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GAMS — A User's Guide

1. multiplication and division addition and subtraction unary and binary They are listed above in precedence order which determines the order of evaluation in an expression without parentheses Consider for example x 5 4 3 2 For clarity this could have been written x 5 4 3 2 In both cases the result is 41 ts It is better to use parentheses than to rely on the precedence of operators since it prevents errors and clarifies intentions ts Expressions may be freely continued over many lines an end of line is permissible at any point where a blank may be used Blanks may be used for readability around identifiers parentheses and operator symbols Blanks are not allowed within identifiers or numbers and are significant inside the quote marks used to delimit labels x n is calculated inside GAMS as exp n log x This operation is not defined if x has a negative value and an error will result If the possibility of negative values for x is to be admitted and the exponent is known to be an integer then a function call power x n is available Three additional capabilities are available to add power and flexibility of expression calculations They are indexed operations functions and extended range arithmetic 6 3 2 Indexed Operations In addition to the simple operations explained before GAMS also provides the following four indexed operations sum Summation over controlling index p
2. SOLVE SUMMARY MODEL TRANSPORT OBJECTIVE Z TYPE LP DIRECTION MINIMIZE SOLVER BDMLP FROM LINE 49 xx SOLVER STATUS 1 NORMAL COMPLETION x xx MODEL STATUS 1 OPTIMAL OBJECTIVE VALUE 153 6750 RESOURCE USAGE LIMIT 0 110 1000 000 ITERATION COUNT LIMIT 5 1000 The status reports are preceded by the same string as an error message so you should probably develop the habit of searching for all occurrences of this string whenever you look at an output file for the first time The desired solver status is 1 NORMAL COMPLETION but there are other possibilities documented in Section 10 5 page 91 which relate to various types of errors and mishaps There are eleven possible model status s including the usual linear programming termination states 1 OPTIMAL 3 UNBOUNDED 4 INFEASIBLE and others relating to nonlinear and integer programming In nonlinear pro gramming the status to look for is 2 LOCALLY OPTIMAL The most the software can guarantee for nonlinear programming is a local optimum The user is responsible for analyzing the convexity of the problem to determine whether local optimality is sufficient for global optimality 24 A GAMS Tutorial by Richard E Rosenthal In integer programming the status to look for is 8 INTEGER SOLUTION This means that a feasible integer solution has been found More detail follows as to whether the solution meets the relative and absolute optimality tolerances that the user specifies 2 11 7 So
3. lagval2 s leadval s lagval2 s 1 lagval2 s val s 2 leadval s 1 leadval s 1 val s option decimals 0 display val lagval2 leadval The results are shown below TERR 7 PARAMETER VAL SPRING 10 SUMMER 15 AUTUMN 12 WINTER 8 s 7 PARAMETER LAGVAL2 SPRING 12 SUMMER 8 AUTUMN 10 WINTER 15 5 7 PARAMETER LEADVAL SPRING 8 SUMMER 10 AUTUMN 15 WINTER 12 The parameter lagval2 is used for reference while lagval1 if used for assignment Notice that the case of circular lag and lead operators does not lead to any non existent elements The difference between reference and assignment is therefore not important Note that the following two statements from the example above lagval2 s val s 2 leadval s 1 val s are equivalent to lagval2 s 2 val s leadval s val s 1 The use of reference and assignment have been reversed with no difference in effect 13 6 Lags and Leads in Equations The principles established in the previous section follow quite naturally into equation definitions A lag or lead operation in the body of an equation to the right of the symbol is a reference and if the associated label is not defined the term vanishes A lag or lead to the left of the is a modification to the domain of definition of the equation The linear form may cause one or more individual equations to be suppressed t All lag and lead operands must be exogenous The
4. 7 2 1 The Syntax The declaration of a variable is similar to a set or parameter declaration in that domain lists and explanatory text are allowed and recommended and several variables can be declared in one statement var type variable s var_name text 1 var_name text Var_type is the optional variable type that is explained in detail later Var_name is the internal name of the variable also called an identifier in GAMS An identifier has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long The accompanying text is used to describe the set or element immediately preceding it This must not exceed 254 characters and must all be contained on the same line as the identifier it describes One important difference between variable and parameter declarations is that values cannot be initialized in a variable declaration A typical variable statement adapted from RAMSEY is shown below for illustration variables k t capital stock trillion rupees c t consumption trillion rupees per year i t investment trillion rupees per year utility utility measure The declaration of k above implies as usual that references to k are restricted to the domain of the set t A model that includes k will probably have several corresponding variables in the associated mathematical programming 66 Variables problem most likely one for each member
5. Consider the following example log log The following message will be written to the log file log with leading blanks ignored All special symbols will log be substituted out before this text is sent to the log file log This was line system incline of file system incnamef log The log file that results by running the lines above looks as follows Starting compilation CC GMS 0 138 Kb The following message will be written to the log file with leading blanks ignored All special symbols will be substituted out before this text is sent to the log file This was line 5 of file C PROGRAM FILES GAMSIDE CC GMS CC GMS 7 138 Kb Starting execution empty program Status Normal completion Note that system incline has been replaced by 5 which is the line number where the string replacement was requested Also note that system incname has been substituted by the name of the file completed with the absolute path Also note that the leading blanks on the second line of the example are ignored maxcol n 255 Sets the right margin for the input file All valid data is before and including column n in the input file All text after column n is treated as comment and ignored Consider the following example maxcol 30 set i vienna rome set definition scalar a 2 3 scalar definition The text strings set definition and scalar definition are treated as comments and ignored since they b
6. If an additional name is provided for row and used in the second index position then there will be two controlling indices and GAMS will make assignments over the full Cartesian product all 100 values Consider the following example alias row rowp b row rowp 7 7 r row r rowp 6 2 6 Extended Range Identifiers in Assignments The GAMS extended range identifiers can also be used in assignment statements as in a row col 10 inf a row col 1 inf Extended range arithmetic will be discussed later in this Section The values most often used are NA in incomplete tables and INF for variable bounds 6 2 7 Acronyms in Assignments Acronyms can also be used in assignment statements as in acronym monday tuesday wednesday thursday friday parameter dayofweek dayofweek wednesday t Acronyms contain no numeric value and are treated as character strings only 6 3 Expressions An expression is an arbitrarily complicated specification for a calculation with parentheses nested as needed for clarity and intent In this section the discussion of parameter assignments will continue by showing in more detail the expressions that can be used on the right of the sign All numerical facilities available in both standard and extended arithmetic will be covered 6 3 1 Standard Arithmetic Operations The standard arithmetic symbols and operations are eK exponentiation 54 Data Manipulations with Parameters
7. growth t in an iterative rather than a parallel way In this example there is one statement in the scope of the loop and one driving or controlling set A loop is often used to perform iterative calculations Consider the following example which uses finds square roots by Newton s method This example is purely for illustration in practice the function sqrt should be used Newton s method is the assertion that if x is an approximation to the square root of v then x v x 2 is a better one set i set to drive iterations i 1 i 100 parameter value i used to hold successive approximations scalars target number whose square root is needed 23 456 sqrtval final approximation to sqrt target curacc accuracy of current approximation reltol required relative accuracy 1 0e 06 abort target lt 0 argument to newton must be positive target value i 1 target 2 curacc 1 loop i curacc gt reltol value i 1 0 5 value i target value i sqrtval value i 1 curacc abs value i 1 value i 1 abs value i 1 3 abort curacc gt reltol square root not found option decimals 8 display square root found within tolerance sqrtval value The output is e 18 square root found within tolerance 18 PARAMETER SQRTVAL 4 84313948 final approximation to sqrt target nae 18 PARAMETER VALUE used to hold successive approximations i 1 11 72800000 i 2 6 86400000 i
8. handle spaces and or We could use the original and use s3 which will strip and makes the name short gmsrerun cmd will resubmit runit cmd echo echo off gt 3runit cmd echo 1 2 gt gt 3runit cmd echo gmscr_nx exe 2 gt gt 3runit cmd echo echo OK gt 3finished gt gt 3runit cmd echo exit gt gt 3runit cmd echo start b 3runit cmd gt nul gt 3gmsrerun cmd start b 3runit cmd gt nul exit 1 6 1 Grid Submission Testing The grid submission process can be tested on any GAMS program without having to change the source text The solvelink 4 option instructs the solve statement to use the grid submission process and then wait until the results are available and then loads the solution into the GAMS data base The solvelink option can be set via a GAMS command line parameter or via assignment to a the model attribute Once the model instance has been submitted for solution GAMS will check if the job has been completed It will keep checking twice the reslim seconds allocated for this optimization job and report a failure if this limit has been exceed After successful or failed retrieval of the solution gams will remove the grid directory unless we have used gamskeep or have set the gams keep parameter 1 7 Glossary and Definitions 245 1 7 Glossary and Definitions BCH Condor GAMS GDX HPC SUN Grid Compute Utility Branch amp Cut amp Heuristic High throughput computing sy
9. offinline turn off in line comments ontext on text following lines are comments offmargin turn off margin marking Options affecting input data format dollar sets the dollar character onempty allow empty data initialization statements offdigit off number precision check onend allow alternate program control syntax offempty disallow empty data initialization statements oneps interpret eps as 0 offend disallow alternate program control syntax onglobal force inheritance of parent file settings offeps disallow interpretation of EPS as 0 onwarning relax domain checking for data offglobal disallow inheritance of parent file settings use205 Release 2 05 language syntax offwarning enforce domain checking for data use225 Release 2 25 Version 1 language syntax ondigit on number precision check use999 latest language syntax Options affecting output format double double spaced listing follows ondollar turns the listing of DCO lines on eject advance to next page oninclude include file name echoed to listing file hidden ignore text and do not list onlisting input file s echoed to listing file lines next number of lines have to fit on page onupper following lines will be printed in uppercase offdollar turns the listing of DCO lines off single single spaced listing follows offinclude turn off listing of include file names stars sets characters in listing file offlisting turns off echoing input file s to listing file stitle set subtitle and reset
10. 182 GAMS option 217 LP model type 15 78 It relational operator 30 103 mapping sets 39 maps 264 INDEX symbol listing 89 symbol reference 87 MARCO example from GAMSLIB 81 marginal 69 98 165 value m 67 matrix element 165 max function 55 74 maxcol dollar control option 203 maxExecError function 59 maximizing 80 mcp GAMS call parameter 182 GAMS option 217 MCP model type 16 78 MEXSS example from GAMSLIB 147 min function 55 74 mincol dollar control option 204 minimizing 80 minlp GAMS call parameter 182 GAMS option 218 MINLP model type 16 78 mip GAMS option 218 MIP model type 15 78 95 miqcp GAMS call parameter 182 GAMS option 218 MIQCP model type 15 mod function 55 model library 169 statistics 92 status 94 styles 29 syntax of statement 77 types 78 model status error no solution 94 infeasible 94 integer solution 94 model attributes bratio 78 domlim 78 domusd 78 iterlim 78 iterusd 78 limcol 78 limrow 78 modelstat 78 numequ 78 numinfes 78 numnz 78 numopt 78 numvar 78 optca 78 optcr 78 optfile 78 reslim 78 resusd 78 scaleopt 78 solprint 78 solveopt 78 solvestat 78 sysout 78 workspace 78 model classification CNS 78 DNLP 78 LP 78 MCP 78 MINLP 78 MIP 78 MIQCP 78 MPEC 78 NLP 78 QCP 78 RMINLP 78 RMIP 78 RMIQCP 78 model generation 165 model list 165 model status error unknown 94
11. Model portfolio fsum dmean dvar Solve portfolio using nlp minimizing variance 10 3 Compilation Output This is the output produced during the initial check of the program often referred to as compilation It contains two or three parts the echo print of the program an explanation of any errors detected and the maps The next four sub sections will discuss each of these in detail 10 3 1 Echo Print of the Input File The Echo Print of the program is always the first part of the output file It is just a listing of the input with the lines numbers added The offlisting directive would turn off the listing of the input file A Quadratic Programming Model for Portfolio Analysis ALAN SEQ 124a This is a mini mean variance portfolio selection problem described in gt GAMS MINOS Three examples by Alan S Manne Department of Operations Research Stanford University May 1986 9 This model has been modified for use in the documentation Note that the first line number shown is 9 If the lines on the input are counted it can be seen that this comment line shown above appears after 8 lines of dollar directives and comments The line starting title has caused text of the users choice to be put on the page header replacing the default tile which just announces GAMS The following directives are used to display more information in the output file and we be discussed The text within the ontext offtext pair is listed without
12. Thus it is very useful to have the table format for data entry An example of a two dimensional table or matrix is provided the transportation model Table d i j distance in thousands of miles new york chicago topeka seattle 2 5 1 7 1 8 san diego 2 5 1 8 1 4 The effect of this statement is to declare the parameter d and to specify its domain as the set of ordered pairs in the Cartesian product of i and j The values of d are also given in this statement under the appropriate heading If there are blank entries in the table they are interpreted as zeroes As in the list format GAMS will perform domain checking to make sure that the row and column names of the table are members of the appropriate sets Formats for entering tables with more columns than you can fit on one line and for entering tables with more than two dimensions are given in Chapter 5 page 43 2 4 3 Data Entry by Direct Assignment The direct assignment method of data entry differs from the list and table methods in that it divides the tasks of parameter declaration and parameter assignment between separate statements The transportation model contains the following example of this method Parameter c i j transport cost in thousands of dollars per case c i j f d i j 1000 It is important to emphasize the presence of the semicolon at the end of the first line Without it the GAMS compiler would attempt to interpret both lines as parts of the same statem
13. Used to complete a file name for sysinclude If the sdir option is not set the GAMS system directory is searched ts Unlike idir additional directories cannot be set with sdir The string passed will be treated as one directory Passing additional directories will cause errors t Note that if the sdir parameter is set the default system include directory is not searched Consider the following illustration gams myfile sdir mydir GAMS searches for any referenced sysinclude file in the directory mydir tabin tabin 8 tab spacing This option sets the tab spacing By default tabs are not allowed in GAMS However the most common setting is 8 which results in the positions of the tabs corresponding to columns 1 9 17 and the intermediate columns being replaced by blanks Values O tabs are not allowed 1 tabs are replaced by blanks n tabs are 1 n 1 2n 1 tformat tf 0 time format This option controls the time format in the listing file The three date formats correspond to the various con ventions used around the world For example the time 7 45 PM will be written as 19 45 00 with the default tf value of 0 and as 19 45 00 with tf 1 Values 0 hh mm ss 1 hh mm ss topmargin tm 0 top margin This option controls the width of the top margin of the text in the listing file If tm is greater than 0 blank lines added at the top of a page trace trace tezt trace file name The trace file name is completed using the cu
14. You can find a complete example of a grid enabled transport model in the GAMS model library At a final note we have made no assumptions about what kind of solvers and what kind of computing environment we will operate The above example is completely platform and solver independent and it runs on your Windows laptop or on a massive grid network like the Condor system without any changes in the GAMS source code I 4 Advanced use of Grid Features In this section we will describe a few special application requirements and show how this can be handled with the current system Some of those applications may involve thousands of model instances with solution times of many hours each Some may fail and require resubmission More complex examples require communication and the use of GAMS facilities like the BCH Branch amp Cut amp Heuristic which submit other models from within a running solver 1 4 1 Very Long Job Durations Imagine a situation with thousands of model instances each taking between minutes and many hours to solve We will break the master program into a submitting program an inquire program and a final collection program We will again use the previous example to demonstrate the principle We will split the GAMS code of the modified QMEANVAR GAMS code into three components qsubmit qcheck and qreport The file qsubmit gms file will include everything up to and including the new submit loop To save the instances we will need a uniqu
15. allowed for the solver The solver will stop as soon as the limit on time usage has been reached The default limit on time usage is 1000 seconds This limit can be changed by entering a line containing the statement option reslim xx in the program before the solve statement where xx is the required limit on CPU time in seconds ITERATION COUNT LIMIT 5 1000 These two entries provide the number of iterations used by the solver as well as the upper limit allowed for the solver The solver will stop as soon as this limit is reached The default limit on iterations used is 1000 This limit can be changed by entering a line containing the statement option iterlim nn in the program before the solve statement where nn is the required limit on the iterations used EVALUATION ERRORS 0 0 These two entries provide the number of numerical errors encountered by the solver as well as the upper limit allowed for the solver These errors result due to numerical problems like division by 0 This is suppressed for LP RMIP and MIP models since evaluation errors are not applicable for these model types The default limit on evaluation errors used is 0 This limit can be changed by entering a line containing the statement option domlim nn in the program before the solve statement where nn is the required limit on the evaluation errors allowed The SOLVER STATUS and MODEL STATUS require special explanation The status for the solver the state of the
16. can be read as condition1 and condition2 t For nested dollar conditions all succeeding expressions after the dollar must be enclosed in parentheses 11 4 Conditional Assignments 107 Consider the following example u k s k t k a k K s k t k and i are sets while u k and a i are parameters The assignment will be made only for those members of k that are also members of both s and t Note the position of the parenthesis in the dollar condition The statement above can be rewritten as u k s k and t k a k ts To assist with the readability of statements it is strongly recommended to use the logical and operator instead of nesting dollar operators 11 4 Conditional Assignments The statement comprising the example in the Section before was a conditional assignment In this example the dollar condition was on the left hand side of the assignment ts The effect of the dollar condition is significantly different depending on which side of the assignment it is in ts In many cases it may be possible to use either of the two forms of the dollar condition to describe an assignment In such a case clarity of logic should be used as the criterion for choice The next two subsections describe the use of the dollar condition on each side of the assignment 11 4 1 Dollar on the Left The example illustrated in the section above uses the dollar condition on the left hand side of the assignment statemen
17. functions can be imported from an external library into a GAMS model Apart from the import syntax the imported functions can be used in the same way as intrinsic functions In particular they can be used in equation definitions Some function libraries are included with the standard GAMS software distribution but GAMS users can also create their own libraries using an open programming interface Simple examples in the programming languages C Delphi and Fortran come with every GAMS system Contact support gams com for detailed instructions Using Function Libraries Function libraries are made available to a model using a compiler directive FuncLibIn lt InternalLibName gt lt ExternalLibName gt Note that the Function Library Facility gives you complete control over naming so that potential name conflicts between libraries can be avoided The lt InternalLibName gt will be used to refer to the library inside your model source code The lt ExternalLibName gt is the one given the library when it was created To access libraries included with your GAMS distribution you use the library s name with no path GAMS will look for the library in a standard place within the GAMS installation To access a library that is not part of the standard GAMS distribution the external name must include the absolute path of the library s location When processing the FuncLibIn directive GAMS will validate the library make the included functions available for
