box with the cells directly to the left of the current selection of cells or above them if the entire row is selected If this is not the range of cells you want you can type the correct range in or select the button on the right edge of the text box to bring up a cursor for cell selection Report on Type Dual Value Select Dual Value to prompt What sBest to return the dual value of the adjustable or constraint cells specified in For Cell Range To enter a dual value function put the cursor in the cell for which you want to find the dual value
526. ze or minimize any adjustable cell or any equation that depends upon one or more adjustable cells Other frequent targets for minimization are waste conflict time required surplus and risk A maximization cell could be something tangible an equation representing total output or something less concrete such as a calculation to estimate employee job satisfaction or the effectiveness of customer service You may specify no more than one cell to be maximized or minimized Whenever you designate a best cell any previously specified best cell returns to being a non optimized cell In a scenario with multiple goals you should consider maximizing or minimizing one goal and constraining the others or combining goals into a single equation to be maximized or minimized For example if the goals for your factory are to maximize production output and minimize costs there are clearly trade offs between the two goals You can choose to 1 Maximize output while constraining costs to be less than a desired level 2 Minimize costs while constraining output to be greater than a desired level 3 Combine both goals into a single equation of output minus total cost and maximize the single equation None Select None to void any previously specified best cell If no best cell is specified in a model What sBest will try to find a solution that satisfies all constraints and relationships in the model without trying to maximize or minimize any particular c

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