Habread User Manual
Contents
1. Use Split Character Split Character r3 Figure 7 Reading the MPS file 3 2 1 Creating the BIO2 data Now in order to read the MPS file and create the BIO2 Table Figure 8 press the BIO button After verifying that all the polygon and regime names are correct and after deleting any undesired rows ensure that each polygon is assigned a DoNothing regime as explained in Example 1 Unlike Example 1 DoNothing regimes did not exist in the MPS file for this example Thus one has to create a DoNothing regime by inserting a row at the top of the BIO2 file using row and filling it in with the first polygon name and a regime name DN A value of 0 is assigned to this regime Now hit the AddDoNothing button to add a DoNothing regime to all the other polygons As discussed in Example 1 whenever you select Exit from the HabRead File menu the current settings are saved to a default location in the hbr subdirectory You can also select SaveSettings to save your settings to another location When you restart HabRead it automatically loads the settings saved in the default location Also whenever you push the Save button on the BIO2 or on a Flow table the table is saved to the default location Note that the Edit menu for each table has an UnDo option so you can recover if you make changes that are incorrect Habread User Manual Draft Do not distribute 18 Polygon Regime Value 0 x002. there are at most 8 valid regimes If there is no overlap between the regimes included in the bio 2 and the flow datasets then you ll get an error message like this no valid regimes for polygon xyz This also implies that the valid regimes for a polygon can change when a new component is added to the objective function In fact the new component could make a polygon s current regime invalid When this happens Habplan will switch to a new valid regime ASAP but not instantly Do nothing options are specified in the Flow components as contributing to year 0 or alternatively as having 0 flow or both Note that a do nothing in one flow component might result in output for another flow component For example doing nothing relative to clear cutting could result in a flow of habitat The do nothing option must also appear in Bio 2 components in order for it to be valid for a polygon This implies that it must be ranked relative to the other regimes Hopefully you can think of a meaningful way to accomplish this ranking For example you might decide that the regime that yields the lowest present net value is equal to doing nothing and rank them accordingly A do nothing indicated by year 0 in Flow signals the blocksize components that this option doesn t contribute to blocks If you want it to contribute to blocks then you d have to give the year when it contributes even though the output may be zero See the material on the Block Form for more on
3. values for period 1 F1A2 has values for period 2 etc If your MPS file is constructed in a similar fashion then HabRead should work for you Habread User Manual Draft Do not distribute 10 2 4 Comments on Regime Naming Conventions Habplan was developed with the implicit assumption that regime names have similar meaning across stands ie they are stand independent For example regimes called CC 1 and CC 2 might mean to clearcut the stand in years 1 and 2 However MPS files often use random regime encodings such that regime X for stand i has no relationship to regime X for stand j Fortunately most of the features in Habplan will work when regime names are stand dependent The following things won t work in Habplan when regime names are stand dependent 1 The Spatial Model SMOD Component 2 indicating Not Block options for the Block BK Component and 3 indicating Block options for the CCFLOW Component All of these capabilities depend on regime naming to be stand independent There seems to be no work around for the Spatial Model Component but there is for the Block Component This work around is made possible by the fact that many MPS files already have a clearcut flow incorporated i e there are decision variables that allow the LP formulation to place constraints on the amount of clearcutting by period Go to the Habplan documentation for more information about Block components but a Block component has a parent
4. working with large MPS files For example if the MPS file has 10 million lines you could use 2 Gigabytes of RAM You need a special file to get Habplan to enforce these management units by assigning the same regime to each polygon in a unit This unitFile can be created by pushing the save button on the Expand Units Form This will save a text file that has 3 columns polygon unit and size Point Habplan to this file so it knows what management units to enforce 3 2 4 Outputting Results to Habplan In order to output each data table to a directory where habplan can access the files for each table select Writedata under the table s File menu Save the data to a designated directory from where Habplan will read the files and do not include the column names when saving when you press save a window will pop up giving you the option to include or exclude the column names It is advisable to save each component with a clearly understandable file name e g save BIO2 data as bio2 data and save cash flow data as MNCFL data specific to this example These files can now be input directly into Habplan This is done by filling out an Edit Form for the respective components in Habplan Habread User Manual Draft Do not distribute 24 3 3 Example 3 Polygon Regime Decision Variables in Fixed Width Fields Converting from Per Acre Hectare Outputs to Whole stand Outputs Similar to Example 2 the following example is based on data
5. 001 o 79409 07 x00001 947 16 80 Save MpsRead Translate Expand AddDoNothing Figure 8 BIO2 Table The next step is to create the flow data 3 2 2 Creating FLOW data Using the AddFlow option under the HabRead Flow menu add as many flow compo nents maximum of 99 as you need So too one can delete unneeded flow components using the RemoveFlow option For this example we have chosen to include 4 flow components At the top of the HabRead window click on the first flow tab Flow 1 Now assuming that the MPS file has accounting variables that provide the sum of each Flow for each period in the planning horizon supply the prefix of the first flow accounting variable in the Flow1 Make Tool window Figure 9 For this example MNCFL is the prefix for the accounting variable that sums cash flow per period in the planning horizon e g MNCFLO1 refers to cash flow in period 1 Type MNCFL in the Flow1 Make Tool and press the Generate button to fill in the Flow Table Figure 9 Now after conducting the Consistency and Habread User Manual Draft Do not distribute 19 Fill operations as described in section 3 1 2 you are ready to click on the second flow tab Flow 2 and repeat this process for the Flow 2 component and all the subsequent flow components Figures 10 11 and 12 The data is now ready to be output to file
6. 1 Example of flow data Poly ID Regime ID Year Output 1 16 0 0 179 187 196 204 210 216 222 228 R2 h2 hb2 bh2 h2 bh2 b2 WH CON DOK cCornr 2r CON DOK WDNR In general polygon id and regime id can be any arbitrary name Instead of polygon 1 regime 1 you could name it polygon P1 and regime R1 for example However using integer regime values has some advantage since the entry forms for some components allow you to use notation like 1 15 to indicate regimes 1 through 15 Of course this only works for integer regime names Don t use regime 0 Regime 0 is used by the biological type 1 component to indicate that data being input are not training data Also the output is an integer it takes much less memory to store integers than floating points Option 16 is a do nothing option in the above dataset Do nothing options are denoted with year 0 and usually with output 0 Year 0 indicates that this period of this option does not contribute to blocksizes and this will be auto detected by the blocksize component for this flow Finally remember that regimes can have variable numbers of output years For example regime 1 may produce output in years 1 and 21 while regime 20 only produces output in year 20 There is no requirement for the data input file to be rectangular for flow components If you like rectangular files however you could create extra dummy periods for your regimes with year 0 For example suppose regime 2