18. limcol output pagesize profile suppress topmargin dumpparms logfile logoption save sets compile time error limit singe keyword value pair option error message option force workfile translation keep flag default CNS solver sets current directory error message file name execution time error limit sets input search path sets library include directory default LP solver default MINLP solver nonlinear instructions search length secondary parameter file symbol reference file default RMINLP solver sets scratch directory first line written to gamsnext scratch name solver dictionary file name solver instruction file name solver solution file name sets configuration file name sets system directory trace file name strings passed to subsystems control Z indicator sets input file name optimization level for GAMS execution option file indicator sets tab spacing sets bottom margin in listing file sets date format default column listing sets output file name sets page size global execution profiling option compilation listing option sets top margin in listing file controls parameter logging sets log file name log file option sets save file name Table C 1 GAMS command line parameters 192 The GAMS Call D Dollar Control Options D 1 Introduction The Dollar Control Options are used to indicated compiler directives and options Dollar control options are not part of the GAMS langua
19. listing 92 comma in data lists 32 in put statements 134 comment dollar control option 197 using eolcom 33 using inlinecom 33 compilation 163 actions during 172 errors 99 errors at time 100 output 86 complement a set operation 117 compress 233 Compressed and Encrypted Input Files 233 conditional expressions numerical values 105 operator precedence 105 using set membership 104 with logical operators 104 with numerical relationship operators 103 constant set 163 constraint 163 continuous 163 control reference type 88 controlling index 52 set 47 149 controlling sets 163 cos function 55 cosh function 55 cosine function 251 CRAZY example from GAMSLIB 62 101 ctrlm GAMS call parameter 173 ctrlz GAMS call parameter 173 curdir GAMS call parameter 173 cvPower function 55 data entered as parameters 44 entered as tables 46 entry 43 handling aspects of equations 75 manipulations with parameters 51 type 29 data types 163 decimals GAMS option 217 decimals global option 130 declaration 163 of a model 77 parameter 44 scalar 43 separation between and definition of 28 statements 28 table 45 decompress 233 default 163 defined a reference type 88 definition 164 of a model 77 of data 29 of equation 72 of scalars 44 of symbols 29 statements 28 definition statements 164 dformat GAMS call parameter 174 difference set oper
20. or symbolic definition equation starts for the symbol ASSIGNED This is when values are replaced because the identifier appears on the left of an assignment statement IMPL ASN This is an implicit assignment an equation or variable will be updated as a result of being referred to implicitly in a solve statement CONTROL This refers to the use of a set as the driving index in an assignment equation loop or other indexed operation sum prod smin or smax REF This is a reference the symbol has been referenced on the right of an assignment in a display in an equation or in a model or solve statement 10 3 Compilation Output 89 10 3 3 The Symbol Listing Map The next map is called the Symbol Listing All identifiers are grouped alphabetically by type and listed with their explanatory texts This is another very useful aid to have handy when first looking into a large model prepared by someone else The symbol listing map can be turned on by entering a line containing onsymlist at the beginning of the program Symbol Listing SETS I securities J Aliased with I PARAMETERS HIGHRISK variance of highest security risk LOWYIELD yield of lowest yielding security MEAN mean annual returns on individual securities TARGET target mean annual return on portfolio 7 V variance covariance array squared annual return VARIABLES VARIANCE variance of portfolio X fraction of portfolio invested in asset i EQUATIONS DMEAN
21. 1 6 3 Expressions 59 ghourSDAY gleap SDAY gmillisec SDAY gminute SDAY gmonth SDAY gsecond SDAY gyear SDAY jdate YEAR MONTH DAY jnow jstart jtime HOUR MIN SEC any any any any any any any any none none any returns Gregorian hour of day from a serial day number date time where Jan 1 1900 is day 1 returns 1 if the year that corresponds to a serial day number date time where Jan 1 1900 is day 1 is a leap year else returns 0 returns Gregorian milli second from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian minute of hour from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian month from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian second of minute from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian year from a serial day number date time where Jan 1 1900 is day 1 returns a serial day number starting with Jan 1 1900 as day 1 returns the current time as a serial day number starting with Jan 1 1900 as day 1 returns the time of the start of the GAMS job as a serial day number starting with Jan 1 1900 as day 1 returns fraction of a day that corresponds to hour minute and second GAMS utility and performance functions errorLevel execError gamsRelease gamsVersion handleCollect HANDLE handleDelete HANDLE none
22. 3 5 14062471 i 4 4 85174713 i 5 4 84314711 i 6 4 84313948 i 7 4 84313948 16 3 The If Elseif Else Statement The if else statement is useful to branch conditionally around a group of statements In some cases this can also be written as a set of dollar conditions but the if statement may be used to make the GAMS code more readable An optional else part allows you to formulate traditional if then else constructs 16 3 1 The Syntax The syntax for an if elseif else statement is 16 3 The If Elseif Else Statement 151 if condition statements felseif condition statements else statements where condition is a logical condition t One cannot make declarations or define equations inside an if statement 16 3 2 Examples Consider the following set of statements pCi f lt 0 1 p i f gt 0 and f lt 1 p i 2 p i f gt 1 p i 3 q j f lt 0 1 q j gt 0 and lt 1 q j 2 q j gt 1 q j 3 They can be expressed using the if elseif else statement as if f lt 0 p i 1 q j 1 elseif f gt 0 and f lt 1 pCi p i 2 a j q j 2 else p i p i 3 a j q j 3 Dis The body of the if statement can contain solve statements For instance consider the following bit of GAMS code if ml modelstat eq 4 model ml was infeasible relax bounds on x and solve again x up j 2 x up j solv
23. 4 A Error Message 170 DOMAIN VIOLATION FOR ELEMENT Example 4 Similarly if we mistakenly enter dem j instead of b j as the right hand side of the demand constraint the result is 2 11 GAMS Output 21 45 demand j sum i x i j g dem j AK 140 Error Message 140 UNKNOWN SYMBOL ENTERED AS PARAMETER Example 5 The next example is a mathematical error which is sometimes committed by novice modelers and which GAMS is adept at catching The following is mathematically inconsistent and hence is not an interpretable statement For alli XC zij 100 2 There are two errors in this equation both having to do with the control of indices Index 7 is over controlled and index 7 is under controlled You should see that index 7 is getting conflicting orders By appearing in the quantifier for all 7 it is supposed to remain fixed for each instance of the equation Yet by appearing as an index of summation it is supposed to vary It can t do both On the other hand index j is not controlled in any way so we have no way of knowing which of its possible values to use If we enter this meaningless equation into GAMS both errors are correctly diagnosed meaninglss i sum i x i j e 100 Ao 125 149 ERROR MESSAGES 125 SET IS UNDER CONTROL ALREADY This refers to set i 149 uncontrolled set entered as constant This refers to set j A great deal more information about error reporting is given in Section 10 6
24. A Fist Bele oo colarse sr ae ee ee ee ee a a 233 He The CEFILES Gamsllb Model cc cec causse Re oe La eae Eee ew Re 234 HA The ENCRYPT GAMBLIB Model ee mave ee ck ee ee EON Ee ee EERO See 235 I The GAMS Grid Computing Facility 237 Li Tatroduction 2 64 2544 46c8 4808 Beau dd eee a ade ed de de a e ad i e A 237 LE Basie COMBOS ion cid A A AE ES Oe Oe eS 237 La A First Example eae id ee a ee ae EE A DE ee ee 238 La Advanced use of Grid Featur s occ qa Re a e a 240 10 TABLE OF CONTENTS 1 5 1 6 L 14 1 Very Long Job Durations Summary of Grid Features L5 1 Grid Handle Functions 1 5 2 Grid Model Attributes 1 5 3 Grid Solution Retrieval L54 Grd Directory ceai epa so Architecture and Customization 1 6 1 Grid Submission Testing Glossary and Definitions J Extrinsic Functions J l J 2 J 3 J 4 J 5 TRUE Ci ace a OE a A A Rw x Fitpack Library gt gt ss ecni ee ev iape ee Piecewise Polynomial Library K Installation and System Notes Index Stochastic LIDrAEF o cr ec sara niaaa taaa Trigonometric Library List of Tables 21 2 2 dad 3 1 3 2 3 3 3 4 4 1 6 1 6 2 6 3 fel Sl 8 2 11 1 14 2 113 14 1 14 2 C 1 D 1 E 1 Jud J 2 Jo J 4 J 5 Data for the transportation problem adapted from Dantzig 1963 6 The basic components of a GAMS model a 8 Permissible variable types oo c 6 kk ee a ar
25. ARCTAN CEIL SETS I canning plants J markets PARAMETERS A capacity of plant i in cases B demand at market j in cases Cc transport cost in thousands of dollars per case D distance in thousands of miles F freight in dollars per case per thousand miles VARIABLES X shipment quantities in cases Z total transportation costs in thousands of dollars EQUATIONS COST define objective function DEMAND satisfy demand at market j SUPPLY observe supply limit at plant i MODELS TRANSPORT FILES FILE Current file name for FILE xxx use PREDEFINED DIAG SAMEAS This serves as a simple description of the symbols used in a model and can be used in reports and other documentation onjoff symxref onsymxref This option controls the following gt Collection of cross references for identifiers like sets parameters and variables gt Cross reference report of all collected symbols in listing file gt Listing of all referenced symbols and their explanatory text by symbol type in listing file This is also reported by using onsymlist Consider the following slice of code 210 Dollar Control Options offsymxref set j i will not show 1 3 display i onsymxref k 1 yes The resulting listing file will contain the following symbol reference reports SYMBOL TYPE REFERENCES I SET DECLARED 1 DEFINED 1 REF 1 K SET DECLARED 1 ASSIGNED 6 SETS I this is set declaration K some more on off text The ontext
26. Consequently the cr value remains constant throughout the writing of items for the next put statement even if multiple items are displayed It s behavior is similar to that of cl 15 13 3 Last Line Control These suffixes control the last line used in a writing area 11 last line used in window hd11 header last line t111 title last line Unlike the row and column control the last line suffix is updated continuously Last line suffixes are especially useful for modifying the various writing areas of a page gt The t111 and hd11 suffixes may not hold values applicable to the current page because when the title or header blocks are modified they correspond to the title or header blocks of the next page whenever the window has been written to on the current page t Not only can this suffix be used to determine the last line used in a writing area but it can also be used to delete lines within this area In the following example the header section will be completely deleted by resetting the hd11 suffix to 0 file out puthd out This header statement will be eliminated out hdll 0 In this example a header is initially written By changing the hd11 suffix to 0 the cursor is reset to the top of the header block Consequently the header will not be written unless something new is added to the header block 146 The Put Writing Facility 15 14 Paging Control In addition to the automatic paging which occurs wh
27. Dynamic Sets 2 0er ra ee SEL DEDOS lt 2 as aa A AA Had A eR ok AAA T241 A ca a a ece eri i eae aw ee eet EAB ee ee ea 124 2 Set Intersection padi bk be a A a A eR ee ee A a lado Got LORCA eee eR OSES ee 1244 Bet Difference ias coca coro deea ae ee ee A da ee ee PURE ak hk ey a BE Hk BO a hep PP ase ay a Sin Se BE Be a Se ee S 13 Sets as Sequences Ordered Sets 13 1 13 2 13 3 13 4 13 5 13 7 a c e ae e a ro ee Be De ee ee ee Pee Pe eee EG a e o o a we a Ordered and Unordered Bets aa acie a acca oe a a ek ah A a E A A eee a Ord ond GATA o cir EN E Tasi The Ord DE A AE A A A De ee els 1332 Tho Carer i ch E A A a E aaaea Lag and Lead Operators is s ea corn a e a E is ee ae ee eS Lags and Leads la Assignments so io a a Pe aaa 13 5 1 Linear Lag and Lead Operators Reference o e 00002080 13 5 2 Linear Lag and Lead Operators Assignment o 13 5 3 Cironlar Lag and Lead Operators i a A ee ee es Logs and Leads in Relais o nk eh a we a ee ee ee we Pe Ee ee es 13 6 1 Linear Lag and Lead Operators Domain Control o o 13 6 2 Linear Lag and Lead Operators Reference o 13 6 3 Circular Lag and Lead Operators 2 005 644 ce aa a o Se ee CG ee we a A Oe RAE Be ed he Bod Rae kw ee Ga 14 The Display Statement 14 1 14 2 14 3 14 4 14 5 Troon ke Gob Bane eee ee es ea ee Ok LG eS Owe ow alee es ThS Gyi so ya eg ee eer A Ral eo ee Oe ee ee Sa
28. ECS ee E Se ede BA SO ee A ae A The Label Order in Displays o o e e cei etenari e a ER eee eee ee eS MAL Eepe saa e a a bere AA ee Ne bd oe Meee ee Display COPOS osa e AR RA A AI A a aA 14 5 1 Global Display Controls ca cso vaa na 6 eee eee a a 11532 Local Display Control scores AAA We Ee de 14 5 3 Display Statement to Generate Data in List Format 15 The Put Writing Facility 15 1 15 2 15 3 15 4 eg AN EES Se Oe RRR eee eee ee eee ee The Gym 2 6 he DERE SH OER OME Oe Se a AR RRS Ba Berea ewe Ss iat pl at gs ee ee ae ae ae eS a a a Rae ee ae hte se A Mahe PUE be a ee ee Eee he eee Rae SSE aA ee Bie ee amp ee 15341 Dehwnig Piles isra 6 we Klee A ARS SO RS ee ae Pee ew alae Ial Assisuloa Piles e he ek ee we Ae eee Se a e AA Ws Come a las ra ype i ke a ek A oe eh eS ee AE ee se 113 113 113 113 113 114 114 115 115 115 116 116 116 116 117 117 117 117 117 119 119 119 120 120 121 121 121 122 122 123 123 124 124 125 125 127 127 127 127 128 129 129 130 130 131 TABLE OF CONTENTS 15 5 15 6 15 7 15 8 15 9 15 10 15 11 15 12 15 13 15 14 15 15 15 16 15 17 15 4 4 Appendingtoa File Page Formata La oa ee A Page SOELIONS 2 ciar A AA 15 6 1 Accessing Various Page Sections UGS LAB is aa we a ee A a ee BO Ge Positioning the Cursor ona Page Systemi WINER 2 ee ee a Dee eee ea A E Re Re as 159 1 Tex
29. ENDOG ARGUMENT S IN FUNCTION 9 Error Messages 51 Endogenous function argument s not allowed in linear models 54 Endogenous operands for not allowed in linear models 256 Error s in analyzing solve statement More detail appears Below the solve statement above 3 ERROR S 0 WARNING S USER ERROR S ENCOUNTERED 10 6 Error Reporting 101 10 6 3 Execution Errors Execution time errors are usually caused by illegal arithmetic operations such as division by zero or taking the log of a negative number GAMS prints a message on the output file with the line number of the offending statement and continues execution A GAMS program should never abort with an unintelligible message from the computer s operating system if an invalid operation is attempted GAMS has rigorously defined an extended algebra that contains all operations including illegal ones The model library problem CRAZY contains all non standard operations and should be executed to study its exceptions Recall that GAMS arithmetic is defined over the closed interval INF INF and contains values EPS small but not zero NA not available and UNDF the result of an illegal operation The results of illegal operations are propagated through the entire system and can be displayed with standard display statements However remember that one cannot solve a model or save a work file if errors have been detected previously 10 6 4 Solve Errors The execution of a s
30. Examples occ bee ee ae eA eee a 4 17 Special Language Features Ir 17 2 17 3 a o o s ae ni eae BAS we p goia e aa Bee dees Special MIP Features naaa ee 17 2 1 Types of Discrete Variables 17 2 2 Special Order Sets of Type 1 SOS1 17 2 3 Special Order Sets of Type 2 SOS2 17 2 4 Semi Continuous Variables 17 2 5 Semi Integer Variables 17 2 6 Setting Priorities for Branching Model Scaling The Scale Option ve The Seale Option 4 22 ve Soe perk ee ee a 1142 Variable Sealing coccion ow aoa TABLE OF CONTENTS 9 Vide Equation Sealing cosida a A A e wa AR e e a 159 UPA calme GT DONATOR o ic a BERE A ARA EA te R S a 160 Appendix 162 A Glossary 163 B The GAMS Model Library 169 C The GAMS Call 171 C1 The Generic no frills GAMS Call ae s sa ee e khoe naay ka a 171 C 1 1 Specifying Options through the Command Line o o 171 C 2 List of Command Line Parameters ooo 2 ss 172 C 3 Detailed Description of Command Line Parameters o 172 D Dollar Control Options 193 DL Tatoducthidi lt o oao aa eA ee a a A A 193 DIL TEMA ce be ri A AA wo E A AR 193 DS Listar Dellas Control Options ico occ ra sii dc e a Ee AAA 193 D 3 Detailed Description of Dollar Control Options 0202000004 194 E The Option Statement 215 EL INTEOUBIONS ck A se ae Re aa Re
31. GAMS coordinator The person who looks after the administration of a GAMS system and who will know what solvers are available and can tell you who to approach for help with GAMS problems Unlikely to apply to personal computer versions identifiers Names given to data entities Also called symbols index position s Another way of describing the set s that must be used when referencing a symbol of dimensionality one or more i e a vector or a matrix inequality constraint A constraint in which the imposed relationship between the columns is not fixed but must be either greater than or equal to or less than or equal to a constant The GAMS symbols g and 1 are used in equation definitions to specify these relationships infeasible Used to describe either a model that has no feasible solution or an intermediate solution that is not feasible although feasible solutions may exist See feasible above initialization Associating initial values with sets or parameters using lists as part of the declaration or definition or for parameters only using table statements list One of the ways of specifying initial values Used with sets or parameters most often for one dimensional but also for two and higher dimensional data structures list format One of the ways in which sets and parameters can be initialized and all symbol classes having data can be displayed Each unique label combination is specified in full with the associated non d
32. GAMS introduced with the first version of Release 2 25 The setting of the use205 option allows if to be used as an identifier since it was not a keyword in Release 2 05 use225 This option sets the GAMS syntax to that of first version of Release 2 25 This is mainly used for backward compatibility New keywords have been introduced in the GAMS language since the first version of Release 2 25 Models developed earlier that use identifiers that have since become keywords will cause errors when run with the latest version of GAMS This option will allow one to run such models Consider the following example use225 set for 1 2 3 scalar x The word for is a keyword in GAMS introduced with the later versions of Release 2 25 The setting of the use225 option allows for to be used as an identifier since it was not a keyword in the first version of Release 2 25 use999 This option sets the GAMS syntax to that of the latest version of the compiler This option is the default Consider the following example use225 set for 1 2 3 scalar x use999 for x 1 to 3 display x The word for is used as a set identifier by setting the option use225 and later the keyword for is used as a looping construct by setting the language syntax to that of the latest version by setting use999 E The Option Statement E 1 Introduction The option statement is used to set various global system parameters that control output detail solution proc
33. George B 1963 Linear Programming and Extensions Princeton University Press Princeton N J 6 A GAMS Tutorial by Richard E Rosenthal units of all entities are specified and fourth the units are chosen to a scale such that the numerical values to be encountered by the optimizer have relatively small absolute orders of magnitude The symbol K here means thousands of dollars The names of the types of entities may differ among modelers For example economists use the terms exogenous variable and endogenous variable for given data and decision variable respectively In GAMS the terminology adopted is as follows indices are called sets given data are called parameters decision variables are called variables and constraints and the objective function are called equations The GAMS representation of the transportation problem closely resembles the algebraic representation above The most important difference however is that the GAMS version can be read and processed by the computer Plants Shipping Distances to Markets 1000 miles Supplies New York Chicago Topeka Seattle 2 5 1 7 1 8 350 San Diego 2 5 1 8 1 4 600 Demands 325 300 275 Table 2 1 Data for the transportation problem adapted from Dantzig 1963 As an instance of the transportation problem suppose there are two canning plants and three markets with the data given in table 2 1 Shipping distances are in thousands of miles and shipping costs are assumed
34. INTERMEDIATE NONOPTIMAL This is again an incomplete solution but it appears to be feasible 8 INTEGER SOLUTION An integer solution has been found to a MIP mixed integer problem There is more detail following about whether this solution satisfies the termination criteria set by options optcr or optca 9 INTERMEDIATE NON INTEGER This is an incomplete solution to a MIP An integer solution has not yet been found 10 INTEGER INFEASIBLE There is no integer solution to a MIP This message should be reliable 11 LIC PROBLEM NO SOLUTION The solver cannot find the appropriate license key needed to use a specific subsolver ERROR UNKNOWN After a solver error the model status is unknown ERROR NO SOLUTION An error occurred and no solution has been returned No solution will be returned to GAMS because of errors in the solution process 14 NO SOLUTION RETURNED A solution is not expected for this solve For example the convert solver only reformats the model but does not give a solution 15 SOLVED UNIQUE This indicates a unique solution to a CNS model 16 SOLVED A CNS model has been solved but multiple solutions may exist 17 SOLVED SINGULAR A CNS model has been solved but the point is singular 18 UNBOUNDED NO SOLUTION The model is unbounded and no solution can be provided 19 INFEASIBLE NO SOLUTION The model is infeasible and no solution can be provided This is the list of possible SOLVER STATUS messages 1 NORMAL
35. Numerical Value Logical Value 1 lt 2 3 lt 4 2 True 2 lt 1 and 3 lt 4 0 False 4 5 3 10 8 17 125 True 4 5 3 or 10 8 l True 4 and 5 2 3 lt 6 2 True 4 and 0 2 3 lt 6 0 False Table 11 3 Examples of logical conditions 11 3 The Dollar Condition This section introduces the dollar operator which is one of the most powerful features of GAMS The dollar operator operates with a logical condition The term condition can be read as such that condition is valid where condition is a logical condition t The dollar logical conditions cannot contain variables Variable attributes like 1 and m are permitted however The dollar operator is used to model conditional assignments expressions and equations The following subsection provides an example that will clarify its use The next section will deal individually with the topic of using dollar conditions to model conditional assignments expressions and equations respectively 11 3 1 An Example Consider the following simple condition if b gt 1 5 then a 2 This can be modeled in GAMS using the dollar condition as follows a b gt 1 5 2 If the condition is not satisfied no assignment is made Note that one can read the as such that to clarify the meaning a such that b is greater than 1 5 equals 2 11 3 2 Nested Dollar Conditions Dollar conditions can be also nested The term conditioni condition2
36. SUMMARY part of the listing file shows the limit was used rmip default This option controls the solver used to solve rmip models For details cf option cns rminlp default This option controls the solver used to solve rminlp models For details cf option cns seed 3141 This option resets the seed for the pseudo random number generator solprint on This option controls the printing of the model solution in the listing file Using this specification suppresses the list of the solution following a solve on The solution is printed one line per row and column in the listing file off Solution details are not printed Although this saves paper we do not recommend it unless you understand your model very well and solve it often E 3 Detailed Description of Options 219 solslack 0 This option causes the equation output in the listing file to contain slack variable values instead of level values 0 Equation output in listing file contains level values between lower and upper bound values ik Equation output in listing file contains slack values between lower and upper bound values solveopt merge Controls the way solution values from a solve are returned to GAMS merge Old and new values merged together and new values over write old ones replace All old values associated with a variable or equation are reset to default values before new solution values are returned sysout off This option controls the printing of
37. Sets Sets can be assigned in a similar way to other data types One difference is that arithmetic operations cannot be performed on sets in the same way that they can on value typed identifiers parameters or variables and equations subtypes A dynamic set is most often used as a controlling index in an assignment or an equation definition or as the controlling entity in a dollar controlled indexed operation 12 2 1 The Syntax In general the syntax in GAMS for assigning membership to dynamic sets is set_name domain_name domain_label yes no Set_name is the internal name of the set also called an identifier in GAMS Yes and no are keywords used in GAMS to denote membership or absence respectively from the assigned set ts The most important principle to follow is that a dynamic set should always be domain checked at declaration time to be a subset of a static set or sets ts It is of course possible to use dynamic sets that are not domain checked and this provides additional power flexibility lack of intelligibility and danger Any label is legal as long as the dimensionally once established is preserved 12 2 2 Illustrative Example The following example adapted from ZLOOF is used to illustrate the assignment of membership to dynamic sets 114 Dynamic Sets set item all items dish ink lipstick pen pencil perfume subitemi item first subset of item pen pencil subitem2 item second subset of item
38. a group of price equations and totp is an equation that sums all the sectoral prices The domestic prices pd used in the calculation of the average price pbar are divided by four because there are four sectors in this example Also the 1 is appended to pd to indicate that this is the level of the variable in the solution of the model namely in dualmodel Thus the iterative procedure uses solution values from one iteration to obtain parameter values for the next one In particular both pbar and pd are used to compute the demand d for the i th product in time period t d i t Also the base year demand db and the growth factor g are used in that calculation Then when the new final demand vector d is calculated the two blocks of equations are solved again 9 5 Making New Solvers Available with GAMS This short section is to encourage those of you who have a favorite solver not available through GAMS Linking a solver program with GAMS is a straightforward task and we can provide documents that describe what is necessary and provide the source code that has been used for existing links The benefits of a link with GAMS to the developer of a solver are several They include gt Immediate access to a wide variety of test problems gt An easy way of making performance comparisons between solvers gt The guarantee that a user has not somehow provided an illegal input specification gt Elaborate documentation particularly of input formats is not
39. about nonlinear models The NON LINEAR N Z entry refers to the number of nonlinear matrix entries in the model All forms of nonlinearity do not have the same level of complexity For example x y is a simpler form of nonlinearity than exp x y So even though both these terms count as 1 nonlinear entry in the matrix additional information is required to provide the user with a feel for the complexity of the nonlinearity GAMS provides the CODE LENGTH entry as a good yardstick for this purpose There are two other entries DERIVATIVE POOL and CONSTANT POOL that provide some more information about the nonlinearity In general the more nonlinear a problem is the more difficult it is to solve The times that follow statistics are also useful The GENERATION TIME is the time used since the syntax check finished This includes the time spent in generating the model The measurement units are given and represent ordinary clock time on personal computers or central processor usage CPU time on other machines 10 5 4 The Solve Summary This is the point chronologically speaking where the model is solved and the next piece of output contains details about the solution process It is divided into two parts the first being common to all solvers and the second being specific to a particular one The section of the solve summary that is common for all solvers is first discussed The corresponding section for the example model is shown below SOLV
40. amounts of resources This option sets an absolute termination tolerance which means that the solver will stop and report on the first solution found whose objective value is within optca of the best possible solution optcr 0 1 This option sets a relative termination tolerance for problems containing discrete variables which means that the solver will stop and report on the first solution found whose objective value is within 100 optcr of the best possible solution profile 0 This option is used to generate more information on program execution profiles This option is equivalent in function to the profile command line parameter 0 No execution profile is generated in listing file 1 The listing file reports execution times for each statement and the number of set elements over which the particular statement is executed 2 Specific times for statements inside control structures like loops profiletol 0 0 This option sets profile tolerance in seconds All statements that take less time to execute than this tolerance are not reported in the listing file qcp default This option controls the solver used to solve qcp models For details cf option cns reslim 1000 This option causes the solver to terminate the solution process after reslim units of processor time have been used and the current solution values are returned to GAMS The units are seconds on the wall clock for PCs or CPU seconds for larger machines The SOLUTION
41. and expose Purge will remove any information associated with this symbol Hide will make the symbol and all its information invisible Protect prevents changes to information Expose will revert the symbol to its original state Secure Restart Files The GAMS licensing mechanism can be used to save a secure model in a secure work file A secure work file behaves like any other work file but is locked to a specific users license file A privacy license the license file of the target users is required to create a secure work file The content of a secure work file is disguised and protected against unauthorized access via the GAMS license mechanism A special license is required to set the access controls and to create a corresponding secure work file Reporting features have been added to allow audits and traces during generation and use of secure work files Work files are used to save and restart the state of a GAMS program Depending on the context we refer to those files as work files save files or restart files 228 Secure Work Files G 2 A First Example The model TRNSPORT from the GAMS model library will be used to illustrate the creation and deployment of a secure work file Assume we want to distribute this model but have concerns about proprietary formulations and data In addition we would like to protect the user from making unintentional modifications to the model We assume that the objective function and the supply con
42. are general nonlinear terms involving only smooth functions in the model but no discrete variables The functions were classified as to smoothness in the previous chapter DNLP Nonlinear programming with discontinuous derivatives This is the same as NLP except that non smooth functions can appear as well These are more difficult to solve than normal NLP problems The user is strongly recommended not to use this model type RMIP Relaxed mixed integer programming The model can contain discrete variables but the discrete requirements are relaxed meaning that the integer and binary variables can assume any values between their bounds MIP Mixed integer programming Like RMIP but the discrete requirements are enforced the discrete variables must assume integer values between their bounds RMIQCP Relaxed mixed integer quadratic constraint programming The model can contain both discrete variables and quadratic terms The discrete requirements are relaxed This class of problem is the same as QCP in terms of difficulty of solution RMINLP Relaxed mixed integer nonlinear programming The model can contain both discrete variables and general nonlinear terms The discrete requirements are relaxed This class of problem is the same as NLP in terms of difficulty of solution MIQCP Mixed integer quadratic constraint programming Characteristics are the same as for RMIQCP but the discrete requirements are enforced MINLP Mixed integer nonline
43. are not equal terminate H 4 The ENCRYPT GAMSLIB Model The ENCRYPT model from the GAMS Model Library contains a more elaborate example of the use of encrypted files Note the use of LICENSE DEMO which overrides the currently installed license with a demo license which has the secure file option enabled Title Input file encryption demo ENCRYPT SEQ 318 ontext Input files can be encrypted and use the save privacy license file mechanism for managing the user password Similar to compression we offer an encrypt utility to lock any file to a specific target license file Once a file has been encrypted it can only be read by a gams program that has the matching license file There is no inverse operation possible you cannot recover the original GAMS file from the encrypted version To create an encrypted file we need a license file which has the security option enabled To allow easy testing and demonstration a special temporary demo license can be created internally and will be valid for a limited time only usually one to two hours In the following example we will use the GAMS option license DEMO to use a demo license with secure option instead of our own license file Also note that we use the same demo license file to read the locked file by specifying the GAMS parameter plicence LICENSE offtext get model ondollar ca amslib q trnsport call gamslib q p encrypt and try to decrypt call rm f t1 gms
44. as explanatory text labels parameters variable or equation values In the basic structure shown above the first line defines the one or more files which you intend to write to The second line assigns one of these defined files as the current file that is the file to be written to Lastly the third line represents the actual writing of output items to the current file 134 The Put Writing Facility 15 3 An Example It is instructive to use a small example to introduce the basics of the put writing facility The example will be based on the transportation model TRNSPORT The following program segment could be placed at the end of the transportation model to create a report file factors factors dat results results dat put factors put Transportation Model Factors Freight cost f 1 6 Plant capacity loop i put 3 i tl 15 a i put Market demand loop j put 3 j tl 15 b j put results put Transportation Model Results loop i j put i tl 12 j tl 24 x 1 i j 8 4 In the first line the internal file names factors and results are defined and connected to the external file names factors dat and results dat These internal file names are used inside the model to reference files which are external to the model The second line of this example assigns the file factors dat as the current file that is the file which is currently available to be written to In the third
45. barrels ammonia ammonia million tons coke coke million tons sulfur sulfur million tons Notice that text may have embedded blanks and may include special characters such as parentheses There are however restrictions on special characters in text Include slashes commas or semicolons only if the text is enclosed in quotes A set definition like set prices prices of commodities in dollars ounce gold price sil price will cause errors since the slash between dollars and ounce will signal the beginning of the set declaration and the GAMS compiler will treat ounce as the name of the first element Further the slash before gold price will be treated as the end of the set definition and gold price will be treated as a new set However by enclosing the explanatory text in quotes this problem is avoided The following text is valid set prices prices of commodities in dollars ounce 4 2 5 Sequences as Set Elements The asterisk plays a special role in set definitions It is used to relieve the tedium of typing a sequence of elements for a set and to make intent clearer For example in a simulation model there might be ten annual time periods from 1991 to 2000 Instead of typing ten years the elements of this set can be written as set t time 1991 2000 which means that the set includes the ten elements 1991 1992 2000 GAMS builds up these label lists by looking at the differences between the
46. be accessed by errorlevel e 3 process not running anymore or was never running no return code available jobTerminate PID none sends an interrupt signal to the running job with Process ID PID the return value is one if this was succesful otherwise it is zero licenseLevel any returns an indicator of type of license e 0 demo license limited to small models e 1 full unlimited developer license e 2 run time license no new variables or equations can be introduced besides those inherited in a work file e 3 application license only works with a specific work file which is locked to the license file licenseStatus any returns a non zero when a license error is incurred 6 3 Expressions 61 maxExecError none maximum number of execution errors may either be read or assigned to sleep SEC none execution pauses for SEC seconds timeClose none returns the model closing time timeComp none returns the compilation time in seconds timeElapsed none returns the elapsed time in seconds since the start of a GAMS run timeExec none returns the execution time in seconds timeStart none returns the model start time since last restart Table 6 1 GAMS functions Consider the following example of a function used as an expression in an assignment statement x j log y j which replaces the current value of x with the natural logarithm of y over the domain of the index set j Extrinsic Functions Using the GAMS Function Library Facility
47. be defined in the same order in which they are declared 2 7 Objective Function This is just a reminder that GAMS has no explicit entity called the objective function To specify the function to be optimized you must create a variable which is free unconstrained in sign and scalar valued has no domain and which appears in an equation definition that equates it to the objective function 2 8 Model and Solve Statements The word model has a very precise meaning in GAMS It is simply a collection of equations Like other GAMS entities it must be given a name in a declaration The format of the declaration is the keyword model followed by the name of the model followed by a list of equation names enclosed in slashes If all previously defined equations are to be included you can enter a11 in place of the explicit list In our example there is one Model statement model transport all This statement may seem superfluous but it is useful to advanced users who may create several models in one GAMS run If we were to use the explicit list rather than the shortcut a11 the statement would be written as model transport cost supply demand The domains are omitted from the list since they are not part of the equation name The list option is used when only a subset of the existing equations comprises a specific model or sub model being generated Once a model has been declared and assigned equations we are ready to call the s
48. be entered and used as if they were ordinary numbers The following example shows various legal ways of entering numbers 0 156 70 135 095 1 2e10 2e 10 15 e 10 314e5 1 7 0 0 0 0 INF INF EPS NA The letter e denotes the well known scientific notation allowing convenient representation of very large or small numbers For example 1e 5 1 x 107 0 00001 3 56e6 3 56 x 10 3 560 000 GAMS uses a smaller range of numbers than many computers are able to handle This has been done to ensure that GAMS programs will behave in the same way on a wide variety of machines including personal computers A good general rule is to avoid using or creating numbers with absolute values greater than 1 0e 20 t A number can be entered with up to ten significant digits on all machines and more on some 3 4 7 Delimiters As mentioned before statements are separated by a semicolon However if the next statement begins with a reserved word often called keyword in succeeding chapters then GAMS does not require that the semicolon be used The characters comma and slash are used as delimiters in data lists to be introduced later The comma terminates a data element as does an end of line and the slash terminates a data list 3 4 8 Comments A comment is an explanatory text that is not processed or retained by the computer There are three ways to include comments in a GAMS program The first already ment
49. be needed in the same file 9 4 1 Several Models If there are different models then the solves may be sequential as below Each of the models in PROLOG consists of a different set of equations but the data are identical so the three solves appear in sequence with no intervening assignments solve nortonl using nlp maximizing Z solve nortonn using nlp maximizing Z solve nortone using nlp maximizing Z When there is more than one solve statement in your program GAMS uses as much information as possible form the previous solution to provide a starting point in the search for the next solution 9 4 2 Sensitivity or Scenario Analysis Multiple solve statements can be used not only to solve different models but also to conduct sensitivity tests or to perform case or scenario analysis of models by changing data or bounds and then solving the same model again While some commercial LP systems allow access to sensitivity analysis through GAMS it is possible to be far more general and not restrict the analysis to either solver or model type This facility is even more useful for studying many scenarios since no commercial solver will provide this information An example of sensitivity testing is in the simple oil refining model MARCO Because of pollution control one of the key parameters in oil refinery models is an upper bound on the sulfur content of the fuel oil produced by the refinery In this example the upper bound on the sulfur
50. can handle semi continuous variables by checking the relevant section of the Solver Manual ts The lower bound has to be less than the upper bound and both bounds have to be greater than 0 GAMS will flag an error if it finds that this is not the case 17 2 5 Semi Integer Variables Semi integer variables are those whose values if non zero must be integral above a given minimum value This can be expressed algebraically as Either x 0 or x L U By default this lower bound L is 1 and the upper bound U is 100 The lower and upper bounds are set through lo and up In GAMS a semi integer variable is declared using the reserved phrase semiint variable The following example illustrates its use semiint variable x x lo 2 x up 25 The above slice of code declares the variable x to be semi continuous variable that can either be 0 or can take any integer value between 2 and 25 t Not all MIP solvers allow semi integer variables Please verify that the solver you are interested in can handle semi integer variables by checking the relevant section of the Solver Manual gt The lower bound L has to be less than the upper bound U and both bounds have to be greater than 0 GAMS will flag an error during model generation if it finds that this is not the case t The bounds for semiint variables have to take integer values GAMS will flag an error during model generation if it finds that this is not the case 158 S
51. collected as soon a solution is available It may be necessary to wait for some solutions to complete by putting the GAMS program to sleep Note that we have assumed that there will be no errors in any of those steps This of course will not always be the case and elaborate mechanisms are in place to make the operation fail safe 13 A First Example The model QMEANVAR form the GAMS model library will be used to illustrate the use of the basic grid facility This model traces an efficiency frontier for restructuring an investment portfolio Each point on the frontier requires the solution of independent quadratic mixed integer models The original solution loop is shown below Loop p pp ret fx rmin rmax rmin card pp 1 ord pp Solve minvar min var using miqcp xres i p x 1 i report p i inc xi 1 i report p i dec xd 1 i This loop will save the solutions to the model MINVAR for different returns RET Since the solutions do not depend on the order in which they are carried out we can rewrite this loop to operate in parallel The first step is to write the submit loop parameter h pp model handles minvar solvelink 3 Loop p pp ret fx rmin rmax rmin card pp 1 ord pp Solve minvar min var using miqcp h pp minvar handle The model attribute solvelink controls the behavior of the solve statement A value of 3 tells GAMS to generate and submit the model for solution
52. conscientious about keeping the documentation accurate and up to date gt The output of GAMS is easy to read and use The solution report from the solver is automatically reformatted so that related equations and variables are grouped together and appropriately labeled Also the display command allows you to modify and tabulate results very easily gt If you are teaching or learning modeling you can benefit from the insistence of the GAMS compiler that every equation be mathematically consistent Even if you are an experienced modeler the hundreds of ways in which errors are detected should greatly reduce development time gt By using the dollar operator and other advanced features not covered in this tutorial one can efficiently implement large scale models Specific applications of the dollar operator include the following 1 It can enforce logical restrictions on the allowable combinations of indices for the variables and equations to be included in the model You can thereby screen out unnecessary rows and columns and keep the size of the problem within the range of solvability 2 It can be used to build complex summations and products which can then be used in equations or customized reports 3 It can be used for issuing warning messages or for terminating prematurely conditioned upon context specific data edits 26 A GAMS Tutorial by Richard E Rosenthal 3 GAMS Programs 3 1 Introduction This chapter provides