7. 2 0 1 28 0 33 0 36 0 40 0 A n ci EE m LL n CENE MEE 44 0 E 46 0 Figure 6 Checking for Consistency of Polygon Names eje w NIIP PIO eje Je WIM R MMR ho ps ro pele le lO Neem NIASSA N o ojojojojo 16 3 2 Example 2 Polygon Regime Decision Variables in Fixed Width Fields Expanding Management Units to Component Polygons The following example is based on data in which the polygon regime name is combined into a single variable name e g X00062074 would be cutting unit 62 regime 74 In other words Habread User Manual Draft Do not distribute IT the first 6 characters of this combined variable name give the polygon name and the rest give the regime name As for example 1 the first step is to open the MPSReadTool and select the desired MPS file The primary difference between examples 1 and 2 however are that the polygon regime names are combined into a single variable for example 2 and are not separated by a split character as in example 1 Therefore one would not check the Use Split Character box Figure 7 Instead one would leave the Use Split Character box unchecked and enter 6 into the Polygon Regime Split Column box This would ensure that the first 6 characters of the polygon regime name are assigned to the polygon name and the rest to the regime name MPS Read Tool File jhome jaggett myjava Habread1 example FRMPSXblue Polygon Regime Split Column 6
8. 2 to convert management units to component polygons You will now need to provide a dbf file that includes the following columns 1 Polygon and 2 Units and Habread User Manual Draft Do not distribute 26 3 Size Proceed by setting the filepath to your dbf file on the Expand window Now press the SetColumns button to select the column names that correspond to Polygon Unit and Size If these selected column names are in the dbf file they will be located automatically Next press the Read button to read the dbf file Now simply check the Per Polygon option on the Expand window and then press the BIO2 button on the MPS Read Tool to generate the BIO2 data from the mps file Then press the Expand Units button and the units will be split out into their component polygons and turned into whole stand values at the same time as shown in Figure 17 This process can also be used when you only want to expand the mps values into whole stand values In this case the Polygon and the Unit variables should be set to the same column in the dbf file This particular dbf column should correspond to the names for the stands in the mps file 3 3 2 Handling Spatial Issues For Pre Cut Stands The beginning of a planning horizon is usually designated as year 1 in Habplan However there will almost always be pre cut stands that were cut 1 2 or more years before the start of the planni
9. Click on Properties then Shortcut and then under Run select Minimize Now to open HabRead simply double click on the HabRead shortcut Note that the java interpreter allocates 16 MB of RAM by default To run big problems get more RAM by starting HabRead like this java mx256m Habread This would allow for 256 MegaBytes It is wise to make this number as large as your computer will allow i e java mx2000m Habread1 will give 2 GigaBytes of RAM 6 Known Bugs This section lists bugs that are known and not yet fixed Users can provide information on other bugs that they uncover Please send email about bugs you find 1 There are no known bugs at this time 7 Future Directions 1 Still working on finishing version 1 8 APPENDIX Background on Harvest Scheduling The way in which a harvest scheduling problem is mathematically formulated is referred to as the model of the problem More specifically the model refers to the way in which the objective function and constraints are formulated Two commonly spoken of models are Model I and Model II formulations The primary difference between the two is that Habread User Manual Draft Do not distribute 37 Model I choice variables are acres in a management unit whereas Model II choice variables are acres in an age class In other words a Model I formulation tracks each management unit e g forest stand throughout its existence and the identification of indivi
10. Flow component from which it gets information about when management activities occur If no regimes are designated as NotBlock then the Block component assumes that all regimes contribute to block size Therefore simply let the clearcut flow component be the parent of the block component and it will automatically treat every parent action that produces non zero output as a block creating action This will give the desired control of block sizes 3 How to Use HabRead The following examples will step you through the process of using HabRead The first step is to get HabRead installed and running on your computer as outlined in the installation instructions 5 HabRead can help you set up special management units that consist of multiple polygons Each polygon in a unit is assigned the same management regime This capability is discussed at the end of example 2 HabRead also has the ability to convert per acre outputs to whole stand outputs assuming the necessary data is provided in the form of a dbf file This capability is discussed in example 3 Habread User Manual Draft Do not distribute 11 3 1 Example 1 Polygon Regime Decision Variables Separated by a Character This mps datafile was generated by Habplan using the built in LpMPS capability The mps file comes with Habread and can be found in the Habread1 example test directory The first step is to open the MPSReadTool Figure 2 press the file button then select the habplan2LP mps f
11. Habread User Manual NCASI Statistics and Model Development Group Version 1 May 10 2005 Abstract Converting data to new formats can be a laborious task Forest harvest scheduling is a data intensive activity that has given rise to complex matrix generators for creating input to Linear Program solvers HabRead is a program that helps you convert data in Linear Program MPS format into files that Habplan can read The purpose is to harness the years of development that went into the matrix generator so that users can add Habplan to their suite of landscape planning tools NCASI http ncasi uml edu Habread User Manual Draft Do not distribute Contents 1 Introduction 2 Habplan and Linear Programming Overview 21 Metropolis algorithini Liu s us RR Romo o nk m o IK OR RETRO GE ROS x Rs 22 LPformulaton e 2 06 444 ek Saw 9m 3s koX E ee Yeu oem ok 3 83 2 3 How does HabRead deconstruct the MPS file 2 44 Comments on Regime Naming Conventions 2o o o o o 9 os How to Use HabRead 3 1 Example 1 Polygon Regime Decision Variables Separated by a Character AIL rene the BIO data oad cn ok e Qo hex 3 OR Rc oe Ren al Cung FLOW dataci Euseb be we fex 4 e RS Ee cs RS E 413 Outputting Results to Habpl m s cs o ess a RS 3 2 Example 2 Polygon Regime Decision Variables in Fixed Width Fields Ex panding Management Units to Component Polygons 21 Creating he BlOZ data uod esce h