53. content of the fuel oil produced in the refinery In this example the upper bound on the sulfur content of fuel oil was set at 3 5 percent in the original data for the problem First the model is solved with this value Next a slightly lower value of 3 4 percent is used and the model is solved again Finally the considerably higher value of 5 percent is used and the model is solved for the last time After each solve key solution values the activity levels are associated with z the process levels by process p and by crude oil type cr are saved for later reporting This is necessary because a following solve replaces any existing values The complete sequence is parameter report process level report qs upper fuel oil sulfur 3 5 solve oil using lp maximizing phi report cr p base z 1 cr p report sulfur limit base qs upper fuel oil sulfur qs upper fuel oil sulfur 3 4 solve oil using lp maximizing phi report cr p one z l cr p 82 Model and Solve Statements report sulfur limit one qs upper fuel oil sulfur qs upper fuel oil sulfur 5 0 solve oil using lp maximizing phi report cr p two z l cr p report sulfur limit two qs upper fuel oil sulfur display report This example shows not only how simpl
54. default MPEC solver copyright messages sets put directory relative or absolute path default RMIP solver script executed at the end of a GAMS run script mailbox file name solver control file name solver dictionary file name solver matrix file name solver status file name symbol file name sets system library directory unit insert file operations sets working directory Parameters affecting input file processing ctrlm g205 multipass optdir stringchk control M indicator sets version compatibility controls multiple pass facility option file directory controls string substitution check Parameters affecting output in listing file appendout case leftmargin limrow pagecontr pagewidth stepsum tformat output listing file append option sets output case sets left margin in listing file default row listing page control sets page width controls step summary in listing file sets time format Parameters affecting other files appendlog ferr logline restart xsave log file append option sets compilation error message file name controls amount of line tracing to log file sets restart file name extended save file name cerr eolonly errmsg forcework keep cns curdir errnam execerr inputdir libincdir lp minlp nlcon parmfile reference rminlp scrdir scriptfrst scrnam solverdict solverinst solversolu subsys sysdir trace userl ctrlz input opt optfile tabin botmargin dformat
55. definition of mean return on portfolio DVAR definition of variance FSUM fractions must add to 1 0 MODELS PORTFOLIO 10 3 4 The Unique Element Listing Map The following map is called the Unique Element Listing All unique elements are first grouped in entry order and then in sorted order with their explanatory texts The unique element listing map can be turned on by entering a line containing onuelxref at the beginning of the program Unique Element Listing Unique Elements in Entry Order 1 hardware software show biz t bills Unique Elements in Sorted Order 1 hardware show biz software t bills ELEMENT REFERENCES hardware DECLARED 11 REF 19 26 28 show biz DECLARED 11 REF 21 26 30 software DECLARED 11 REF 20 26 29 t bills DECLARED 11 REF 22 26 31 10 3 5 Useful Dollar Control Directives This sub section reviews the most useful of the Dollar Control Directives These must not be confused with the dollar exception handling operators that will be introduced later the similarity of terminology is unfortunate 90 GAMS Output The dollar control directives are compiler directives that can be put in the input file to control the appearance and amount of detail in the output produced by the GAMS compiler offlisting onlisting This directive stops the echo print of the input file onlisting restores the default offsymxref offsymlist onsymxref onsymlist These four directives are used to control the production of symbol m
56. description for each C 3 Detailed Description of Command Line Parameters This section describes each of the command line parameters in detail These parameters are in alphabetical order for easy reference In each of the following options an abbreviation and the default value if available are bracketed action a ce Processing option GAMS currently processes the input file in multiple passes The three passes in order are Compilation During this pass the file is compiled and syntax errors are checked for Data initialization statements like scalar parameter and table statements are also processed during this stage Execution During this stage all assignment statements are executed Model Generation During this stage the variables and equations involved in the model being solved are generated Values c compile only execute only ce compile and execute r restart The a e setting can only be used during restart on files that have previously been compiled since models first need to be compiled before they can be executed appendlog al 0 log file append option This option is used in conjunction with the lo 2 setting where the log from the GAMS run is redirected to a file Setting this option to 1 will ensure that the log file is appended to and not rewritten Values O reset log file 1 append to log file appendout ao 0 output listing file append option Setting this option to 1 will ensure that the listing file is a
57. details Examples of legal identifiers are 36 Set Definitions i i15 countries s0051 whereas the following identifiers are incorrect 25 currency food amp drink 4 2 3 Set Elements The name of each set element can be up to 63 characters long and can be used in quoted or unquoted form The unquoted form is simpler to use but places restrictions on characters used in that any unquoted label must start with a letter or digit and can only be followed by letters digits or the sign characters and Examples of legal unquoted labels are Phos Acid 1986 1952 53 A September H2504 Line 1 In quoted labels quotes are used to delimit the label which may begin with and or include any legal character Either single or double quotes can be used but the closing quote has to match the opening one A label quoted with double quotes can contain a single quote and vice versa Most experienced users avoid quoted labels because they can be tedious to enter and confusing to read There are a couple of special circumstances If one wants to make a label stand out then to put asterisks in it and indent it as below is common A more subtle example is that it is possible to use GAMS keywords as labels if they are quoted If one need to use labels like no ne or sum then they will have to be quoted Examples of quoted labels are gt TOTAL Match 10 incr 12 foot Line 1 t Labels do not have a value The label 1986 does no
58. diego new york 2 250000000000000e 001 san diego chicago 1 620000000000000e 001 san diego topeka 1 260000000000000e 001 positive variable x i j shipment quantities in cases parameter a i capacity of plant i in cases seattle 3 500000000000000e 002 san diego 6 000000000000000e 002 parameter b j demand at market j in cases new york 3 250000000000000e 002 chicago 3 000000000000000e 002 topeka 2 750000000000000e 002 equation demand j satisfy demand at market j equation supply i observe supply limit at plant i equation cost define objective function EDITS FOR INPUT FILE END OF DUMP 176 The GAMS Call Note that all the data entering the model in the solve statement has been regenerated The parameter d has not been regenerated since it does not appear in the model but the parameter c is Changing the value of the parameter dumpopt will result in alternate names being used for the identifiers in the regenerated file dumpparms dp 0 GAMS parameter logging The dumpparms parameter provides more detailed information about the parameters used during the current run Values O no logging 1 lists accepted parameters 2 log of file operations plus parameters Note that with dp 2 all the file operations are listed including the full path of each file on which any operation is performed eolonly ey 0 single key value pair option By default any number of keywo
59. domain control is often a matter of taste 13 7 Summary 125 13 6 3 Circular Lag and Lead Operators In the case of circular lag and lead operators the difference between its use in domain control and as reference is not important because it does not lead to any equations or terms being suppressed Consider the following artificial example set s seasons spring summer autumn winter variable prod s amount of goods produced in each season avail s amount of goods available in each season sold s amount of goods sold in each season equation matbal s matbal s avail s 1 e prod s sold s In this example four individual examples are generated They are listed below avail summer e prodn spring sold spring avail autumn e prodn summer sold summer avail winter e prodn autumn sold autumn avail spring e prodn winter sold winter Note that none of the equations are suppressed 13 7 Summary This chapter introduced the concept of ordering in sets All the features in GAMS that dealt with this issue including the ord and card functions as well as the linear and circular forms of the lag and lead operators were described in detail 126 Sets as Sequences Ordered Sets 14 The Display Statement 14 1 Introduction In this chapter we will provide more detail about display statements including the controls that a user has over the layout and appearance of the output The
60. dumpparms 191 eolonly 191 errmsg 191 error 191 expand 191 ferr 191 forcework 191 g205 191 input 191 inputdir 191 inputdirl 191 leftmargin 191 libincdir 191 license 191 logfile 191 logline 191 262 INDEX logoption 191 multipass 191 nocheck 191 optfile 191 output 191 pagecontr 191 pagesize 191 pagewidth 191 profile 191 putdir 191 reference 191 relpath 191 restart 191 save 191 serdir 191 stepsum 191 stringchk 191 subsys 191 suppress 191 sysdir 191 sysincdir 191 tabin 191 tformat 191 topmargin 191 workdir 191 GAMS coordinator 165 GAMS execution output column listing 92 equation listing 91 Model statistics 92 solve summary 93 GAMS output echo print 86 example 85 introduction 85 report summary 98 solution listing 97 symbol listing map 89 symbol reference map 87 GAMS call Introduction 171 specifying options 171 GAMS language items Characters 30 GAMS language items 29 Comments 32 declarative statements 28 Delimiters 32 identifiers 30 Labels 31 Numbers 32 reserved words 30 text 31 GAMSLIB 169 gamsRelease function 59 gamsVersion function 59 gday function 58 gdow function 58 ge relational operator 30 103 geometric distribution 250 ghour function 58 gleap function 58 gmillisec function 58 gminute function 58 gmonth function 58 goto dollar control option 199 grid computing 237 gsecond function 58 gt
61. ee eke a a wee eo oe ee ee SG Se ee tt ee Gs Hee oe ee eS oe ee Eid ee 8 Equations Gl 2 ee ta p ewe ea bee PEER AEE ODS ee Re eR a 82 Equation Declarations lt lt lt 6 46 24 aw eae PR ee DR Ree EAR ee Eee A Sl The GVW e oaa ma opii ee ane See BA ee a ee ed eS 8 2 2 Ati Illustrative Example cocida a So Egustiom Dehmitieis cas cs a DADE BE LRA ee REESE Hw Be SA Sal a se cen eM ow Pha be bee DEA Ae ee be ee OR eas Boo An lustratie Example acuosas OE RR BEER EEE AER REEDED OS Sea Scalar Equations a 6 2 4 50024 Soa e BERGA de A RE eH SoA Indexed Equations o s ce e soarece da ae ee eR a eee Oe ee B 3 0 Using Labels Explicitly in Equations o co as ee ee e ea 8 4 Expressions in Equation Definitions lt e es cas srodno tu Goe sekten ee 8 41 Arithmetic Operators in Equation Definitions s sses eses auessa sda sa BAD Functions in Eguation Definitions o cgo 6404 204 eee sa A asa A 8 4 3 Preventing Undefined Operations in Equations ooa e 85 Data Handling Aspects of Equations 9 at eee i A A 9 Model and Solve Statements S Tniroduction ociosa e o oe A ee ee a A ee a S 42 The Model Staremeit coords 22 aa eee bee a a a aa U2 The Sylow gt ons ad iaie A A A A eae e BS 9 2 2 Classification of Models ee S Or Model Aries 6 oe a a eee ee Oe ee ee go AA aa 43 The Solve Statement osos 6 caked MERAY DED LR REE REE DE E S Gob The Gynt ecr eri e a ae el eS de ee oe PAE A 9 3 2 Requirements for a Valid Solve
62. entered as set 170 Domain violation for element k 2 ERROR S 0 WARNING S C 3 Detailed Description of Command Line Parameters 177 Note that numbers 170 and 120 flags the two errors as they occur but the errors are explained only at the end of the source listing However if the code is run using the option errmsg 1 the resulting listing file contains the following 1 set i 1 10 set j i 10 11 Hook 170 k 170 Domain violation for element 2 parameter a jj 12 25 0 l CK 120 xx 120 Unknown identifier entered as set 3 2 ERROR S 0 WARNING S Note that the explanation for each error is provided immediately following the error marker errnam errnam tezt error message file name Used to change the name GAMSERRS TXT The name text will be used as is errorlog er 0 error messages are written to log file Values O no error messages to log file n number of lines for each error written to log file execerr execerr 0 execution time error limit Entering or processing a solve statement with more than execerr will abort Values O no errors allowed limit n don t execute solve if more errors expand ef tezt expand file name The expand parameter generates a file that contains information about all the input files processed during a particular compilation The names of the input files are composed by completing the name with the current directory The following example illustrates the use of the expan
63. equation loop options scalars table alias equations lt a or Semicong mian all file maximizing ord semiint until and files minimizing parameter set using assign for model parameters sets variable binary free models positive smax variables card ge na prod smin while diag gt ne putpage solve xor display if negative puttl sosi yes else inf no repeat sos2 The reserved non alphanumeric symbols are g Table 3 3 Reserved words and symbols 3 4 3 Identifiers Identifiers are the names given to sets parameters variables models etc GAMS requires an identifier to start with a letter followed by more letters or digits The length of an identifier is currently limited to 63 characters 3 4 Language Items 31 Identifiers can only contain alphanumeric characters letters or numbers Examples of legal identifiers are a a15 revenue x0051 whereas the following identifiers are incorrect 15 casg milk amp meat t A name used for one data type cannot be reused for another 3 4 4 Labels Labels are set elements They may be up to 63 characters long and can be used in quoted or unquoted form The unquoted form is simpler to use but places restrictions on characters used in that any unquoted label must start with a letter or digit and can only be followed by letters digits or the sign characters and Examples of unquoted labels are Phos Acid 1986 1952 53 A September H2504 Line 1 In quoted labels quotes are used to deli
64. failed call gams t3 license DEMO gdx t3 dumpopt 19 lo gams lo if errorlevel 1 abort model t3 failed call gdxdiff trnsport t3 system redirlog if errorlevel 1 abort results for trnsport and t3 are not equal check for hidden output call grep this is hidden t3 1st gt system nullfile if not errorlevel 1 abort did not hide in listing call grep this is hidden t3 dmp gt system nullfile if not errorlevel 1 abort did not hide in dump file The GAMS Grid Computing Facility I 1 Introduction As systems with multiple CPUs and High Performance Computing Grids are becoming available more widely the GAMS language has been extended to take advantage of these new environments New language features facilitate the management of asynchronous submission and collection of model solution tasks in a platform independent fashion A simple architecture relying on existing operating system functionality allows for rapid introduction of new environments and provides for an open research architecture A typical application uses a coarse grain approach involving hundreds or thousands of model solutions tasks which can be carried out in parallel For example gt Scenario Analysis gt Monte Carlo Simulations gt Lagrangian Relaxation gt Decomposition Algorithms gt Advanced Solution Approaches The grid features work on all GAMS platforms and have been tailored to many different environments like the Condor Resource
65. failed model and solver status This file will be overwritten by the final step of the solution process and will be read when calling execute_loadhandle 4 Place all standard GAMS solver interface files into the above instance directory 244 The GAMS Grid Computing Facility 5 Execute the submission wrapper called gmsgrid cmd under Windows or gmsgrid run under Unix These submission scripts are usually located in the GAMS system directory but are found via the current path if not found in the GAMS system directory The grid submission script gmsgrid cmd or gmsgrid run is called with three arguments needed to make a standard GAMS solver call 1 The solver executable file name 2 The solver control file name 3 The solver scratch directory The submission script then does the final submission to the operating system This final script will perform the following steps call the solver call a utility that will create the final gdx file gmsgrid gdx set the completion signal finished If we want to use the function handlesubmit we also have to create the gmsrerun cmd or gmsrerun run script which could later be used to resubmit the job For example the default submission script for Windows is shown below echo off gams grid submission script argl solver executable 2 control file 3 scratch directory gmscr_nx exe processes the solution and produces gmsgrid gdx note 3 will be the short name because START cannot
66. for a set 5 3 2 An Illustrative Examples The fragment below is adapted from MEXSS We also show the set definitions because they make the example clearer Set i steel plants hylsa monterrey hylsap puebla j markets mexico df monterrey guadalaja parameter dd j distribution of demand mexico df 55 guadalaja 15 5 4 Tables 45 The domain checking specification for dd means that there will be a vector of data associated with it one number corresponding to every member of the set j listed The numbers are specified along with the declaration in a format very reminiscent of the way we specified sets in this simple case a label followed by a blank separator and then a value Any of the legal number entry formats are allowable for the value The default data value is zero Since monterrey has been left out of the data list then the value associated with dd monterrey the market share in monterrey would be zero We can also put several data elements on a line separated by commas parameter a i seattle 350 san diego 600 b i seattle 2000 san diego 4500 As with sets commas are optional at end of line 5 3 3 Parameter Data for Higher Dimensions A parameter can have up to 20 dimensions The list oriented data initialization through the parameter statement can be easily extended to data of higher dimensionality The label that appears on each line in the one dimensional case is replace
67. for the display statement there is much greater flexibility and control over the output of individual items In this chapter the working of the put writing facility is described as well as the syntax for accessing files and globally formatting documents using file suffixes for various attributes of a file The put writing facility enables one to generate structured documents using information that is stored by the GAMS system This information is available using numerous suffixes connected with identifiers models and the system Formatting of the document can be facilitated by the use of file suffixes and control characters The put writing facility generates documents automatically when GAMS is executed A document is written to an external file sequentially a single page at a time The current page is stored in a buffer which is automatically written to an external file whenever the page length attribute is exceeded Consequently the put writing facility only has control of the current page and does not have the ability to go back into the file to alter former pages of the document However while a particular page is current information placed on it can be overwritten or removed at will 15 2 The Syntax The basic structure of the put writing facility in its simplest form is file fname s put fname put item s where fname represents the name used inside the GAMS model to refer to an external file Items are any type of output such
68. generates a random number with normal distribution with mean MEAN and standard deviation STDDEV see Math World value of 7 3 141593 computes a polynomial over scalar x where result Ag A x2 Agu A3x this has a maximum of 6 arguments default setting A3 A 0 returns Y where Y must be an integer another possible com mand is x Y generates a random number with binomial distribution where n is the number of trials and p the probability of success for each trial see MathWorld generates a random number between LOW and HIGH with sens 2 linear distribution SLOPE must be greater than HICH LOW generates a random number between LOW and HIGH with triangular distribution MID is the most probable number see MathWorld rounding x DECPL declares the number of decimal places default setting DECPL 0 returns x for x y gt 0 another possible command is x y Sigmoid calculation 3 ot see MathWorld sign of x returns 1 if x gt 0 1 if x lt 0 and 0 if x 0 signed power another possible command is sign x abs x Y where Y must be greater than 0 returns the sine of the argument x where x must be in radians see Math World returns the hyperbolic sine of x where x must be in radians see Math World smooth linear exponential function SP means smoothing pa rameter default setting SP 150 smooth linear logarithm base 10 SP means smoothing pa rameter default setti
69. given the file name is completed using the system include directory By default the system include directory is set to the GAMS system directory The default directory can be reset with the sdir command line parameter Consider the following example sysinclude abc x y This call first looks for the include file GAMS System Directory abc and if this file does not exist looks for GAMS System Directory abc gms The arguments x and y are passed on to the include file to interpret as explained for the batinclude option Consider the following example sysinclude c abc myinc inc x y This call first looks specifically for the include file c abc myfile inc title This option sets the title in the page header of the listing file to text which follows immediately the keyword title The next output line will appear on a new page in the listing file Consider the following example title Production Planning Model stitle Set Definitions use205 This option sets the GAMS syntax to that of Release 2 05 This is mainly used for backward compatibility New keywords have been introduced in the GAMS language since Release 2 05 Models 214 Dollar Control Options developed earlier that use identifiers that have since become keywords will cause errors when run with the latest version of GAMS This option will allow one to run such models Consider the following example use205 set if 1 2 3 scalar x The word if is a keyword in
70. have been marked INFES NOPT or UNBND in the solution listing section The sum of infeasibilities will be shown if it the reported solution is infeasible The error count in is only shown if the problem is nonlinear k REPORT SUMMARY 0 NONOPT O INFEASIBLE O UNBOUNDED 0 ERRORS If our example had display output for reporting it would come here 10 5 8 File Summary The last piece of the output file is important it gives the names of the input and output disk files If work files save or restart have been used they will be named here as well xe FILE SUMMARY INPUT C PROGRAM FILES gamsIDE ALAN GMS OUTPUT C PROGRAM FILES gamsIDE ALAN LST 10 6 Error Reporting All the comments and description about errors have been collected into this section for easy reference when disaster strikes 10 6 Error Reporting 99 Effective error detection and recovery are important parts of any modeling system GAMS is designed around the assumption that the error State is the normal state of modeling Experience shows that most compilations during the early stages of development will produce errors Not to Worry The computer is much better at checking details that the human mind and should be able to provide positive feedback and suggestions about how to correct errors or avoid ambiguities Developing a model is like writing a paper or an essay many drafts and rewrites are required until the arguments are presented in the most effective wa