12. ally forces the user to encode the polygon names and regime names in order to stay within the limited field width A typical encoding scheme would be to code polygon 10001 with regime 128 as decision variable 10001128 because this fits into the 8 character field in the fixed format MPS file HabRead allows the user to provide a translation table to tanslate the coded polygon and regime names back to something more readable before inputting them into Habplan For example you might want to change polygon 10001 to District8 Stand1 and regime 128 to CC 2010 The translation option will not work if your regime names are stand dependent see 2 4 HabRead attempts to construct a Bio2 file for Habplan by pulling out the non zero ob jective function coefficients from the MPS file Figure 1 HabRead infers the polygon names and regime names by looking at the names of the z variables associated with these non zero coefficients HabRead assumes that variable names can be deconstructed to separate polygon and regime names by following certain patterns The 2 basic schemes that HabRead uses are 1 The Polygon Regime name is separated by a special character such as or 2 The first n characters give the polygon name and the rest give the regime name Likewise HabRead attempts to construct a Flow file by looking for user specified Flow prefixes In this example Figure 1 the prefix is F1A and HabRead assumes that rows labeled F1A1 contain flow
13. and this FLOW Table If there are polygons that appear in the FLOW table but not in the BIO2 table then you need to manually fix things Usually you need to delete the rows from the FLOW table that don t show up in the BIO2 table If there are no miss matches between the BIO2 and FLOW tables then you are ready to write this data out for Habplan use If polygons are missing from the FLOW table that appear in the BIO2 table Habplan will have problems Fill in the missing polygons by pressing the Fill button on the FLOW table This will pull all polygons and regimes that appear in BIO2 into the FLOW table if they aren t already represented They will be given a 0 0 output value that appears in year 1 Therefore it won t affect the schedule but Habplan will be happy Fill gives you some summary Fig 5 information that helps you assess the correctness of the FLOW table data The Fill step is needed because Habplan will only use regimes that appear in all objective function components Habplan assumes that regimes that don t appear in all components are disallowed This was supposed to be a feature that allows you to change allowed regimes when entering a new objective function component Finally you should run a consistency check to ensure that the Flow and BIO2 tables contain the same polygons Habplan will abort if polygons aren t consistent across all com ponents Press the consistency button and 2 tables will appear One table gives
14. clude or exclude the column names These files can now be input directly into Habplan This is done by filling out an Edit Form for the respective components in Habplan 4 Habplan Data Formats Some discussion follows about the data formats that Habplan uses However only the data that can be garnered from MPS files is discussed For example Habplan also uses neighbor data for controling block sizes but that is discussed elsewhere Habread User Manual Draft Do not distribute 31 4 1 Flow Data Each flow component requires a data set For each polygon there is one row for each regime that is allowed A disallowed regime is simply not included in the data for the polygon which prevents that regime from ever being assigned to that polygon For example maybe you can t allow clearcutting for polygon 10 because it s near a stream Be careful with multiple flows that each flow dataset contains all allowed regimes even if some of the regimes produce 0 output for some of the flows A simple example of some flow data follows Note that outputs are polygon totals NOT per acre or per hectare For regimes with multiple output years the format calls for entering the years and then the outputs so if polygon 2 had 2 years of output for option 3 you have 2 3 yri yr2 out1 out2 For the data depicted below polygon 1 can only be assigned option 16 while polygon 2 could have options 1 8 Habread User Manual Draft Do not distribute 32 Table
15. commas or tabs Just push the Run button to perform the translation The translation is applied to all Bio2 and Flow tables so Habread User Manual Draft Do not distribute 13 you might want to save this for last Also be careful of running translations multiple times If any of the same names can appear in the left and right columns of the translation files repeated translations could lead to erroneous results Polygon Regime Translate Tool Polygon File ideus myjava Habread 1fexample test habplan2LP poly Regime File us myjava Habread1 example test habplanzLP regime je Figure 4 Translating Polygon and Regime Names Whenever you select Exit from the HabRead File menu the current settings are saved to a default location in the hbr subdirectory You can also select SaveSettings to save your settings to another location When you restart HabRead it automatically loads the settings saved in the default location Also whenever you push the Save button on the BIO2 or on a Flow table the table is saved to the default location Note that the Edit menu for each table has an UnDo option so you can recover if you make changes that are incorrect 3 1 2 Creating FLOW data Some of the steps required to properly fill out a FLOW data table depend on having all of the polygon names in the BIO2 table so complete the BIO2 table before moving to a FLOW tab Notice that you can add and remove flow
16. data we need to convert these per acre outputs to whole stand outputs The Expand Units option discussed in the previous example can be used for this purpose After reading the MPS file by pressing the BIO2 button press the Expand button on the bottom of the BIO2 Table This will open up the same Expand window that was Habread User Manual Draft Do not distribute 25 ZF BIO2 Table File Edit Tools Polygon Regime 10001 0001 0001 0001 003 0001 0001 0001 0001 0001 0002 0002 0002 0002 0002 0002 0002 erara OuUu SV a Row Row Save MpsRead Translate Expand AddDoNothing Figure 16 Before Converting Outputs to Whole stand Values ul e na Ee Fr ag d LAR L9 A VT ST ST oT Pol ead bs us 4 o LIEN w o 82 90 18 99 82 76 69 20 88 28 88 15 ojo o o M ojojoj o 35 37 23 22 30 89 o Ke o ojojo oJ ojojio o ojojo OL ST F Expand Management Units to Polygons SS BIO2 Table File Edit Tools Polygon File libread1 example rest Stds4077 dbf Polygon Regime Value 5078 36 v Per Polygon 5264 41 POLYGON v SURE 5140 68 IGFID ly 5313 0 5311 82 POLYACRE v 0 0 7883 61 Eam pm pune ons E MpsRead Translate AddDoNothing Figure 17 After Converting Outputs to Whole stand Values used in Example
17. dual stands is maintained A Model II formulation tracks a given management unit until it is clearcut after which the new regenerating stand is merged with all other management units cut during the same cutting period These combined management units now at age zero become a new management unit age class with a new identity Thus Model I looks at a management unit and all the alternatives for managing it throughout a planning horizon number of years in the future for which a plan or projection is made which is often multiple rotations Model II looks at an age class and the alternatives for managing that age class for a single rotation Habplan uses a Model I formulation The primary advantage of using a Model I rather than a Model II formulation is the ability to track all management units throughout their ex istence which is a requirement when spatial constraints are included in a harvest scheduling problem 8 1 Solving the Harvest Scheduling Problem As opposed to the model itself the solution technique is the mathematical programming technique that is used to solve the model T wo discrete catagories of solution algorithms are 1 optimization and 2 simulation Linear programming is a widely used mathematical programming tool for computing optimal solutions to problems involving the allocation of scarce resources This optimization algorithm seeks to improve on simulation outputs by sorting through harvest schedules to produce elevat
18. e correspondence between the units in your dbf file and the units in the mps file HabRead tries to do something reasonable even when things are less than ideal Note that you can select the undo option under the edit menu to return to the original BIO2 table if necessary The next step would be to click on a flow tab and press the expand button at the bottom of the Flow Table This will expand the units in the Flow table to correspond to the expanded BIO2 table Note that you should create the Flow data from the mps file before expanding the BIO2 Table The Flow table is referring to the BIO2 Polygon unit names and regimes as it reads the mps file If you read the mps file after BIO2 has been expanded you ll end up with lots of meaningless Do Nothing regimes in the Flow table For very large problems you may run out of memory on your computer if you try to create more than one Flow component at a time In this case create the BIO2 component expand it and then save the result for Habplan Then click undo to return to the original BIO2 table Now go to the first Flow tab and read in a Flow component Expand the Flow data and save it Then read in another Flow component into the first flow tab expand it and save it Repeat this process until all Flows have been read expanded and saved This will allow you to handle larger problems than is possible if you read each flow into a separate flow tab In general you need lots of RAM if you are
19. ed combinations of objectives This is done through the ranking of possible harvest schedules using an objective function LP was the first optimization method applied to maximize harvestable volumes or Net Present Values NPV and has thus been around for many years The primary shortcoming of LP however is its limited ability to account for spatial aspects of harvest scheduling Thus what LP suggests to be the optimal solution usually turns out to be impossible in the real world With increasing emphasis placed on spatial concerns such as fragmentation and patch size in forest management and the continued introduction of new spatially oriented envi ronmental and social constraints spatial simulation techniques continue to be developed These simulation algorithms mimic processes in harvest scheduling seeking ultimately to arrive at the same outcome that would occur had the situation been played out in real life Thus these simulation algorithms do not offer one optimal solution as does LP but rather Habread User Manual Draft Do not distribute 38 in principal they compute a range of harvest schedules that are all feasible At this stage we are not aware of any available simulation based harvest scheduling packages that report multiple feasible solutions Other harvest scheduling packages seem to simply converge on the best solution Habplan however does have the capability to report multiple feasible solutions Although these sim
20. ee CY SURE see Se osx mex Cua FLOW dataa saa 9 eR ee Re ee cxx XE emos 5 2 9 Expanding Management Unite e s sehia 9x r3 gs 3 2 4 OQOutputting Results to Habpl n s s sa s es See 3n 3 8 Example 3 Polygon Regime Decision Variables in Fixed Width Fields Con verting from Per Acre Hectare Outputs to Whole stand Outputs 10 10 11 Habread User Manual Draft Do not distribute 2 3 3 1 Creating the BIO2 data and Converting to Whole stand Outputs 24 3 3 2 Handling Spatial Issues For Pre Cut Stands 26 Bod Cr ate FLOW Data lt eor ee ugue Bok ee EP Ree Poia osi 28 694 Outputting Results to Habpl gm s is s 6 24 0008 648 S xS 29 4 Habplan Data Formats 29 Al Flow Data 43 ek ae eae eee ewe COLOR ee wee we a 30 42 Biological Type tl Data lt e gt o d e s poeb ke Re ee ee we 32 4 3 Comments on Preparing Input Data a aoaaa a 32 5 Installing the Program 33 6 Known Bugs 35 7 Future Directions 35 8 APPENDIX Background on Harvest Scheduling 35 8 1 Solving the Harvest Scheduling Problem 36 List of Figures 1 Example of an LP Tableau o ses setak ae Diaa RGR oe Bea XC d 6 2 Dupat Che MPS data scs siorino E dopes ae eae ee s EE dei ES 11 3 Create the BIO2 Table zw ovo BY Baw BR Baw eke Re eoe od 12 Habread User Manual Draft Do not distribute 3 10 11 12 13 14 15 16 17 18 19 20 Translating Polygon and Regime Names 13 Gen
21. ent units with their component polygons This also apportions the output for the unit among the polygons according to their sizes After this the BIO2 Table should look something like Figure 14 EI Expand Management Unlis to Polygons 127777 o B M do ae oe File Edit Tools Polygon File Jhome pvandeus myjava Habread1 i Polygon Regime Value DN 0 0 POLYGON 001 411473 24 002 386508 72 003 361178 28 Zr z J004 339326 2 005 314153 19 size v 006 285866 02 F 007 255302 03 g SetColumns Read Expand Units Save 008 225807 1 Figure 14 After Expanding Management Units to Component Polygons Along with everything else the expansion puts the polygons in BIO2 into the same order as they appear in the dbf file This is important if you have a shapefile and want to use it with Habplan Shapes in a shapefile must correspond to rows in the accompanying dbf file Polygons that appear in the dbf file but don t have a unit that appears in the BIO2 file are inserted into the expanded BIO2 file with only a DO Nothing regime This is to maintain the one to one correspondence with a shapefile Finally units that have no polygon members in the dbf file are tacked on to the bottom of the BIO2 data This will allow Habplan to utilize the shapefile and incorporates all of your management units In an Habread User Manual Draft Do not distribute 23 ideal world there would be a complet
22. erating Flow Data lt lt 44 aa eod uo hx o dem AUR Oe E oe d 15 Checking for Consistency of Polygon Names 16 Reading the MPS file 4046442464 X 93x e ORG oe 9 x HS 17 BIO2 Table i ce ke Boe RS He eS ES Sey 2 we OER Oe RR OO 18 Flow1 Make Tool and Flow1 Table 00 4 19 Flow2 Table for controlling clearcut acres e a oce 2 llle 20 Flow3 Table for controlling regenerated acres oaoa o 20 Flow4 Table for controlling thinned acres a 21 Before Expanding Management Units to Component Polygons 22 After Expanding Management Units to Component Polygons 22 Un c MU EP 24 Before Converting Outputs to Whole stand Values 25 After Converting Outputs to Whole stand Values 25 Expand Units Form Setup for Pre Cutting sls 27 Flow Data for a Stand Cut 1 Year Before the Planning Horizon 28 Flow 1 Table for Controlling Clearcut Acres lens 29 List of Tables 1 Example of flow dat ooe aoe tamaaa 24 2S 94 A RS RUE E 31 Habread User Manual Draft Do not distribute 4 1 Introduction Foresters have traditionally used linear programming LP for harvest scheduling Math ematical Programming System MPS format is commonly used for feeding data into an LP solver Many forestry organizations have developed sophisticated systems for generating MPS files since virtually all LP solvers can read this format HabRead i