71. if a system is licensed for secure work files and usually requires a target license file which will contain the user or target encryption key Once a file has been encrypted it cannot be decrypted any more The use of a PLICENSE parameter will specify the target or privacy license to be used as a user key for encrypting Decompression and encrypting is done on the fly into memory when reading the GAMS system files GAMS will recognize if a file is just plain text or compressed and or encrypted and will validate and process the files accordingly Finally all compressed and encrypted files are of course platform independent as any other GAMS input file H 2 A First Example The model TRNSPORT from the GAMS model library will be used to illustrate the creation of a compressed input file First we will copy the model from the GAMS model and create a compressed version Spaces are recognized as separators between the source and target file names which means you have to use quotes single or double if the filenames contain spaces gt gamslib trnsport gt echo compress trnsport gms t1 gms gt t2 gms gt gams t2 Compress Source C support 28Dec trnsport gms Compress Target C support 28Dec t1 gms gms Compress Time Omsec Now we can treat the compressed input files like any other GAMS input file and the listing files will be identical because the decompressed input is echoed just like any normal input line 234 Compressed a
72. illustrate the modeling capabilities GAMS offers For example the mathematical specification of cropping patterns can be represented handily in GAMS Another example of the system s capability is the style for specifying initial solutions as staring points in the search for the optimal solution of dynamic nonlinear optimization problems Finally some models have been selected for inclusion because they have been used in other modeling systems Examples are network problems and production planning models These models permit the user to compare how problems are set up and solved in different modeling systems Most of the models have been contributed by GAMS users The submission of new models is encouraged If you would like to see your model in a future release of the library please send the model and associated documents and reports to GAMS Development Corporation The most convenient way Windows only to access the model library is from within the GAMS IDE by going through File Model Library Open GAMS Model Library A window will pop up and give you access to all models Another way to access the library is through the gamslib command This command copies a model from the library directory into the current directory If you enter gamslib without any parameters the command syntax will be displayed as shown below gt gamslib modelname target or gt gamslib modelnum target where modelname is the modelname modelnum is the model se
73. instance is missing if not handlestatus h instance abort yes model instance instance not ready minvar handle h instance execute_loadhandle minvar display x 1 xi 1 xd 1 gt gams qanalyze r submit gdir c test grid instance p4 Once all jobs are completed we can continue with the second part which will contain the collection loop for simplicity without the repeat loop because we would not run the final collection program unless we are satisfied that we got most of what we wanted Then the qreport gms file could look like loop pp handlestatus h pp minvar handle h pp execute_loadhandle minvar xres i pp zilli report pp i inc xi 1 i report pp i dec xd 1 i display handledelete h pp trouble deleting handles h pp 0 xres i pp h pp na We would restart the above program from the save file that was created by the submitting job like gt gams qreport r submit gdir c test grid Note that it would not be necessary to run the job out of the same directory we did the initial submission We don t even have to run the same operating system 1 5 Summary of Grid Features To facilitate the asynchronous or parallel execution of the solve solution steps we have introduced three new functions a new model attribute a new gdx load procedure and a new GAMS option GridDir 242 The GAMS Grid Computing Facility 1 5 1 Grid Handle Functions HandleCollect han
74. integer infeasible 94 intermediate noninteger 94 intermediate infeasible 94 intermediate nonoptimal 94 locally optimal 94 optimal 94 unbounded 94 modelstat model attribute 79 option 79 mpec GAMS call parameter 182 MPEC model type 16 78 multipass GAMS call parameter 182 multiple solves 81 na extended range value 32 63 ncpCM function 55 nepF function 55 ncpVUpow function 55 ncpVUsin function 55 ne relational operator 103 negBinomial distribution 250 nlcon INDEX 265 GAMS call parameter 183 nlp GAMS option 218 NLP model type 15 78 nocheck GAMS call parameter 183 nocr GAMS call parameter 183 nonbasic 165 nonlinear equations 91 programming 67 78 nonlinear nonzero 165 nonoptimal 165 nonsmooth 165 nonzero element 165 nopt solution marker 98 normal completion a solver status 95 normal distribution 249 normal function 55 not relational operator 115 number of rows and columns in display 129 numequ model attribute 79 numinfes model attribute 79 numnz model attribute 79 numopt model attribute 79 numvar model attribute 79 objective row or function 165 objective value 166 objective variable 166 on offdigit dollar control option 204 on offdollar dollar control option 204 on offempty dollar control option 204 on offend dollar control option 205 on offeolcom dollar control option 206 on offeps dollar control option 20
75. line of the example writing to the document begins using a put statement with the textual item Transportation Model Factors Notice that the text is quoted The slashes following the quoted text represent carriage returns The example continues with another textual item followed by the scalar f Notice that these output items are separated with commas Blanks commas and slashes serve as delimiters for separating different output items As mentioned above the slash is used as a carriage return Commas and blank spaces serve as item delimiters These delimiters leave the cursor at the next column position in the document following the last item written In most cases the blank and the comma can be used interchangeably however the comma is the stronger form and will eliminate any ambiguities In the fifth line of the program above the cursor is repositioned to the first column of the sixth row of the output file where another textual item is written The cursor control characters and serve to reposition the cursor to a specific row or column as designated by the row or column number following the cursor control character Lastly the put statement is terminated with a semicolon Next the parameters a and b are written along with their corresponding set labels Only one element of the index set can be written using a put To write the entire contents of the parameters a and b the put statement is embedded inside a loop which iterates over the
76. needed gt Access to the existing community of GAMS users for marketing or testing This completes the discussion of the model and solve statements In the next chapter the various components of GAMS output are described in some detail 84 Model and Solve Statements 10 GAMS Output 10 1 Introduction The output from GAMS contains many aids for checking and comprehending a model In this chapter the contents of the output file are discussed Ways by which the amount of diagnostic output produced can be controlled will also be discussed although complete lists of all these controls are not given until later A small nonlinear model ALAN by Alan S Manne is used to illustrate the output file and list it piece by piece as we discuss the various components The possibilities for extension to large models with voluminous output which is when the diagnostics are really useful should be apparent The output from a GAMS run is produced on one file which can be read using any text editor The default name of this output file depends on the operating system but Appendix C describes how this default can be changed The display statement described in detail in Chapter 14 can be used to export information from the GAMS program to the listing file 10 2 The Illustrative Model ALAN is a portfolio selection model whose object is to choose a portfolio of investments whose expected return meets a target while minimizing the variance
77. not returns 1 if x 0 else returns 0 another possible command is not x bool_or x y DNLP boolean or returns 0 if x y 0 else returns 1 another possible command is x or y bool_xor x y DNLP boolean xor returns 1 if exactly one argument is 0 else returns 0 another possible command is x xor y ifThen cond iftrue else DNLP first argument contains a condition e g gt y If the condi tion is true the function returns iftrue else it returns else rel_eq x y DNLP relation equal returns 1 if x y else returns 0 another possible command is x eq y rel_ge x y DNLP relation greater equal returns 1 if x gt y else returns 0 another possible command is x ge y rel_gt x y DNLP relation greater than returns 1 if x gt y else returns 0 an other possible command is x gt y rel_le x y DNLP relation less equal returns 1 if x lt y else returns 0 another possible command is x le y rel_1t x y DNLP relation less than returns 1 if x lt y else returns 0 another possible command is x 1t y rel ne x y DNLP relation not equal returns 1 if x y else returns 0 another possible command is x ne y Time and Calendar functions gday SDAY gdow SDAY any any returns Gregorian day from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian day of week from a serial day number date time where Jan 1 1900 is day
78. of a scalar equation which contains only scalar variables Note that in general scalar equations may contain indexed variables operated on by index operators Consider the following example from CHENERY dty td e sum i y i 8 3 4 Indexed Equations All the set references in scalar equations are within the scope of index operations many references can therefore be included in one equation However GAMS allows for equations to be defined over a domain thereby developing a compact representation for constraints The index sets to the left of the are called the domain of definition of the equation t Domain checking ensures that the domain over which an equation is defined must be the set or a subset of the set over which the equation is declared Consider the following example of a singly indexed equation meaning one that produces a separate constraint for each member of the driving or controlling set dg t g t e mew t xsi t m t As t has three members three constraints will be generated each one specifying separately for each member of t the dependence of g on m Mew and xsi are parameters the data associated with them are used in building up the individual constraints These data do not have to be known when the equation is defined but do have to be when a model containing the equation is solved The extension to two or more index positions on the left of the should be obvious There
79. of how a work file is used in a tree structured way one work file is used with many different but probably very small input files to produce many different output files File handling is less likely to be a problem than in the sequential case above F 3 5 The GAMS Runtime License We assume the model and the data have been completely separated as shown above with file1 gms containing only the model and file2 gms containing only the data The developer of the model can run the first model with the following command gams filel s trans and then distribute the file trans g00 file that result along with the example file2 gms If the end user has a run time license for GAMS they will not be able to see the model nor change it by adding any new variables or equations The end user will only be able to change the data and run the model developed during the save process However the end user will have full control of the data and will be able to manipulate the number of elements in the set and the values of the various scalars parameters and tables The end user will run the model with the following command gams file2 r trans 226 The Save and Restart Feature G Secure Work Files G 1 Introduction When models are distributed to users other than the original developers or embedded in applications to be deployed by other developers issues of privacy security data integrity and ownership arise We may have to hide protect
80. of the program a list of all error numbers encountered together with a description of the probable cause of each error will be printed The error messages are self explanatory and will not be listed here It is worth noting that it is easy to produce a model that does not do what you want it to do but does not contain errors in the sense that the term is being used in this section The best precaution is to check your work carefully and build in as many automatic consistency checks as possible One mistake that may cause confusion is if a GAMS reserved word is used for a label or an identifier In this case it is impossible to provide helpful messages for technical reasons 100 GAMS Output t In some cases an error may not be detected until the statement following its occurrence where it may produce a number of error conditions whose explanations seem quite silly Always check carefully for the cause of the first error is such a group and look at the previous statement and especially for missing semicolons if nothing seems obvious The following example illustrates the general reporting format for compiler errors 1 set c crops wheat corn wheat longaname RK 172 2 parameter price c wheat 200 cotton 700 CK 170 3 Error Messages 170 Domain violation for element 172 Element is redefined sex 2 ERROR S 0 WARNING S xxk USER ERROR S ENCOUNTERED 10 6 2 Compilation Time Errors The reporting format for
81. offense like our missing semicolon to generate five intimidating error messages The lesson here is concentrate on fixing the first error and ignore the other The first error detected in line 17 code 97 indicate that GAMS thinks the symbols in line 17 are a continuation of the documentary text at the end of line 16 rather than a direct assignment as we intended The error message also appropriately advises us to check the preceding line for a missing semicolon Unfortunately you cannot always expect error messages to be so accurate in their advice The compiler cannot read your mind It will at times fail to comprehend your intentions so learn to detect the causes of errors by picking up the clues that abound in the GAMS output For example the missing semicolon could have been detected by looking up the c entry in the cross reference list to be explained in the next section and noticing that it was never assigned SYMBOL TYPE REFERENCES 03 PARAM DECLARED 15 REF 17 Example 3 Many errors are caused merely by spelling mistakes and are caught before they can be damaging For example with Seattle spelled in the table differently from the way it was introduced in the set declaration we get the following error message 4 sets 5 i canning plants seattle san diego 6 j markets new york chicago topeka 7 8 table d i j distance in thousand of miles 9 new york chicago topeka 10 seatle 2 5 E 1 8 OK 170 11 san diego 2 5 1 8 1
82. offtext pair encloses comment lines Line numbers in the compiler listing are suppressed to mark skipped lines Consider the following standard comment line ontext Everything here is a comment until we encounter the closing offtext like the one below offtext another standard comment line The resulting listing file is as follows 1 standard comment line Everything here is a comment until we encounter the closing offtext like the one below 7 another standard comment line t GAMS requires that every ontext has a matching offtext and vice versa onjofFJuellist offuellist This option controls the complete listing of all set elements that have been entered in the listing file The unique element listing in the listing file generated by running TRNSPORT with onuellist is as follows Unique Element Listing Unique Elements in Entry Order 1 SEATTLE SAN DIEGO NEW YORK CHICAGO TOPEKA Unique Elements in Sorted Order 1 CHICAGO NEW YORK SAN DIEGO SEATTLE TOPEKA Note that the sorted order is not the same as the entry order This is explained in Section 12 2 on off uelxref offuelxref This option controls the collection and listing in the listing file of cross references of set elements Consider the following slice of code onuelxref set i this is set declaration one two three k i offuelxref set j i will not show two onuelxref k one yes The resulting listing file will cont
83. operators are listed below lt lt strictly less than 104 Conditional Expressions Assignments and Equations le lt less than or equal to eq equal to ne lt gt not equal to ge gt greater than or equal to gt gt strictly greater than The following example of a numerical relationship illustrates its use as a logical condition sqr a gt a This condition evaluates to False if 1 lt a lt 1 For all other values of a this condition evaluates to True Note that the same expression can also be written as sqr a gt a 11 2 3 Logical Operators The logical operators available in GAMS are listed below not not and and or inclusive or xor exclusive or The truth table generated by these logical operators is given in table 11 1 Operands Results a b a and b a or b a zor b not a 0 0 0 0 0 1 0 non zero 0 1 1 1 non zero 0 0 1 1 0 non zero non zero 1 1 0 0 Table 11 1 Truth table of logical operators 11 2 4 Set Membership Set membership can also be used as a logical condition The label results in a logical value of True if it is a member of the set in question and False if it is not This is used with subsets and dynamic sets Consider the following example for illustration set i 1 10 subi i 1 3 The set subi i results in a logical value of True for all elements that belong to subi and False for all elements of i that do not belong to subi The use of set membership as
84. or purge some parts of the model before it can be released The information to be protected can be of numeric or symbolic nature For example Privacy A Social Accounting Matrix supplied by a Statistical Office is required in a general equilibrium model to be used by the Ministry of Finance The data from the statistical office needs to be protected for obvious privacy reasons and the model experiments are used to evaluate policy options that are highly confidential Most of the model structure is public most of the data however is private and model results need to be transformed in such a way as to prohibit the discovery of the original data Security Components of a model contain proprietary information that describes mathematically a chemical reaction The associated algebra and some of the data are considered of strategic importance and need to be hidden completely The final model however will be used at different locations around the world Integrity Data integrity safeguards are needed to assure the proper functioning of a model Certain data and symbolic information needs to be protected from accidental changes that would compromise the operation of the model To address these issues access control at a symbol level and secure restart files have been added to the GAMS system Access Control The access to GAMS symbols like sets variables parameters and equations can be changed once with the compile time commands purge hide protect
85. page offupper following lines will be printed in case as entered title set title reset subtitle and page Options affecting listing of reference maps offsymlist off symbol list onsymlist on symbol list offsymxref off symbol cross reference listing onsymxref on symbol cross reference listing offuellist off unique element listing onuellist on unique element listing offuelxref off unique element cross reference onuelxref on unique element cross listing Options affecting program control abort abort compilation kill kill data connected with identifier batinclude batch include file label label name as entry point from goto call executes program during compilation libinclude library include file clear clear data connected with identifier onglobal turns on global options echo echo text onmulti turns on redefinition of data error generate compilation error offglobal turns off global options exit exit from compilation offmulti turns off redefinition of data goto go to line with given label name phantom defines a special set element if conditional processing shift DOS shift operation include include file sysinclude system include file DCO Dollar Control Option Table D 1 Dollar control options D 3 Detailed Description of Dollar Control Options This section describes each of the dollar control options in detail The dollar control options are listed in alpha betical order for easy reference In each of
86. parameter definition 45 in set definition 40 in sets 40 in tables 47 double dollar control option 197 driving set 164 dual value m 67 dumpopt GAMS call parameter 174 dumpparms GAMS call parameter 176 dynamic set 164 assigning membership membership to 113 assignments over the domain of 114 dollar assignments 115 equations defined over the domain of 115 example 113 in equations 116 indexed operations 116 introduction 113 syntax 113 using dollar controls with 115 with multiple indices 114 e format 130 164 echo dollar control option 198 eDist function 55 eject dollar control option 198 GAMS option 217 encrypt 233 end of line 31 46 endogenous 164 arguments 74 entropy function 55 eolcom dollar control option 198 eolonly GAMS call parameter 176 eps a reserved word 30 definition 63 used with variables 98 eq a relational operator 103 equation 164 indexed 73 listing 91 scalar 73 equation declaration 71 example 71 72 syntax 71 equation definition arithmetic operators 74 functions 74 preventing undefined operations 74 syntax 72 errmsg GAMS call parameter 176 errnam GAMS call parameter 177 error 260 INDEX dollar control option 199 GAMS call parameter 176 handling 62 no solution 94 other 95 reporting 98 reporting compilation 99 reporting compilation time errors 100 reporting execution errors 101 reporting solve errors 101 setup
87. priority scale scaling up upper bound 15 9 3 Set Value Items Set value items are easy to work with To output the set value only the identifier along with its index set has to be used In the example from Section 15 9 1 consider altering the loop statement to read loop i put i tl j i gt i te j The resulting output file looks like follows subset of sites il NO Seattle i2 NO Portland i3 YES San Francisco i4 YES Los Angeles i5 YES The second columns represents whether the element belongs to set j or not 15 10 Global Item Formatting It is often important to be able to control the display format of output items In this section we describe how this is done For formatting purposes output items are classified into four categories These are labels numeric values set values and text For each global formatting of the field width and field justification is possible 15 10 1 Field Justification The possible global justifications are right value 1 left value 2 and center value 3 The field justification is represented by the following file suffixes lj label justification default 2 nj numeric justification default 1 Sj set value justification default 1 tj text justification default 2 142 The Put Writing Facility 15 10 2 Field Width This is done using the following file suffixes lw label field width default 12 DW numeric field width default 12 SW set value field width d