23. eriod of the planning horizon on the Expand Units form Figure 18 Expand Management Units to Polygons Poly gon File home pvandeus myjava Habread 1 Per Polygon ommo v SEQSTAND v POLYACRE v PREBLOCK v CUT PERIOD onc nea f Boana vos sn Figure 18 Expand Units Form Setup for Pre Cutting There is a difference between the PreCut Year values in the dbf file and the precut years that go into Habplan Flow data files In Habplan the precut value is a lag that is interpreted relative to the beginning of the planning horizon Therefore 1 in the Flow data is equivalent to a 0 in the dbf PreCut Year column when the first period for Habplan is 1 When the first period of the planning horizon is 2 then a 1 in the Flow data means the stand was precut in year 1 If you don t want to use the precut feature in Habread just set the PreCut Indicator variable to none and Habread ignores precutting This is what Figure 19 the Flow data might look like when precutting is implemented The stand was cut 1 year before the start of the planning horizon It is available for cutting again in planning horizon years 18 19 or 20 It is important to note that this only effects Block Components that are subcomponents of the Flow component that has precut lags in its data If the flow component will not have a Block component then set the PreCut Indicator variable to none For example if you have a flow component specifically f
24. few seconds Habread should appear on your screen If you add the HabRead directory to your CLASSPATH you can run HabRead from any location in your directory structure You had to deal with CLASSPATH when you installed the Jave J2SE so it won t be explained again here Make sure the bin directory for the J2SE is in your path so your machine can find the java compiler If you get the error that HabRead1 class isn t found and you executed the command java HabRead1 from within the Habread1 directory then there is probably a CLASSPATH variable set on your machine that doesn t allow java to search the current directory If that happens try executing like this java classpath Habread1 where the tells java to look in the current directory It may be convenient to create a desktop shortcut for HabRead If operating on Windows do the following e Open Wordpad and type the following command line java mx256m classpath Habread1 Habread User Manual Draft Do not distribute 36 e Under the Habread1 directory save this as a text only bat file e g h bat e Now right click your mouse Select New and Shortcut Input the full file pathname for the h bat file and follow the rest of the instructions as laid out in Windows You may want to name the icon Habread e Once you have created this shortcut in order to prevent the Dos Window opening each time you open HabRead right click on the HabRead icon
25. gorithm is well known and is based on maximizing or mini mizing an objective function subject to constraints It is generally specified as Max Z cx subject to Az lt r x gt 0 where Z is the objective function value c is a vector of coeffcients representing the con tribution of the decision variables x is a vector of decision variables A is a matrix of Habread User Manual Draft Do not distribute T coefficients measuring the effect of the constraints on the decision variables and r is a vector of constraints The components of Figure 1 and their relation to the LP setup will be explained briefly row by row In the first row column labels the decision variables r represent the proportion of polygon i that is assigned to regime j correspond to x in the general LP format The variables defined as F Y are F low accounting variables that represent the volume flow of flow component n in Y ear t The Row Type determines the sign of the mathematical expression where e E equality e L less than or equal to e G greater than or equal to The RHS Right Hand Side refers to the value of the right hand side of the mathematical expression corresponds to r in the general LP format The objective function coefficients second row c x Figure 1 are taken directly from the Bio2 file correspond to c in the general LP format The following is an example of data from the Bio2 file upon which the example tableau Fig
26. has a second dummy period for polygon 1 as follows 12101200 The first period has an output of 120 for year 1 and the second period has output 0 in year 0 Habread User Manual Draft Do not distribute 33 4 2 Biological Type II Data The Type II biological component allows the user to specify the relative ranking of each regime for each stand Suppose you want to bias Habplan toward assigning the regime that produces the most PNV for each stand Then you need to assign a ranking for each regime In situations where the information is available to use the Type 2 biological approach it is to be preferred over the type 1 method since it provides the user with more control The data format for this component is very simple The first column is polygon id the second is the option and the last column is the rank There is one row for each stand and regime The following data show a situation where stand 1 must be assigned to regime 2 the only regime given but stand 2 could be assigned to regimes 1 3 with regime 3 being preferred The size of the numbers is irrelevant only the ranking is important Therefore ranks 1 2 3 give the same result as 1 16 37 121 210 1 220 4 230 5 4 3 Comments on Preparing Input Data This section includes discussion on naming regimes and the procedure to indicate the valid regimes for individual polygons Habplan is very flexible with regard to polygon and regime names You can basically use whatever name
27. ile in the test directory Alternatively you can abbreviate the path to files that are in the Habread example directory so test habplan2LP mps is a sufficient path This file has polygon and regime names separated by a dollar sign so be sure to check the Use Split Character box 7 MPS Read Tool File lideus myjava Habread 1 example test habplan2LP mps Polygon Regime Split Column 5 _ vi Use Split Character Split Character Figure 2 Input the MPS data 3 1 1 Creating the BIO2 data Now press the BIO2 button to read the MPS file and create the BIO2 Table Figure 3 At this point you need to carefully examine the polygon and regime names in the BIO2 Table to make sure that they are all correct There is a selection tool that can be accessed under the Tools menu on the BIO2 Table that will help you search for specific polygon and regime names You can delete multiple rows by selecting them and pushing the delete button on the selection tool A single row can be deleted by pushing the row button on the BIO2 Table Regimes that represent doing nothing are important in Habplan and we call them DoNothing regimes For example Habplan might break up a large clearcut block by assigning a DoNothing regime to one of the polygons There is an AddDoNothing button on the Bio2Table that helps you ensure that each polygon has a DoNothing regime assigned toit For this example regime 1 is DoNothing If y
28. in which the polygon regime name is combined into a single variable name However for this example only the first 5 characters of the combined variable name give the polygon name with the remaining characters giving the regime name Therefore after opening the MPSReadTool Figure 15 and entering the filepath to the desired MPS file one would leave the Use Split Character box unchecked and enter 5 into the Polygon Regime Split Column box This would ensure that the first 5 characters of the polygon regime name are assigned to the polygon name and the rest to the regime name MPS Read Tool File home jaggett myjava Habread 1 example Test ex3 mp Polygon Regime Split Column 5 Use Split Character Split Character BIO2 Figure 15 MPS Read Tool 3 3 1 Creating the BIO2 data and Converting to Whole stand Outputs If we were to follow the same procedure as laid out in Examples 1 and 2 to create the BIO2 file we would now press the BIO2 button and the resulting table would look like the table shown in Figure 16 Note that for this example DoNothing regimes were included in the MPS file as regime 9999 Therefore there is no need for us to manually insert DoNothing regimes Also this example is different from the previous two in that we know that the output values in the MPS file are per acre outputs Habplan however deals only with whole stand outputs Therefore before saving the BIO2
29. indicating do Nothing regimes 5 Installing the Program HabRead is written in Java to be compliant with Sun Microsystems Java Development Kit Version 1 2 or higher which can be downloaded free from http java sun com j2se As this is written the current version is JAVA 2 Platform Standard Edition v 1 5 also called JAVA 5 You only need to install the Java Runtime Environment JRE to run HabRead However you need the entire J2SE to be able to use the jar command mentioned below Note that the jar command seems to be identical to the unzip command which you may Habread User Manual Draft Do not distribute 35 already have If you have unzip then you only need the JRE HabRead is a standalone program Java programs are often run as Applets in a web browser However HabRead requires access to system resources like reading and writing files which is considered a security violation for Applets HabRead will run under Linux Unix Apple and Windows operating systems Installing the program involves picking a starting directory where you put the hab plan jar file and then typing e jar xvf habread jar This will uncompress the files that are in a Java Archive jar file The JAR utility comes with the J2SE If you only want to download the JRE you should be able to unzip the jar file using the PKUNZIP utility You will now have a directory called HabReadl Now type the following e cd Habread e java Habread After a
30. is that Habplan deals with whole stand outputs not per acre values If the values in the MPS file are per acre then they need to be converted to whole stand You will need to provide a file of stand sizes in order for HabRead to do this internally The mechanisms of this procedure will be dealt with later Another important point is that Habplan typically deals in annual increments or periods Often an LP planning horizon is broken down into 5 or 10 year periods Furthermore the period length can vary For example the planning horizon might be broken into four 5 year periods followed by four 10 year periods for a total horizon length of 60 years Habplan could handle 5 or 10 year periods but the period length shouldn t vary When dealing with Habread User Manual Draft Do not distribute 5 spatial issues like block size and green up windows it is usually necessary to have annual increments instead of multi year planning periods The Habplan and LP objective functions are quite different which is why Habplan can t utilize all of the data in an MPS file The following subsections give a brief overview of the Metropolis algorithm MA and the objective function that Habplan uses There is also an overview of the LP Model I formulation that is compatible with Habplan Finally there is a discussion about how HabRead extracts data from an MPS file See the Appendix for some additional background on harvest scheduling and the Model I and Model II form
31. le F Y These constraints are named F A which refers to the F low A ccounting constraint for flow component n in year t The flow volumes the ap values associated with each decision variable are taken from the associated Flow file The following is an example of data from the Flow file upon which the example tableau Figure 1 is based 111100 1 2 2 200 211150 2 2 2 200 The numbers in the first column represent the polygon ID the numbers in the second column represent the regime assigned to the polygon the numbers in the third column represent the year in which output occurred and the numbers in the fourth column represent the contribution of each decision variable to the flow volume of a given year F Y The seventh and eighth rows in Figure 1 constitute the flow constraints which are dif ferent from the flow accounting constraints These constraints are imposed to control the Habread User Manual Draft Do not distribute 9 trend and variability of periodic flow and have the following form Dey x my t 1 T 1 where U and L are user defined upper and lower proportions to control the change in flow from one time to the next 2 3 How does HabRead deconstruct the MPS file HabRead can input an MPS file that is either in the traditional fixed field width format or in a more flexible variable field width format The variable format can have fields separated by white space commas or tabs The fixed field format usu
32. led temperature parameter as with simulated annealing as presented by Lockwood and Moore 1993 Rather the individual component weights can be adjusted for finer control of convergence properties Habread User Manual Draft Do not distribute 6 The objective function is a sum of components multiplied by weights The components of interest when using HabRead are FLOW and BIO2 components FLOW components deal with maintaining even flow of a particular quantity over time BIO2 components allow you to bias the results of a Habplan run to favor regimes with larger ranks Typically the ranking is based on present net value so regimes that make more money are favored However the ranking could be based on habitat value as well 2 2 LP formulation A brief introduction to the type of LP formulation that is compatible with Habplan is useful For convenience a simple LP example is summarized in the form of a tableau Figure 1 This example consists of 4 decision variables 1 flow component and a planning period of 2 years This simple LP problem will be referred to for explanation purposes Row Name i X5 X4 X FLY FY Row Type RHS Description cix 10 20 30 40 0 0 Objective function P 1 1 E 1 Acreage constraint P 1 1 E 1 Acreage constraint FA 100 150 a E 0 Flow accounting FA 200 250 1 E 0 Flow accounting Fil 0 9 1 L 0 Flow constraint FH 1 1 1 L 0 Flow constraint Figure 1 Example of an LP Tableau The linear programming al
33. ng horizon These stands will contribute to blocksizes in the first few years of the planning horizon until they green up and should be accounted for Habplan provides two ways to do this 1 Start the planning horizon several years ahead of the current year 2 Designate pre cut years in a flow file as negative numbers The first method requires you to designate the early years of the planning horizon as byGone on the Habplan Flow Edit Form The regimes that were actually applied are supplied for the stands in the byGone years Habplan makes no effort to schedule things in these byGone years since they are in fact already scheduled The second approach may often be easier to implement and Habread can help you The idea is to create a Flow dataset that has years when precutting occurred designated by 1 1 year before the start of the planning horizon 2 2 years before etc In order to do this there must be 2 additional columns in the polygon dbf file The first is the PreCut Indicator column This column will contain a symbol such as Y to indicate that this Habread User Manual Draft Do not distribute 2T polygon or stand was pre cut The second column is the PreCut Year column which gives the period when the pre cutting occurred relative to planning period 1 For example a 0 means it occurred in period 0 1 in period 1 and 1 would mean in period 1 There is also a space to give the Indicator and the first p