88. program and the model what the solution looks like are characterized and a complete list of possible MODEL STATUS and SOLVER STATUS messages is given below Here is a list of possible MODEL STATUS messages 1 OPTIMAL This means that the solution is optimal It only applies to linear problems or relaxed mixed integer problems RMIP 2 LOCALLY OPTIMAL This message means that a local optimum has been found This is the message to look for if the problem is nonlinear since all we can guarantee for general nonlinear problems is a local optimum 10 5 Output Produced by a Solve Statement 95 3 UNBOUNDED This means that the solution is unbounded This message is reliable if the problem is linear but occasionally it appears for difficult nonlinear problems that are not truly unbounded but that lack some strategically placed bounds to limit the variables to sensible values 4 INFEASIBLE This means that the linear problem is infeasible Something is probably misspecified in the logic or the data 5 LOCALLY INFEASIBLE This message means that no feasible point could be found for the nonlinear problem from the given starting point It does not necessarily mean that no feasible point exists 6 INTERMEDIATE INFEASIBLE This means that the current solution is not feasible but that the solver program stopped either because of a limit iteration or resource or because of some sort of difficulty Check the solver status for more information 7
89. relational operator 30 GTM example from GAMSLIB 110 111 gumbel distribution 249 gyear function 58 handleCollect function 59 handleDelete function 59 handleStatus function 59 handleSubmit function 59 heapFree function 59 heapLimit function 59 heapSize function 59 hidden dollar control option 199 holdfixed model attribute 79 hyperGeo distribution 250 ide GAMS call parameter 179 identifiers 165 if dollar control option 199 if elseif else a statement 150 example 151 syntax 150 ifThen function 58 impl asn reference type 88 include dollar control option 201 index position s 165 indices controlling 54 INDUS example from GAMSLIB 48 inequality constraint 165 inf an extended range value 101 as a variable bound 75 128 extended range value 32 63 variable bound 66 infeasible 92 94 98 165 infes solution marker 98 initial values 28 68 initialization 88 165 INDEX 263 of data 43 of parameters 44 inlinecom dollar control option 201 input GAMS call parameter 179 inputdir GAMS call parameter 179 inputdirl to inputdir18 GAMS call parameter 179 integer infeasible 94 solution 94 variable 67 78 intermediate infeasible 94 noninteger 94 nonoptimal 94 intersection set operation 117 invGaussian distribution 249 iteration default limit 94 interrupt 95 iterlim GAMS option 217 model attribute 79 option 94 95 iterusd model a
90. scaling are exclusively based on algorithmic needs GAMS has been developed to increase the efficiency of modelers and one of the best ways seems to be to encourage modelers to write their models using a notation that is as natural as possible The units of measurement are one part of this natural notation and there is unfortunately a potential conflict between what the modeler thinks is a good unit and what constitutes a well scaled model 17 3 1 The Scale Option To facilitate the translation between a natural model and a well scaled model GAMS has introduced the concept of a scale factor both for variables and equations The notations and definitions are quite simple Scaling is turned off by default Setting the model suffix scaleopt to 1 turns on the scaling feature For example model mymodel all mymodel scaleopt 1 solve mymodel using nlp maximizing dollars The statement should be inserted somewhere after the model statement and before the solve statement In order to turn scaling off again set the model scaleopt parameter to 0 before the next solve The scale factor of a variable or an equation is referenced with the suffix scale i e the scale factor of variable x i is referenced as x scale i Note that there is one scale value for each individual component of a multi dimensional variable or equation Scale factors can be defined using assignment statements The default scale factor is always 1 GAMS scaling is in mos
91. specific equation is used in a solve statement This gives GAMS programs substantial organizational flexibility 3 3 Data Types and Definitions There are five basic GAMS data types and each symbol or identifier must be declared to belong to one of the following groups acronyms models sets equations parameters variables Scalars and tables are not separate data types but are a shorthand way to declare a symbol to be a parameter and to use a particular format for initializing the numeric data Definitions have common characteristics for example parameter a i j input output matrix data type keyword identifier domain list text The domain list and the text are always optional characteristics Other examples are set time time periods model turkey turkish fertilizer model variables X y Z In the last example a number of identifiers separated by commas are declared in one statement 3 4 Language Items Before proceeding with more language details a few basic symbols need to be defined and the rules for recognizing and writing them in GAMS established These basic symbols are often called lexical elements and form the building blocks of the language They are characters delimiters labels reserved words and tokens comments text numbers identifiers indents 30 GAMS Programs Each of these items are discussed in detail in the following sub sections t As noted previously we can use any mix of lower and upper case GAM
92. structure 14 5 Display Controls 131 first one b 5 63559 first two a 2 93930 first two b first three b 6 31610 second one a INF second one b second two a second two b 19 83500 0 02873 10 34570 1 00370 17 29948 INF Five places of decimals are shown and three labels are used to mark the rows and one on the column Since this is a four dimensional structure there are no remaining indices to be used as sub table labels on the plane and we now have the results in one piece The option statement is checked for consistency against the dimensionality of the identifier and error messages issued if necessary Here is an example that puts two indices on each of the row and column labels and retains five decimal places option x 5 2 2 display x The output is 12 PARAMETER X a i first one first two 2 93930 first three second one INF second two 14 5 3 Display Statement to Generate Data in List Format a four dimensional structure a ii b i b ii 5 63559 0 02873 10 34570 6 31610 1 00370 17 29948 INF 19 83500 This is a special use of the local display controls to generate data in list format using the display statement This is when all the labels are spelled out for each value as in the parameter style of data initialization The format of the option is option ident d value 0 c value and in this case the c value specifies the maximum number of items displayed on a line T
93. subitem1 ink yes subitem1 lipstick subitem2 item yes subitem2 perfume display subitem1 subitem2 yes no Note that the sets subitem1 and subitem2 are declared like any other set The two sets become dynamic because of assignments They are also domain checked the only members they will ever be able to have must also be members of item And item is a static set and henceforth its membership is frozen The first two assignments each add one new element to subiteml The third is an example of the familiar indexed assignment subitem2 is assigned all the members of item The output caused by the display statement that will reveal the membership of the sets is shown below for verification See 7 SET SUBITEM1 first subset of item INK P LIPSTICK PEN r PENCIL 7 SET SUBITEM2 second subset of item DISH gt INK gt LIPSTICK PEN 7 PENCIL ts The elements are displayed in the order specified in the declaration of item 12 2 3 Dynamic Sets with Multiple Indices Dynamic sets like static sets can have up to 20 dimensions The following example illustrates assignments for multi dimensional sets Sets item items sold pencil pen sup suppliers bic parker waterman supply item sup supply pencil bic yes supply pen sup yes All the mechanisms using asterisks and parenthesized lists that we introduced in the discussion on static sets in chapter 4 are available for dynamic
94. than the zero tolerance level set by nz In many situations it is important to know that these small values exist The default is 1 0 displayed in F or E format 1 rounded to fit fields 2 displayed in scientific notation numeric zero tolerance nz Sets the tolerance level for which a number will be rounded to zero for display purposes When it is set equal to zero rounding is determined by the field width Default value is 1 0e 5 The maximum size of a displayed number must fit within 20 spaces using at most 10 significant digits The remaining 10 spaces are used for the sign exponential notation or padding with zeros 15 12 1 Illustrative Example The following illustrative example shows the results of different combinations of these numeric file suffixes The example uses five combinations of the numeric file suffixes nd nz nr and nw Four number values each of which is shifted by three decimal places from its predecessor are used with these suffix combinations The com binations are chosen to show various format results when these suffix values are used together in put statements set c suffix combinations combi comb4 value indices valuei value3 table suffix c numeric suffix combinations nd nz nr nw comb1 3 0 0 12 comb2 3 le 5 0 12 comb3 3 le 5 1 12 comb4 8 0 0 10 comb5 6 le 5 2 12 parameter value v test values valuel 123 4567 value2 0 1234567 value3 0 0001234567 file out put out
95. the listing file eolcom This option redefines the end of line comment symbol which can be a one or two character sequence By default the system is initialized to but not active The oneolcom option is used to activate the end of line comment The eolcom option sets oneolcom automatically Consider the following example eolcom gt set i 1 2 gt set declaration parameter a i gt parameter declaration The character set gt serves as the end of line comment indicator GAMS requires that one not reset the eolcom option to the existing symbol The following code is illegal since eolcom is being reset to the same symbol as it is currently D 3 Detailed Description of Dollar Control Options 199 eolcom gt eolcom gt error This option will issue a compilation error and will continue with the next line Consider the following example if not exist myfile error File myfile not found will continue anyway This checks if the file myfile exists and if not it will generate an error with the comment File not found will continue anyway and then compilation continues with the following line exit This option will cause the compiler to exit stop reading from the current file This is equivalent to having reached the end of file Consider the following example scalara a 5 3 display a exit end a at5 display a The lines following the exit will not be compiled goto i
96. the following dollar control options the default value if available is D 3 Detailed Description of Dollar Control Options 195 bracketed abort This option will issue a compilation error and abort the compilation Consider the following example if not system filesys UNIX abort We only do UNIX This attempts to stop compilation if the operating system is not Unix Running the above example on a non Unix platform results in the compilation being aborted and the following listing file 2 abort We only do UNIX AK 343 Error Messages 343 Abort triggered by above statement batinclude The batinclude facility performs the same task as the include facility in that it inserts the contents of the specified text file at the location of the call In addition however it also passes on arguments which can be used inside the include file batinclude file argl arg2 The batinclude option can appear in any place the include option can appear The name of the batch include file may be quoted or unquoted while arg1 arg2 are arguments that are passed on to the batch include file These arguments are treated as character strings that are substituted by number inside the included file These arguments can be single unbroken strings quoted or unquoted or quoted multi part strings The syntax has been modeled after the DOS batch facility Inside the batch file a parameter substitution is indicated by using the character f
97. the installation program will create a default GAMS project in a subdirectory of your home folder Otherwise your existing GAMS projects will be preserved Choose the default solvers Run the GAMS IDE by double clicking gamside exe from the GAMS directory To view or edit the default solvers choose File Options gt Solvers from the IDE You can accept the existing defaults if you wish but most users want to select new default solvers for each model type Run a few models to test the GAMS system The on line help for the IDE Help GAMS IDE Help Topics gt Guided Tour describes how to copy a model from the GAMS model library run it and view the solution To test your installation run the following models from the GAMS model library LP trnsport objective value 153 675 NLP chenery objective value 1058 9 MIP bid optimal solution 15210109 512 MINLP procsel optimal solution 1 9231 MCP scarfmcp no objective function MPSGE scarfmge no objective function COMMAND LINE INSTALLATION Users wishing to use GAMS from the command line aka the console mode may want to perform the following steps after they have installed the system as described above These steps are not necessary to run GAMS via 254 Installation and System Notes the IDE 1 Run the program gamsinst gamsinst is a command line program used to install and configure GAMS It prompts the user for default solvers to be used for each model ty
98. the output file GAMS has several file suffixes which determine the location of the cursor and the last line of the file These suffixes can also be used to reposition the cursor or reset the last line As such they are instrumental in formatting output items in documents These suffixes are grouped by the title header or window writing area for which they are valid 15 13 1 Current Cursor Column These suffixes have numeric values corresponding to coordinates in the window of the page Because of this they can be used in conjunction with cursor control characters to manipulate the position of the cursor in the output file CC current cursor column in window hdcc header current column tlcc title current column t The convention for updating the values stored for the cc suffix is that it are updated at the conclusion of a put statement Consequently the cc value remains constant throughout the writing of items for the next put statement even if multiple items are displayed The following example illustrates the updating of the cursor control suffixes and the use of cursor control charac ters The example is trivial but instructive scalar lmarg left margin 6 file out put out put lmargt2 out cc out cc 0 0 7 put out cc x out cc y out cc z 7 put out cc out cc 0 0 The following is the resulting file out put out cc 1 x lt z out cc 23 Initially the scalar lmarg i
99. the result is set to undefined UNDF From there on UNDF is treated as a proper data value and does not trigger additional error messages t GAMS will not solve a model if an error has been detected but will terminate with an error condition It is thus always necessary to anticipate conditions that will cause errors such as divide by zero This is most easily done with the dollar control and will be discussed in the next section 6 4 Summary GAMS provides powerful facilities for data manipulation with parallel assignment statements built in functions and extended range arithmetic 64 Data Manipulations with Parameters 7 Variables 7 1 Introduction This chapter covers the declaration and manipulation of GAMS variables Many of the concepts covered in the previous Chapters are directly applicable here A variable is the GAMS name for what are called endogenous variables by economists columns or activities by linear programming experts and decision variables by industrial Operations Research practitioners They are the entities whose values are generally unknown until after a model has been solved A crucial difference between GAMS variables and columns in traditional mathematical programming terminology is that one GAMS variable is likely to be associated with many columns in the traditional formulation 7 2 Variable Declarations A GAMS variable like all other identifiers must be declared before it is referenced
100. the transportation problem contains the expression Sum j x i j that is equivalent to gt xij A slightly more complex summation is used in the following example Sum i j c i j x i j that is equivalent to 7 gt CijTij The last expression could also have been written as a nested summation as follows Sum i Sum j c i j x i j In Section 11 3 page 106 we describe how to use the dollar operator to impose restrictions on the summation operator so that only the elements of i and j that satisfy specified conditions are included in the summation Products are defined in GAMS using exactly the same format as summations replacing Sum by Prod For example prod j x i j is equivalent to Ijz Summation and product operators may be used in direct assignment statements for parameters For example scalar totsupply total supply over all plants totsupply sum i a i 14 A GAMS Tutorial by Richard E Rosenthal 2 6 3 Equation Definition Equation definitions are the most complex statements in GAMS in terms of their variety The components of an equation definition are in order The name of the equation being defined The domain Domain restriction condition optional The symbol Left hand side expression Relational operator 1 e or g Right hand side expression The transportation example contains three of these statements cost z e sum i j c i j x
101. to be 90 00 per case per thousand miles The GAMS representation of this problem is as follows Sets i canning plants seattle san diego j markets new york chicago topeka Parameters a i capacity of plant i in cases seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 Table d i j distance in thousands of miles new york chicago topeka seattle 2 5 1 7 1 8 san diego 2 5 1 8 1 4 Scalar f freight in dollars per case per thousand miles 90 Parameter c i j transport cost in thousands of dollars per case c i j f d i j 1000 Variables x i j shipment quantities in cases Zz total transportation costs in thousands of dollars Positive Variable x Equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j cost z e sum i j c i j xGi j supply i sum j x i j 1 a i 2 2 Structure of a GAMS Model 7 demand j sum i x i j g b j Model transport all Solve transport using lp minimizing z Display x 1 x m If you submit a file containing the statements above as input to the GAMS program the transportation model will be formulated and solved Details vary on how to invoke GAMS on different of computers but the simplest Cno frills way to call GAMS is to enter the word GAMS followed by the input file s name You will see a number of t
102. to the widest possible audience especially those without extensive experience with computers or mathematical programming systems Some familiarity with quantitative methods and mathematical representations is assumed The third part consists of specialized discussions of advanced topics and can be studied as needed Users with large complex or expensive models will find much useful material in this part Introduction A GAMS Tutorial by Richard E Rosenthal 2 1 Introduction The introductory part of this book ends with a detailed example of the use of GAMS for formulating solving and analyzing a small and simple optimization problem Richard E Rosenthal of the Naval Postgraduate School in Monterey California wrote it The example is a quick but complete overview of GAMS and its features Many references are made to other parts of the book but they are only to tell you where to look for more details the material here can be read profitably without reference to the rest of the book The example is an instance of the transportation problem of linear programming which has historically served as a laboratory animal in the development of optimization technology See for example Dantzig 1963 It is a good choice for illustrating the power of algebraic modeling languages like GAMS because the transportation problem no matter how large the instance at hand possesses a simple exploitable algebraic structure You will see that almo
103. what solution to retrieve by setting the minvar handle to the appropriate value Then we can use execute_loadhandle to load the solution for model minvar back into the GAMS data base Using handlestatus and loadhandle instead of the simpler handlecollect adds one more layer of control to the final collection loop We now need one additional if statement inside the above collection loop Repeat loop pp h pp if handlestatus h pp 2 minvar handle h pp execute_loadhandle minvar xres i pp x 1 i report pp i inc xi 1 i report pp i dec xd 1 i display handledelete h pp trouble deleting handles h pp 0 240 The GAMS Grid Computing Facility display sleep card h 0 2 sleep some time until card h O or timeelapsed gt 100 xres i pp h pp na Now we are ready to run the modified model The execution log will contain some new information that may be useful on more advanced applications LOOPS pp pl Soa 46 rows 37 columns 119 non zeroes 311 nl code 7 nl non zeroes a 14 discrete columns Submitting model minvar with handle grid137000002 Executing after solve GDXin C answerv5 gams_srcdev 225j grid137000003 gmsgrid gdx Removing handle grid137000003 The log will now contain some additional information about the submission retrieval and removal of the solution instance In the following sections we will make use of this additional information
104. width is given a value of 0 the field width is variable in size The item width and decimals are delimited with colons as shown above The use of the local format feature as well as the inclusion any of the components for justification field width or the number of decimals is entirely optional The following example shows some examples of the local formatting feature default justification and a field width of variable size with no decimals loop i put dist i 0 0 put Right justified comment gt 50 Center justified truncated comment lt gt 20 left justified scalar with a six space field width and two decimals put f lt 6 2 15 12 Additional Numeric Display Control 143 15 12 Additional Numeric Display Control In addition to the numeric field width and the numeric justification as mentioned in the previous section the following file suffixes can also be globally specified for numeric display number of decimals displayed nd Sets the number of decimals displayed for numeric items A value of 0 results in only the integer portion of a number being displayed The maximum value is 10 The default value is 2 numeric round format nr Allows one to display a numeric value in scientific notation which would otherwise be displayed as zero because of being smaller than the number of decimals allowed by the nd suffix This situation occurs when a number is smaller than the nd specification but is larger
105. with mean MEAN and standard deviation STD_DEV see MathWorld Normal distribution with mean MEAN and standard deviation STD_DEV see MathWorld Pareto distribution with scaling parameter SCALE and shape parameter SHAPE see MathWorld Rayleigh ditribution with parameter SIGMA see MathWorld Student s t distribution with degrees of freedom DF see MathWorld Triangular distribution between LOW and HIGH MID is the most probable number see MathWorld Uniform distribution between LOW and HIGH see MathWorld Weibull distribution with shape parameter SHAPE and scaling parameter SCALE see MathWorld 250 Extrinsic Functions Discrete distributions binomial N P geometric P hyperGeo TOTAL GOOD TRIALS logarithmic P FACTOR negBinomial FAILURES P poisson LAMBDA uniformInt LOW HIGH Binomial distribution with number of trials N and succes probability P in each trial see MathWorld Geometric distribution with succes probability P in each trial see Math World Hypergeometric distribution with total number of elements TOTAL num ber of good elements GOOD and number of trials TRIALS see MathWorld Logarithmic distribution with parameter P FACTOR also called log series distribution see MathWorld Negative Binomial distribution with the number of failures until the ex periment is stopped FAILURES and succes probability P in each trial see MathWorld Poisson distribution with mean L