34. ns that make up a unit Therefore there will be more polygons than units The size column gives the size area of each polygon This is used to apportion the output for a MU to its component polygons If you also have a shapefile that goes with the dbf file you could then use Habgen to generate a file for controlling block size The first step is to read the mps file and create the BIO2 table as discussed previously Then press the Expand button on the bottom of the BIO2 Table This will give you Habread User Manual Draft Do not distribute 22 something like what is shown in Figure 13 A BIO2 Table File Edit Tools Polygon File B home pvandeus myjava Habread1 1 Polygon Regime F Expand Management Units to Polygons 001 79409 07 0 none v 002 94716 80 sone v 003 79409 07 004 97221 33 005 86225 31 Inone v 006 78237 29 007 81394 09 Expand Units 008 78237 29 lana Qee 70 Figure 13 Before Expanding Management Units to Component Polygons The next step is set the file name to your dbf file Then press the SetColumns button to select the column names that correspond to Polygon Unit and Siz e If these names are in the dbf file they will be located automatically Then press the Read button to read the dbf file Finally press the Expand Units button to start the process of replacing the managem
35. or clearcutting then it is a likely candidate for a Block component and could handle precut Habread User Manual Draft Do not distribute 28 Flow 1 Table File Edit Tools Regime 0058 0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 10012 0013 0014 0015 joo1s 0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 Row Row Save FlowTool Consistency Fill Expand Units Figure 19 Flow Data for a Stand Cut 1 Year Before the Planning Horizon stands in its data 3 83 3 Creating FLOW Data The next step is to create the flow data Following the same procedure as laid out in Examples 1 and 2 click on the first flow tab Flow 1 supply the flow prefix and press Generate on the Flow Make Tool to fill in the flow table Note that the Flow Make Tool displays the following words in red Result MPS Polygon Size This indicates that you are dealing with data that has been converted from per acre to whole stand outputs and occurs when the Per Polygon box on the Expand window is checked dealt with in the preceeding section on creating the BIO2 data If the Per Polygon box is not checked the following words are displayed in yellow on the Flow Make Tool Result Untransformed MPS Habread User Man
36. ou select the first row polygon 1 regime 1 in the Bio2 Table and press the AddDoNothing button it will make sure that each Habread User Manual Draft Do not distribute 12 Ho 1454 0 1443 666667 1433 333333 1411 0 1382 222333 d3510 1311332233 1277 655657 1235 666667 1191 666667 1146 333333 1038 5666657 105830 1003 333333 LEE AEG EEERRT 5 5 0 _ Rowe Row Col con Save MpsRead Translate AddDoNothing l Figure 3 Create the BIO2 Table polygon has a DoNothing regime Normally DoNothings won t show up in the LP formu lation because they have a zero objective function coefficient We assigned a value of 1 0 for this problem so they showed up in the MPS file If your data has no DoNothing regimes just insert a row at the top of the file using row and fill it in with the first polygon name and an appropriate regime name like DN and give it a value of 0 Then hit the AddDoNothing button to add this regime to all the other polygons The Translate button opens a tool Figure 4 that allows you to input translation tables to change the names of polygons and regimes to something more readable These are simple text files with 2 columns The regime and the polygon translation files have the same format The first column gives the polygon or regime code and the second column gives the new name The columns are separated by spaces
37. s designed to allow these organizations to add Habplan to their arsenal of planning tools while continuing to use legacy systems HabRead provides a spreadsheet like format that makes it relatively easy to transform an MPS file into Habplan compatible format Habplan is based on a different solution algorithm and objective function than LP so it can not directly utilize all of the information that is embedded in MPS files For example constraints on flows will not be used However much of the basic data can be transformed into Habplan format The objective function coefficients form the basis for Habplan s BIO2 component The data for various kinds of flows can also be utilized 2 Habplan and Linear Programming Overview Habplan uses what has been traditionally called a Model I formulation which requires stand specific information Habplan solutions are integer so only one regime can be assigned to each stand for a particular management schedule LP has no such constraint and it is pos sible for a stand or management unit to be assigned in fractional parts to many regimes In effect this gives LP more degrees of freedom for solving problems with competing con straints The LP solution leaves the final decision about what to actually do in the forester s hands However Habplan does not eliminate the need for a forester s expertise Habplan can provide multiple integer solutions and the forester can select among these alternatives A key point
38. s that will be readable by Habplan Figure 9 Flow1 Make Tool and Flow1 Table Habread User Manual Draft Do not distribute E Flow2 Make Tool Figure 11 Flow3 Table for controlling regenerated acres 20 Habread User Manual Draft Do not distribute 21 Bi5iHB5H BHB HB5H B HB5mB B Bo Polololololololoololo f Figure 12 Flow4 Table for controlling thinned acres 3 2 3 Expanding Management Units MPS data often represent aggregations of stands into management or cutting units MUs In other words what has been previously called a polygon might actually be a MU consisting of several polygons or stands HabRead can help you split these MUs into their component polygons The following section is an extention of Example 2 in that it is based on the same data but we now assume that the MPS data represents MUs and not separate polygons This is also the place where per acre values from the mps file can be expanded to per polygon values which is what Habplan requires In order to split the MUs into their component polygons one has to provide a dbf file that has the following columns 1 Polygon 2 Unit and 3 Size The names in the Unit column should correspond to the names in the MPS file The polygon names correspond to the polygo
39. s you have in your current database for the polygons Likewise any regime name can be used but give serious thought to naming regimes so that it s easy to interpret the output Habplan has to work harder when there are lots of regimes so don t create regimes that represent trivial variations For example cutting in May shouldn t be considered different from cutting in June If 2 polygons are going to be clearcut in 2010 as the only management activity then they are managed under the same regime There should also be a do nothing regime assigned to each polygon unless there is a good reason not to do so e g the polygon was already cut in a byGone year This allows Habplan flexibility in meeting your goals For example it may be impossible to meet blocksize limits unless some polygons are assigned to the do nothing option more on Habread User Manual Draft Do not distribute 34 do nothings in a few paragraphs Usually each polygon has only a subset of regimes that are valid Valid regimes are indicated to Habplan by the way the flow and bio 2 datasets are constructed Specifically only include lines in these datasets for valid regimes Habplan checks all flow components and bio 2 components to determine the valid regimes If anything is included for a regime in both the Bio 2 or Flow data then Habplan assumes its a valid regime for that polygon If there are 10 regimes for polygon xyz in the flow data and 8 regimes in the bio 2 data then