106. 0 Variables x i j shipment quantities in cases z total transportation costs in 1000 Positive Variable x Equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j cost z e sum i j c i j x i j supply i sum j x i j l a i demand j sum i x i j g b j Model transport all Consider the following file say file2 gms Solve transport using lp minimizing z Display x 1 x m Note that TRNSPORT results from appending file2 gms at the end of file1 gms F 2 1 Saving The Work File The information in file1 gms can be stored by using the following call to GAMS gams filei s trans One work file called trans g00 is created in the working directory The Work file preserves all information including declarations values option settings and compiler dollar directives known to GAMS at the end of the run that created them ts The work file is not machine specific it is portable between platforms For example a work file generated on a PC running Windows can be re used on a Sun machine running Solaris F 2 2 Restarting from the Work File Consider the following call gams file2 r trans GAMS reads the work file named trans g00 and regenerates the information stored in file1 gms Then file2 gms is run and the result is as if the two files were concatenated A restarted run also requires a continuati
107. 118 Dynamic Sets 13 Sets as Sequences Ordered Sets 13 1 Introduction In our original discussion of sets in Chapter 4 we said that unless there is a special need to do things differently a one dimensional set should be regarded as an unordered collection of labels In this chapter we will discuss special features that can be used when you need to be able to deal with a set as if it were a sequence For example in economic models that explicitly represent conditions in different time periods it is necessary to refer to the next or previous time period because there must be links between the periods As another example stocks of capital are normally tracked through such models by equations of the form stocks at the end of period n are equal to stocks at the end of period n 1 plus net gains during period n Location problems where the formulation may require a representation of contiguous areas as in a grid representation of a city and scheduling problems are other classes of problems in which sets must also have the properties of sequences ts Models involving sequences of time periods are often called dynamic models because they describe how conditions change over time This use of the word dynamic unfortunately has a different meaning from that used in connection with sets but this is unavoidable 13 2 Ordered and Unordered Sets As with sets used in domain checking restrictions are imposed when the set needs to be refe
108. 1991 parameter a t c t a t 1986 ord t c t 1 c t 2 a t 0 display a c The results are shown below a5 6 PARAMETER A Y 1987 1987 Y 1988 1988 Y 1989 1989 Y 1990 1990 Y 1991 1991 6 PARAMETER C Y 1987 1 Y 1988 1 Y 1989 1987 Y 1990 1988 Y 1991 1989 The assignment to a is explained in Section 13 5 1 The assignment to c is different It is best to spell it out in words For each member of t in sequence find the member of c associated with t 2 If it exists replace its value with that of a t If not as with y 1990 and y 1991 make no assignment The first member of t is y 1987 13 6 Lags and Leads in Equations 123 and therefore the first assignment is made to c y 1989 which takes the value of a y 1987 viz 1987 No assignments at all are made to c y 1987 or c y 1988 these two retain their previous values of 1 The lag or lead value does not have to be an explicit constant it can be arbitrary expression provided that it evaluates to an integer If it does not error messages will be produced A negative result causes a switch in sense from lag to lead for example The following is guaranteed to set d t to all zero d t d t ord t 13 5 3 Circular Lag and Lead Operators The following example illustrates the use of circular lag and lead operators set seasons spring summer autumn winter parameter val s spring 10 summer 15 autumn 12 winter 8
109. 2 i j a b c ij3 1 3 a b c d The parenthesis provides a list of elements that can be expanded when creating pairs ts When complex sets like this are created it is important to check that the desired set has been obtained The checking can be done by using a display statement The concepts may be generalized to set with more than two labels per set element Mathematically these are called 3 tuples 4 tuples or more generally n tuples This section ends with some examples to illustrate definitions of multi label set elements Some examples of the compact representation of sets of n tuples using combinations of dots parentheses and commas are shown in table 4 1 Construct Result a b c d a c d b c d a b c d e a c e b c e a d e b d e a 1 x3 c a 1 a 2 a 3 cora 1 c a 2 c a 3 c 1x3 1 3 1 3 1 1 1 1 1 2 1 1 3 3 3 3 Table 4 1 Examples of the compact representation of sets Note that the asterisk can also be used in conjunction with the dot Recall that the elements of the list 1 4 are 1 2 3 4 when examining the examples in table 4 1 4 6 Summary 41 4 6 Summary In GAMS a simple set consists of a set name and the elements of the set Both the name and the elements may have associated text that explains the name or the elements in more detail More complex sets have elements that are pairs or even n tuples These sets with pairs and n tuples are ideal for establishing relationships
110. 20 SECONDS 67 DISPLAY 0 010 0 030 SECONDS 67 GAMS FINI 0 000 0 030 SECONDS The first column provides the line number in the input file of the statement being executed The second column provides the type of statement being executed EXEC INIT denotes the beginning of the execution phase of the GAMS input file GAMS FINI denotes the end of this phase Note that GAMS finishes processing of an input file as soon as a solve statement is processed and passes control to the solver being called After the solver is done GAMS restarts This causes two EXEC INIT GAMS FINI pairs to be generated for TRNSPORT ASSIGNMENT C denotes an assignment statement involving the identifier c SOLVE INIT SOLVE FINI are book ends enclosing the generation of the model TRNSPORT Note that only equations are listed and not variables This happens because GAMS uses an equation based scheme to generate a model The third and fourth columns provide the individual time needed to execute the statement and the cumulative time taken by the GAMS system so far The last column gives the number of assignments generated in the specified line 186 The GAMS Call putdir pdir text put directory This option specifies the directory where the put files are generated and saved If not specified it will be set to the working directory This option does not work if an absolute file name is provided through the file statement acp qcp tezt default QCP solver
111. 32 rayleigh distribution 249 ref reference type 88 reference GAMS call parameter 186 rel_eq function 58 rel_ge function 58 rel_gt function 58 rel_le function 58 rel_lt function 58 rel_ne function 58 relational operator 166 relpath GAMS call parameter 186 report summary 98 reporting format 100 reserved words 30 reslim GAMS option 218 model attribute 79 resource interrupt 95 restart GAMS call parameter 186 resusd model attribute 79 right hand side 166 rminlp GAMS call parameter 186 GAMS option 218 RMINLP model type 16 78 rmip GAMS call parameter 186 GAMS option 218 INDEX 267 RMIP model type 15 78 RMIQCP model type 16 round function 55 rPower function 55 rules constructing tables 46 formating tables 46 save GAMS call parameter 186 scalar 166 equation 73 example 44 statement 43 syntax 43 scale model attribute 79 option 158 scaling models 158 of a variable 159 of an equation 159 of derivate 160 scenario analysis 81 serdir GAMS call parameter 187 scriptexit GAMS call parameter 187 scriptfrst GAMS call parameter 187 scriptnext GAMS call parameter 187 scrnam GAMS call parameter 187 Secure Work Files 227 seed GAMS option 218 semi continuous variables Definition 157 Example 157 semi integer variables definition 157 example 157 semicolon 31 set 166 associated text 36 declaration for multiple sets 37 definition
112. 35 dynamic 113 elements 36 multi dimensional 39 multi dimensional many to many 40 multi dimensional one to one mapping 39 names 35 sequences as set elements 37 simple 35 syntax 35 set operations complement 117 difference 117 intersection 117 union 117 setMode function 251 SHALE example from GAMSLIB 36 shift dollar control option 212 sigmoid function 55 sign function 55 74 signed number 43 44 46 signPower function 55 simple assignment 51 simplex method 166 sin function 55 74 sine function 251 single dollar control option 212 sinh function 55 slack 166 slack variable 166 slash delimiter 32 134 sleep function 59 slexp function 55 sllog10 function 55 slrec function 55 smax operator 54 55 smin operator 54 55 smooth 166 functions 74 solprint GAMS option 218 model attribute 79 solslack GAMS option 219 solution listing 97 solve errors 101 errors messages 100 statement 77 solve statement actions triggered by 80 requirements 80 several in a program 81 several models 81 syntax 80 solve summary 93 evaluation errors 94 iteration count 94 objective summary 94 resource usage 94 solver status 94 solveopt GAMS option 219 268 INDEX model attribute 79 solver 166 solver status 79 94 evaluation error limit 95 iteration interrupt 95 normal completion 95 other errors 95 resource interrupt 95 terminated by solver 95 unknow
113. 50 VARIABLE X M shipment quantities in cases chicago topeka seattle 0 036 san diego 0 009 As seen in reference maps equation listings solution reports and optional displays GAMS saves the documentary text and parrots it back throughout the output to help keep the model well documented 2 12 Summary This tutorial has demonstrated several of the design features of GAMS that enable you to build practical opti mization models quickly and effectively The following discussion summarizes the advantages of using an algebraic modeling language such as GAMS versus a matrix generator or conversational solver gt By using an algebra based notation you can describe an optimization model to a computer nearly as easily as you can describe it to another mathematically trained person gt Because an algebraic description of a problem has generality most of the statements in a GAMS model are reusable when new instances of the same or related problems arise This is especially important in environments where models are constantly changing gt You save time and reduce generation errors by creating whole sets of closely related constraints in one statement gt You can save time and reduce input errors by providing formulae for calculating the data rather than entering them explicitly gt The model is self documenting Since the tasks of model development and model documentation can be done simultaneously the modeler is much more likely to be
114. 6 on offglobal dollar control option 206 on offinclude dollar control option 207 on offinline dollar control option 207 on offlisting dollar control option 207 on offmargin dollar control option 208 on offmulti dollar control option 208 on offnestcom dollar control option 209 on offsymlist dollar control option 209 on offsymxref dollar control option 209 on offtext dollar control option 210 on offuellist dollar control option 210 on offuelxref dollar control option 210 on offupper dollar control option 210 on offwarning dollar control option 211 opt GAMS call parameter 183 optca GAMS option 218 model attribute 79 optcr GAMS option 218 model attribute 79 optdir GAMS call parameter 183 optfile GAMS call parameter 184 model attribute 79 optimal 166 option 166 introduction 215 syntax 215 or relational operator 115 ORANI example from GAMSLIB 38 ordered set 166 card operator 121 circular lag and lead operator 123 introduction 119 lags and leads in assignments 121 lags and leads in equations 123 linear lag and lead operator 122 ord operator 120 output 166 GAMS call parameter 184 output file 166 pagecontr GAMS call parameter 184 pagesize GAMS call parameter 185 pagewidth GAMS call parameter 185 parameter 166 examples 44 higher dimensions 45 266 INDEX statement 44 hdec 144 syntax 44 tlec 144 pareto distribution 249 put lo
115. 8 4 3 Preventing Undefined Operations in Equations Certain operations can be undefined at particular values for the arguments For example the log function is undefined when the argument is 0 Division by 0 is another example While this can easily be determined for exogenous functions and expressions it is a lot more difficult when the operands are variables The expression may be evaluated many times when the problem is being solved One way of preventing an expression from becoming undefined at all intermediate points is by adding bounds to the variable concerned Consider the following function reference from RAMSEY preceded by the bounding of the variables 8 5 Data Handling Aspects of Equations 75 c lo t 0 01 util utility e sum t beta t log c t The bounding on c t away from 0 prevents the log function from being undefined 8 5 Data Handling Aspects of Equations The previous section dealt with the algebraic nature of equations This section deals with the other aspect of an equation it also serves as data As with variables four data values are associated with each unique label tuple unique label combination of every equation In practice these are used mainly for reporting purposes after a solve and so the discussion will be brief The suffixes associated with the four values are 1 m 1o and up as with variables They may be assigned values in assignments this is rare or referenced in expressions or d
116. A Glossary acronym A GAMS data type used to give logical classifications to data points alias An alternative name for a set algorithm This term may be used in two ways It is either a prescription for how to solve a problem or a particular solver system assignment The statement used to change values associated with an identifier basic A classification of a row or column that is in the basis maintained by solution methods that use linear programming iterations binding An inequality constraint is binding when the value of the associated slack is zero bounds Upper and lower limits on the possible values that a column may assume in a feasible solution May be infinite meaning that no limit is imposed column An individual decision variable in the model seen by a solver program Many may be associated with one GAMS variable compilation The initial phase of GAMS processing when the program is being checked for syntax and consistency constant set A set is constant if it remains unchanged It has to be initialized with a set definition statement and cannot be changed using assignment statement Sets used in domain definitions must be constant Sets used in lag operations must be ordered as well Sometimes the word static is used instead of constant constraint A relationship between columns that must hold in a feasible solution There may be many constraints associated with one GAMS equation continuous There are two contexts Firs
117. AMBDA see MathWorld Integer Uniform distribution between LOW and HIGH see MathWorld Table J 3 Random number generators For each distribution in table J 3 the library offers four functions Function Endogenous Description Classifica tion d lt DistributionName gt none generates a random number pdf lt DistributionName gt cdf lt DistributionName gt icdf lt DistributionName gt DNLP none for discrete distributions DNLP none for discrete distributions DNLP none for discrete distributions probability density function cumulative distribution function inverse cumulative distribution func tion J 5 Table J 4 Distribution functions Trigonometric Library This library comes in three versions They come with the GAMS Test Library models trilib01 trilib02 and trilib03 and can be found compiled and as source code written in C Delphi and FORTRAN respectively J 5 Trigonometric Library 251 Function Endogenous Description Classifica tion setMode MODE none sets mode globally could still be overwritten by MODE at Co Sine call possible values are 0 radians and 1 degree cosine x MODE NLP returns the cosine of the argument x default setting MODE 0 sine x MODE NLP returns the sine of the argument x default setting MODE 0 pi any value of 7 3 141593 Table J 5 Trigonometric functions 252 Extrinsic Functions K Installation and System Notes Windows INSTALL
118. ATION de Run windows_x86_32 exe Windows 32bit or windows _x64_64 exe Windows 64bit Both files are either available on the GAMS web site or on the distribution DVD in the directory windows The 32 bit version works both on a 32bit and on a 64bit operating system Please note that the installation may require administrative privileges on your machine The installer will first prompt you for the name of the directory in which to install GAMS We call this directory the GAMS directory You may accept the default choice or pick another directory Please remember if you want to install two different versions of GAMS they must be in separate directories Copy the GAMS license file You will be asked for the GAMS license file gamslice txt during the installation If you are not sure if you have a license file choose No when asked if you wish to copy a license file You can always do this later If no valid license file is found GAMS will still function in the demonstration mode but will only solve small problems All demonstration and student systems do not include a license file If you have a license file you wish to copy to the GAMS directory at this time answer Yes You will now be given the opportunity to browse the file system and find the license file gamslice txt When you have found the correct file choose open to perform the copy Create a project file If this is the first installation of GAMS on your system
119. Also acts as a delimiter between output items In addition to numerals any expression or symbol with a numeric value can be used to follow the and characters The following example illustrates the use of these position controls to write out the value of a parameter a i j in a tabular form file out put out scalar col column number 1 loop i loop j put col a i j col co1 10 put Js 15 8 System Suffixes The complete list of system suffixes that can be used to recover information about the GAMS run are date program execution date ifile input file name ofile output file name page current file page rdate restart file date rfile restart file name rtime restart file time sfile save file name time program execution time title title of the model as specified by title As an illustration consider the example discussed in the previous section One can add page numbers to the title of the report file by modifying the putt1 statement to read puttl class2 GAMS Put Example 65 page system page This causes the word page followed by the page number to appear on the title of every page starting at column 65 15 9 Output Items Output items for the put statement are of the following forms text Any quoted text set element label or text any identifier symbol text or contents of the system suffixes numeric Values associated with parameters variables equations or any of the mo
120. COMPLETION This means that the solver terminated in a normal way i e it was not interrupted by an iteration or resource limit or by internal difficulties The model status describes the characteristics of the accompanying solution 96 GAMS Output 2 ITERATION INTERRUPT This means that the solver was interrupted because it used too many iterations Use option iterlim to increase the iteration limit if everything seems normal 3 RESOURCE INTERRUPT This means that the solver was interrupted because it used too much time Use option reslim to increase the time limit if everything seems normal 4 TERMINATED BY SOLVER This means that the solver encountered difficulty and was unable to continue More detail will appear following the message 5 EVALUATION ERROR LIMIT Too many evaluations of nonlinear terms at undefined values You should use bounds to prevent forbidden operations such as division by zero The rows in which the errors occur are listed just before the solution 6 CAPABILITY PROBLEMS The solver does not have the capability required by the model for example BARON has a more limited set of functions than other solvers 7 LICENSING PROBLEMS The solver cannot find the appropriate license key needed to use a specific subsolver 8 USER INTERRUPT The user has sent a message to interrupt the solver via the interrupt button in the IDE or sending a control C from a command line 9 ERROR SETUP FAILURE The solver encountered a fat
121. E SUMMARY MODEL PORTFOLIO OBJECTIVE VARIANCE TYPE NLP DIRECTION MINIMIZE SOLVER MINOS5 FROM LINE 48 x x SOLVER STATUS 1 NORMAL COMPLETION xxx MODEL STATUS 2 LOCALLY OPTIMAL OBJECTIVE VALUE 2 8990 RESOURCE USAGE LIMIT 0 020 1000 000 ITERATION COUNT LIMIT 5 10000 EVALUATION ERRORS 0 0 The common part of the solve summary is shown above It can be found mechanically by searching for four asterisks The explanation for the information provided in this section follows MODEL PORTFOLIO This provides the name of the model being solved TYPE NLP 94 GAMS Output This provides the model type of the model being solved SOLVER MINOS5 This provides the name of the solver used to solve the model OBJECTIVE VARIANCE This provides the name of the objective variable being optimized DIRECTION MINIMIZE This provides the direction of optimization being performed xxx SOLVER STATUS 1 NORMAL COMPLETION xo MODEL STATUS 2 LOCALLY OPTIMAL These provide the solver status and model status for the problem and are discussed in greater detail at the end of this subsection x OBJECTIVE VALUE 2 8990 This provides the value of the objective function at the termination of the solve If the Solver and Model have the right status this value is the optimum value for the problem RESOURCE USAGE LIMIT 0 109 1000 000 These two entries provide the amount of CPU time in seconds taken by the solver as well as the upper limit
122. Error 59 execSeed 55 exp 55 fact 55 fitFunc 247 fitParam 247 floor 55 frac 55 gamma 55 gammaReg 55 gamsRelease 59 gamsVersion 59 gday 58 gdow 58 ghour 58 INDEX 261 gleap 58 gmillisec 58 gminute 58 gmonth 58 gsecond 58 gyear 58 handleCollect 59 handleDelete 59 handleStatus 59 handleSubmit 59 heapFree 59 heapLimit 59 heapSize 59 ifThen 58 jdate 58 jnow 58 jobHandle 59 jobKill 59 jobStatus 59 jobTerminate 59 jstart 58 jtime 58 licenseLevel 59 licenseStatus 59 log 55 log10 55 log2 55 logBeta 55 max 55 maxExecError 59 min 55 mod 55 ncpCM 55 nepF 55 ncpVUpow 55 ncpVUsin 55 normal 55 pi 55 251 poly 55 power 55 pwpFunc 248 randBinomial 55 randLinear 55 rand Triangle 55 rel_eq 58 rel_ge 58 rel_gt 58 rel le 58 rel_lt 58 rel_ne 58 round 55 rPower 55 setMode 251 sigmoid 55 sign 55 signPower 55 sin 55 sine 251 sinh 55 sleep 59 slexp 55 sllog10 55 slrec 55 sqexp 55 sqlog10 55 sqr 55 sqrec 55 sqrt 55 tan 55 tanh 55 timeClose 59 timeComp 59 timeElapsed 59 timeExec 59 timeStart 59 trunc 55 uniform 55 vcPower 55 g205 GAMS call parameter 178 gamma distribution 249 gamma function 55 gammaReg function 55 GAMS call parameter action 191 appendlog 191 appendout 191 botmargin 191 case 191 cerr 191 ctrlm 191 ctrlz 191 curdir 191 dformat 191 dumpopt 191