40. tabs by selecting the option under the Flow menu You are allowed to have from 1 to 99 flow tabs Begin by supplying the prefix of the flow accounting variable This is based on the assumption that your MPS file has accounting variables that provide the sum of each Flow for each period in the planning horizon For this MPS file row names that begin with F1A Figure 1 contain Flow coefficients F1A1 are year 1 coefficients and F1A2 are for year2 etc Type in the prefix in the Flow Tool Figure 5 and press the Generate button to fill Habread User Manual Draft Do not distribute 14 in the Flow Table The flow table should contain all of the polygons and regimes that appear in the BIO2 Table Usually the DoNothing regimes and maybe entire polygons won t be obtainable from the MPS Flow accounting variables For example if this Flow component is for pine then the hardwood polygons won t be included in the table since they aren t involved in pine accounting However Habplan wants all polygons and regimes to appear in each flow dataset If the BIO2 table had do nothings added before reading the FLOW table the do nothings will be automatically carried over to the FLOW table In fact any regimes that are in BIO2 will be carried over to the FLOW table to ensure consistency However you can do a consistency check to verify this Press the Consistency button on the FLOW Table to find out if there are mis matches between the BIO2
41. the polygons that appear in BIO2 but not in Flow The other table gives polygons in Flow but not in BIO2 You should get the results in Figure 6 which indicate that there are no missings Inconsistencies must be dealt with If there are polygon names that appear in the Flow Table that don t belong then delete them If names need to be added then add them etc Don t ignore iconsistencies because Habplan won t accept the data Habread User Manual Draft Do not distribute 15 F1A ipm p Number of Polygons 419 Max Regimes Per Polygon 16 Years 1 to 15 Rows Row Col cor save FlowToot Consist FlowTool Consistency Figure 5 Generating Flow Data 3 1 3 Outputting Results to Habplan At this stage in HabRead development you need to output each data table to a directory where Habplan can access the files Select WriteData under a table s File menu to output the data to an ascii file Don t use the option of including the column names in the first row of the output file This file can then be input directly to Habplan as either a BIO2 component or a FLOW component This is done by filling out an Edit Form for the component in Habplan Habread User Manual Draft Do not distribute Names In Flow 1 but Not in BIO2 n m File Edit Tools Polygon Row No Missings No Missings Flow 1 Table File Edit Tools b l2 l2 o o o ooo O 1 l2 1 l
42. ual Draft Do not distribute 29 data Now after conducting the Consistency and Fill operations you are ready to click on the second flow tab Flow 2 and repeat this process for the Flow 2 component and all the subsequent flow components The data can now be output to files that are readable by Habplan Habread User Manual Draft Do not distribute 30 Flow1 Make Tool 2 Wes Flow 1 Table File Edit Tools Polygon Regime YET Out1 10001 0001 19 9 03 10001 0002 19 9 03 Generate 10001 0003 19 9 03 10001 0004 19 9 03 10001 0005 20 9 03 T 10001 0006 20 9 03 10001 0007 20 9 03 10001 9999 0 0 10002 0001 16 58 24 10002 0002 17 58 24 10002 0003 18 58 24 10002 0004 19 58 24 0005 20 58 24 0006 16 58 24 0007 16 58 24 B lanne 16 keza Row Save FlowTool Consistency Fill Expand Units Figure 20 Flow 1 Table for Controlling Clearcut Acres 3 3 4 Outputting Results to Habplan As for Examples 1 and 2 in order to output each data table BIO2 and Flow tables to a directory where habplan can access the files for each table select Writedata under the table s File menu Save the data to a designated directory from where Habplan will read the files and do not include the column names when saving when you press save a window will pop up giving you the option to in
43. ulation techniques may not be capable of finding the perfectly optimal solution they are capable of finding near optimal solutions sometimes within a few percent of the optimal Habplan uses a statistical simulation approach based on the Metropolis algorithm It also has limited built in LP capability which is useful in that it allows the user to compare the Metropolis algorithm solution to the non spatial optimal solution However those who are using HabRead already know what the LP solution is and want to find out what Habplan can do Habread User Manual Draft Do not distribute 39 References Lockwood C and T Moore 1993 Harvest scheduling with spatial constraints a simulated annealing approach Canadian Journal of Forest Research 23 468 478 5 Van Deusen P C 1999 Multiple solution harvest scheduling Silva Fennica 33 3 207 216 5 Van Deusen P C 2001 Scheduling spatial arrangement and harvest simultaneously Silva Fennica 35 1 85 92 5
44. ulations 2 1 Metropolis algorithm The Metropolis formulation used here has been described elsewhere Van Deusen 1999 2001 The first step is to select an initial schedule possibly at random which evolves at each iteration The schedule at iteration r is represented by the vector X zj cxW where x represents the regime assigned to polygon i at iteration r Each iteration of the algorithm creates a new and improved schedule that can be compared with other schedules using an objective function E X The overall objective function consists of a weighted sum of components where each component represents a particular sub objective The value of the objective function at iteration r is J E X ug 1 where w is a weight determined from the iteration r schedule and C X is the jth objective function component evaluated at the rth schedule The Metropolis algorithm iteratively considers new proposal regimes as substitutes for the current regime of each polygon The proposal regime is immediately accepted if it improves the overall schedule by decreasing the objective function 1 Proposals that are worse than the current regime can still be accepted according to a computed probability It is possible to escape a solution region that represents a local minima by sometimes accepting changes that don t improve the objective function This algorithm does not attempt to converge on a single best solution by slowly adjusting a so cal
45. ure 1 is based 1110 1 2 20 2130 2 2 40 The numbers in the first column represent the polygon ID the numbers in the second column represent the regime assigned to the polygon and the numbers in the third column represent the contribution of each decision variable c x to the objective function value So the objective function for this example would read as follows Max Z 10 xy 20 X12 30 X21 40 T22 Habread User Manual Draft Do not distribute 8 The third and fourth rows in Figure 1 constitute the acreage constraints of the form Ji 2 sged wedge j l where J is the number of valid regimes for polygon i This set of constraints is imposed to keep LP from assigning more than 100 of the polygon to its set of valid regimes These constraints are named P where i is the polygon number The fifth and sixth rows in Figure 1 constitute the flow accounting constraints which are included to allow LP to keep track of annual outputs of items such as clearcut acres and wood flow Thus these are not constraints in the true sense of the word but rather perform a summing function These constraints are of the form Qnjdij FY 0 A d Tij n t where the relevant z are those polygons and regimes that contribute to the output that is being accounted for in year t and for flow component n and the anj coefficients correspond to A in the general LP format give the contribution of each polygon to summary variab
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