123. Facility 1 Generation The symbolic equations of the model are used to instantiate the model using the current state of the GAMS data base This instance contains all information and services needed by a solution method to attempt a solution This representation is independent of the solution subsystem and computing platform 2 Solution The model instance is handed over to a solution subsystem and GAMS will wait until the solver subsystem terminates 3 Update The detailed solution and statistics are used to update the GAMS data base In most cases the time taken to generate the model and update the data base with the solution will be much smaller than the actual time spent in a specific solution subsystem The model generation takes a few seconds whereas the time to obtain an optimal solution may take a few minutes to several hours If sequential model solutions do not depend on each other we can solve in parallel and update the data base in random order All we need is a facility to generate models submit them for solution and continue At a convenient point in our GAMS program we will then look for the completed solution and update the data base accordingly We will term this first phase the submission loop and the subsequent phase the collection loop Submission Loop In this phase we will generate and submit models for solutions that can be solved indepen dently Collection Loop The solutions of the previously submitted models are
124. GAMS A User s Guide Tutorial by Richard E Rosenthal July 2011 GAMS Development Corporation Washington DC USA Table of Contents 1 Introduction 1 1 1 2 1 3 MIRES o a mu Gow ew A A BA a e aa Ser ark Bela as Pase Fontur o GANG o a a a Se 2 ae a E d a es LAT emerald Progpley eai a ioue a a A ee A A aak an lie Documentation 3 s ua botea eee e o id A HB S a a a EE A Ioe Toma Sondas cra ia a e a a id a Ea A S L24 User Ir ciuda ee a a Ma A a AA es E a E a Gee a Lee Model Libraiy ssaa ci sc AA ae GS Aa ERR ar ai a RLS ew EE Organization Of the Book ea Gh bade eh Ee Ee ee EE ERR ER Rae es 2 A GAMS Tutorial by Richard E Rosenthal 2 1 2 2 2 3 2 4 2 5 2 6 ET 2 8 2 9 2 10 2 12 Tarodd uctign aaa AE AE ARA A EE eS Structure of a GAMS Model ccoc co ee ee E ad be eee eee ONG ce eek A A ae ek SSS Owe be Bee ek Ee e oa ee et ee ge ee A es ee et 241 Data Entry by Lists lt soe coce heed A me DEGREE EET A DEAE Ee ES 242 Data Entry De Table oars be ee ea ee ee ae ea ee ae A Ee eee ee Ges 24 3 Data Entry by Direct Assignment oca we ee ew ee Worle ea hg s E BA Gees BEE ye SS ER AR BO OHS ee ORS o e i ee ek Gee a aces w a ea wee oe ee ee ee A ee ae a 26 Eguation Declaration ok ee OS Se RR KEE EAR MAD ee eee 2 6 2 GAMS Summation and Product Notation ie 0 0 0002 000 e 263 Eguation DERIO cis ee ae eee ee le PP ee eS Pojechine PaO m a p pad dred hk E eee Oo we AR ok ee Ene and Model an
125. Gu to the equation as seen by the algorithm Ga as follows Ga Gu Gs For example consider the following equations positive variables y1 y2 equation eqi eq2 eqi 200 y1 100 y2 1 500 eq2 3xy1 4 y2 g 6 By setting eq1 scale to 100 the model seen by the solver is positive variables y1 y2 equation eqprimel eq2 eqprimel 2 y1 1xy2 1 5 eq2 3xy1 4 y2 g 6 t The user may have to perform a combination of equation and variable scaling until a well scaled model is obtained Consider the following example positive variables x1 x2 equation eqi eq2 eqi 100 x1 5 x2 g 20 eq2 50 x1 10 x2 1l 5 x1 up 0 2 x2 up 1 5 160 Special Language Features Setting the following scale values x1 scale 0 1 eqi scale Buy eq2 scale 53 will result in the solver seeing the following well scaled model positive variables xprime1 x2 equation eqprimel eqprime2 eqprimel 2 xprimei x2 g 4 eqprime2 xprimel 2 xprime2 1 1 xprimel up 2 x2 up 1 5 17 3 4 Scaling of Derivatives For nonlinear models the derivatives also need to be well scaled The derivatives in the scaled model seen by the algorithm i e d Ga d Va are related to the derivatives in the user s model d G d V through the formula d Ga d Va d Gu d Va V Gs The user can affect the scaling of derivatives by scaling both the equation and variable involved Appendix
126. MS please follow the steps below as closely as possible We advise you to read this entire document before beginning the installation procedure 1 Choose a location for the GAMS system directory the directory where the GAMS system files should reside We recommend to choose a name that indicates the distribution of GAMS you are installing For example if you are installing the 23 3 distribution a good choice for the GAMS system directory would be usr gams 23 3 If the directory where you want to install GAMS is not below your home directory you may need to have root privileges on the machine 2 Create the GAMS system directory for instance usr gams 23 3 Go to this directory Make sure pwd returns the name of this directory correctly 3 Transfer the distribution file into the GAMS system directory This file is available from the GAMS DVD or via the web in one large self extracting zip archive with a _sfx exe file extension You can run the archive e g Linux_x86_32_sfx exe on a Linux 32bit system directly from the DVD to extract the necessary files to the system directory For example you might execute the following commands mkdir usr gams 23 3 cd usr gams 23 3 dev dvd linux linux_x86_32_sfx exe 4 To mount the GAMS DVD you may need to be logged in as root We assume you want to mount the DVD over the directory dvd If the directory you want to mount over does not exist you must create it now Once this directory is created
127. Manager a system for high throughput computing from the University of Wisconsin or the Sun Grid Engine Researchers using Condor reported a delivery of 5000 CPU hours in 20 hours wall clock time Disclaimer The use of the term grid computing may be offensive to some purists in the computer science world We use it very loosely to refer to a collection of computing components that allow us to provide high throughput to certain applications One may also think of it as a resurrection of the commercial service bureau concept of some 30 years ago Caution Although these features have been tested on all platforms and are part of our standard release we may change the approach and introduce alternative mechanisms in the future Acknowledgments Prof Monique Guignard Spielberg from the Wharton School at U Penn introduced us to parallel Lagrangian Relaxation on the SUN Grid Environment Prof Michael Ferris from the University of Wisconsin at Madison adopted our original GAMS grid approach to the high throughput system Condor and helped to make this approach a practical proposition 1 2 Basic Concepts The grid facility separates the solution into several steps which then can be controlled separately We will first review what happens during the synchronous solution step and then introduce the asynchronous or parallel solution steps When GAMS encounters a solve statement during execution it proceeds in three basic steps 238 The GAMS Grid Computing
128. NTERMEDIATE NONOPTIMAL OBJECTIVE VALUE 1 0000 102 GAMS Output RESOURCE USAGE LIMIT 0 141 1000 000 ITERATION COUNT LIMIT 0 10000 EVALUATION ERRORS 2 0 EXIT Termination requested by User in subroutine FUNOBJ after 7 calls soe ERRORS S IN EQUATION ONE 2 INSTANCES OF DIVISION BY ZERO RESULT SET TO 0 1E 05 oexx REPORT SUMMARY NONOPT NOPT INFEASIBLE UNBOUNDED ERRORS x xx x NOOR Note that the solver status returned with a value of 5 meaning that the solver has been interrupted because more than domlim evaluation errors have been encountered The type of evaluation error and the equation causing the error are also reported If the solver returns an intermediate solution because of evaluation errors the following solve will still be at tempted The only fatal GAMS error that can be caused by a solver program is the failure to return any solution at all If this happens as mentioned above all possible information is listed on the GAMS output file and any solves following will not be attempted 10 7 Summary This is the end of the sequential discussion of the basic features of the GAMS language All further chapters are geared towards more advanced use of GAMS 11 Conditional Expressions Assignments and Equations 11 1 Introduction This chapter deals with the way in which conditional assignments expressions and equations are made in GAMS The index operations already described are very powerful
129. PL ASN 52 REF 52 TARGET PARAM DECLARED 13 DEFINED 13 REF 47 V PARAM DECLARED 24 DEFINED 24 REF 34 48 VARIANCE VAR DECLARED 38 IMPL ASN 52 REF 48 52 X VAR DECLARED 37 IMPL ASN 52 REF 40 46 47 2 48 For each symbol the name and type of the symbol are first provided For example the last symbol listed is X which is defined to be of type VAR The complete list of data types are given in table 10 1 Entry in symbol reference table GAMS Data Type EQU equation MODEL model PARAM parameter SET set VAR variable Table 10 1 List of GAMS data types Then comes a list of references to the symbol grouped by reference type and identified by the line number in the output file The actual reference can then be found by referring to the echo print of the program which has line numbers on it In the case of the symbol X in the example above the list of references as shown in the symbol reference map are as follows DECLARED 37 IMPL ASN 52 REF 40 46 47 2 48 This means that X is declared on line 37 implicitly assigned through a solve statement on line 52 and referenced on lines 40 46 and 47 The entry 2 48 means that there are two references to X on line 48 of the input file The complete list of reference types is given below DECLARED This is where the identifier is declared as to type This must be the first appearance of the identifier DEFINED This is the line number where an initialization a table or a data list between slashes
130. Parameters statement of the example which is repeated below Parameters a i capacity of plant i in cases seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 This statement has several effects Again they may be self evident but it is worthwhile to analyze them in detail The statement declares the existence of two parameters gives them the names a and b and declares their domains to be i and j respectively A domain is the set or tuple of sets over which a parameter variable or equation is defined The statement also gives documentary text for each parameter and assigns values of a i and b j for each element of i and j It is perfectly acceptable to break this one statement into two if you prefer as follows Parameters a i capacity of plant i in cases seattle 350 san diego 600 Parameters b j demand at market j in cases new york 325 chicago 300 topeka 275 Here are some points to remember when using the list format 1 The list of domain elements and their respective parameter values can be laid out in almost any way you like The only rules are that the entire list must be enclosed in slashes and that the element value pairs must be separated by commas or entered on separate lines 2 There is no semicolon separating the element value list from the name domain and text that precede it This is because the same statement is being used for declaratio
131. Pi scalar i grad rad intrinsic for i 1 to 360 intrinsic cos i 180 pi grad mycos i 1 abort round abs intrinsic grad 4 cos i intrinsic grad rad mycos i 180 pi abort round abs intrinsic rad 4 cos i intrinsic rad variable x equation e e sqr mysin x sqr mycos x e 1 model m e x lo 0 x 1 3 mypi solve m min x using nlp The following lines from the listing file describe the library loaded FUNCLIBIN trilib tridclib Function Library trilib Mod Function Description Type NLP Cosine x MODE Cosine mode 0 default gt rad mode 1 gt grad NLP Sine x MODE Sine mode 0 default gt rad mode 1 gt grad any Pi Pi A description of the libraries included in the GAMS sytem can be found in Appendix J 6 3 4 Extended Range Arithmetic and Error Handling GAMS uses an extended range arithmetic to handle missing data the results of undefined operations and the representation of bounds that solver systems regard as infinite The special symbols are listed in table 6 2 with the brief explanation of the meaning of each GAMS has defined the results of all arithmetic operations and all function values using these special values The results can be inspected by running the model library problem CRAZY As one would expect 1 INF evaluates to INF and 1 EPS to 1 ts The mapval function should be used in comparisons involving extended range arithmetic O
132. S makes no distinction between upper and lower case 3 4 1 Characters A few characters are not allowed in a GAMS program because they are illegal or ambiguous on some machines Generally all unprintable and control characters are illegal The only place where any character is legal is in an Sontext Sofftext block as illustrated in the section on comments below For completeness the full set of legal characters are listed in table 3 2 Most of the uncommon punctuation characters are not part of the language but can be used freely in text or comments AtoZ alphabet atoz alphabet Oto9 numerals amp ampersand double quote pound sign asterisk equals question mark at gt greater than semicolon back slash lt less than single quote colon minus slash comma parenthesis space dollar square brackets underscore dot braces exclamation mark plus percent circumflex Table 3 2 Legal characters 3 4 2 Reserved Words GAMS like computer languages such as C and Pascal uses reserved words often also called keywords that have predefined meanings It is not permitted to use any of these for one s own definitions either as identifiers or labels The complete list of reserved words are listed in table 3 3 In addition a small number of symbols constructed from non alphanumeric characters have a meaning in GAMS abort eps integer not sameas sum acronym eq le option scalar system acronyms
133. Statement en 9 3 3 Actions Triggered by the Solve Statement o 9 4 Programs with Several Solve Statements ee ee 9 4 1 Several Modelg cocida Re a ae ee Be ae a A ee ana 6 TABLE OF CONTENTS 9 4 2 Sensitivity or Scenario Analysis a gt c ss sasore nas nu ee 81 9 4 3 Iterative Implementation of Non Standard Algorithms oaoa aaa 82 9 5 Making New Solvers Available with GAMS o e ee e 83 10 GAMS Output 85 IMA Mr rc rs RARA A ERK Re Rae aS 85 102 The Ubustrativa Model ccoo a A A e a a SS 85 103 Comprlari n QUIBIE gt e s s s dad Oa ee edd a bbe dtae da 86 We Echo Print of the laput File orce eee bk ak ee ke eee Ee ee EES 86 10 3 2 The symbol Reference Map op caera a aces A AR A a 87 10 3 3 The Symbol Listing Map 2 2464 6 04 Se eR a Be wae oY 89 10 34 The Unique Element Listing Map so e es e seara aaao ai er aw ii eee eee 89 10 3 5 Useful Dollar Control Directives i 2 06606 6 4a ee dra a wes 89 ita Executa OUTPUT e 244554 6 84 be eee bees a we ee Pa ae oe ea eee 90 10 5 Output Produced by a Solve Statement ccoo ee EA 91 10 5 1 The Equation Liste qaa pa ak ee a RR ee ee AA a 91 12 The Colima Listing 2 4 4 4 oo og da a Hae eee da ew a a A 92 10 5 3 The Model Statistics ici hor eee A DERE ERG e ie e a EA AGS 92 litha The Solve SUL aces vara bee dee ee A ee bee eS 93 ith Solier EE 96 10 5 0 The Solution Listing 2 syaa e he ee ee ee ee a
134. TRNSPORT looks as follows solve transport using lp minimizing z display x 1 x m One can then run trans2 gms restarting from the saved work files generated from running trans1 gms The result obtained is equivalent to running TRNSPORT t In order to use the dumpopt parameter effectively it is required that the first line in the restart file be the solve statement To illustrate the use of the dumpopt option run the second model using the following command gams trans2 s trans dumpopt 1 where trans is the name of the saved files generated through the save parameter from transi gms A new file trans2 dmp is created as a result of this call and looks as follows This file was written with DUMPOPT 1 at 01 06 97 08 42 39 INPUT C GAMS TEST TRANS2 GMS DUMP C GAMS TEST TRANS2 DMP RESTART C GAMS TEST TRANS G0 with time stamp of 01 06 97 08 42 19 You may have to edit this file and the input file set labelorder dummy set to establish the proper order seattle san diego new york chicago topeka model transport variable z total transportation costs in thousands of dollars set i canning plants seattle san diego set j markets new york chicago topeka parameter c i j transport cost in thousands of dollars per case seattle new york 2 250000000000000e 001 seattle chicago 1 530000000000000e 001 seattle topeka 1 620000000000000e 001 san
135. Target User Name Target User Company A more detailed inspection of the listing file will show that the hidden variables and equations do not appear in the usual equation variable listings and the solution print The hidden items can only be accessed via a public exposed model and a solve statement In the following two sections we will describe secure work files and the access control commands in more detail G 3 Secure Work Files Secure Work Files control access to symbolic and numeric information and can only be read by a specific GAMS user The initial creation or additions to access control requires a special GAMS license Saving Secure Work Files without new access controls does not require a special GAMS license The creation or addition of access control is signaled by the use of the GAMS parameter PLICENSE which gives the name of a privacy license file The shortcut PLICENSE LICENSE sets the privacy license to the current license file This is convenient when experimenting with access controls When a secure work file is written the first time the first and second lines of the current license file and the privacy license file are inserted into the work file This information cannot be changed any more and the original source and the intended target users are locked into the work file A secure work file can be used just like any other work file and new work files can be derived from secure files However their use is restricted to t
136. UMIMIE fol be PS REELS BA Bw Set Definitions 4 1 4 2 4 3 4 4 4 5 4 6 Data DeL 5 2 5 3 5 4 5 5 5 6 Data 6 1 6 2 EattoducholR s es s ben Ram ae Ha we Bd Simple Sets eee da ee L21 The Spa ccoo ede ri 422 Bet Nam s 2 ck cee eee ead aces 4 2 3 Set Elements 4 2 4 Associated Text 2 2 2c es 4 2 5 Sequences as Set Elements 4 2 6 Declarations for Multiple Sets The Alias Statement Multiple Names for a Set Subsets and Domain Checking Multi dimensional Sets 4 5 1 One to one Mapping 4 5 2 Many to many Mapping SUA ee es ae a Ree Entry Parameters Scalars amp Tables Introduction o a eo Ge a A ee SS A A O21 The Syntax s oe ey e RADA GH aoe a 5 2 2 An Illustrative Example PAANS 2 ie ea ae Bt Pe A a cee mal VRS See ook ee ee Be a eS 5 3 2 An Illustrative Examples 5 3 3 Parameter Data for Higher Dimensions TADES coda ta dr o a A eA ALL The Syntax esok asor pa a es 5 4 2 An Illustrative Example 5 4 3 Continued Tables aoaaa aa aaa 5 4 4 Tables with more than Two Dimensions 5 4 5 Condensing Tables 5 4 6 Handling Long Row Labels CIDOS secs eh RK reren EO A Dodl Whe Synta ccd ec ak ee ana Bla es 5 5 2 Illustrative Example PUMA paac ee eA RO ee A oe SRS Manipulations with Parameters IIDOAUEN N oo ee eek ns Pe ee a ee ed The Assignment Statement 6 2 1 Scalar Assignments 6 2 2 Indexed As
137. We will discuss a simplified version of this model The input file is listed for reference Title A Quadratic Programming Model for Portfolio Analysis ALAN SEQ 124a onsymlist onsymxref onuellist onuelxref Ontext This is a mini mean variance portfolio selection problem described in gt GAMS MINOS Three examples by Alan S Manne Department of Operations Research Stanford University May 1986 Offtext This model has been modified for use in the documentation Set i securities hardware software show biz t bills alias i j Scalar target target mean annual return on portfolio 10 lowyield yield of lowest yielding security highrisk variance of highest security risk Parameters mean i mean annual returns on individual securities hardware 8 software 9 show biz 12 t bills IA Table v i j variance covariance array squared annual return 86 GAMS Output hardware software show biz t bills hardware 4 3 1 0 software 3 6 1 0 show biz 1 1 10 0 t bills 0 0 0 0 lowyield smin i mean i highrisk smax i v i i display lowyield highrisk Variables x i fraction of portfolio invested in asset i variance variance of portfolio Positive Variable x Equations fsum fractions must add to 1 0 dmean definition of mean return on portfolio dvar definition of variance fsum sum i x i e 1 0 dmean sum i mean i x i e target dvar sum i x i sum j v i j x j e variance
138. a ee ee ee a OE ee es 12 Organization of GAMS programs lt lt cc ee Re RE a ee aS 29 Legal characters sos ear he a sw A ae eS ae Sale a Se A E a 30 Reserved words and symbols ooo ee ee eee Eee a 30 Rules for constructing identifiers and labels 2 2 0 ee ee 31 Examples of the compact representation of sets e 40 CAs HEMOS ooo ii aor eS ER a be ee De oa SE He Ree DA ce eae a ee Re ees 61 Special symbols for extended arithmetic 2 t ios oe sace a seara a e a G 63 Eyponentiation and Division 2 0 06 20465444544 e a e bee bE a a e a A 63 Variable types and default bounds setea scce ri taco ee 66 Classification of functions with endogenous arguments e 74 Subfield definitions for equations e 75 Lister GAMS data topes cia td A a E AA 88 Truth table of logical operators es cad dora mr e a a wR ee ae ed 104 Operator precedent oaao c noera A a as A 105 Examples of logical conditions ooo eaaa a a we daua eR ee ee aa 106 Default values for lo and up subtypes e e e 128 Default layout of display output 6 4 424248 A a ee ee 128 GAMS command line parameters ee 191 Dollar control Options lt 26 456 6 bare eee kee ra a 194 GAMS optiona cio a EY Ae ek ee ee ee RAPA ADA ee eee Be eee RES 216 io TITIES sc ee a ee ERE RRA Se oe BO Be eee Re eed He RE AS 247 Piecewise polynomial functions gt s e sese ee 248 Fandom num
139. a labels on the row leads to a greater density of information The following example adapted from MARCO illustrates the use of tables with more than two dimensions Sets ci commodities intermediate naphtha naphtha dist distillate gas oil gas oil cr commodities crude oils mid c mid continent w tex west texas q attributes of intermediate products density sulfur table attrib ci cr q blending attributes density sulfur naphtha mid c 272 283 naphtha w tex 272 1 48 dist mid c 292 526 dist wotex 297 2 83 gas oil mid c 295 98 gas oil w tex 303 5 05 s The table attrib could also be laid out as shown below table attrib ci cr q blending attributes w tex density mid c density w tex sulfur mid c sulfur naphtha 272 272 1 48 283 dist 297 297 2 83 526 gas oil 303 303 5 05 98 5 4 5 Condensing Tables All the mechanisms using asterisks and parenthesized lists that were introduced in the discussion of sets are available here as well The following example shows how repeated columns or rows can be condensed with asterisks and lists in parentheses follows The set membership is not shown but can easily be inferred 48 Data Entry Parameters Scalars amp Tables table upgrade strat size tech small techi small tech2 medium techi medium tech2 strategy 1 05 05 05 05 strategy 2 2 2 2 2 strategy 3 2 2 2 2 strategy 4 2 52 table upgradex strat size tech al
140. a logical condition is an extremely powerful feature of GAMS and while its use will be illustrated later on in this chapter its full power becomes clear when considered with the description of dynamic sets later 11 2 Logical Conditions 105 11 2 5 Logical Conditions Involving Acronyms Acronyms which are character string values can be used in logical conditions only with the or lt gt operators only Consider the following example of logical conditions involving the use of acronyms dayofweek wednesday dayofweek lt gt thursday where dayofweek is a parameter and wednesday and thursday are acronyms 11 2 6 Numerical Values of Logical Conditions The previous four sub sections have described the various features in GAMS that can be used as logical conditions However GAMS does not have a Boolean data type t GAMS follows the convention that the result of a relational operation is zero if the assertion is False and one if True Consider the following example for illustration x 1 lt 2 2 lt 3 The expression to the right of the assignment evaluates to 2 since both logical conditions within parenthesis are true and therefore assume a value of 1 Note that this is different from the assignment below x 1 lt 2 or 2 lt 3 which evaluates to 1 due to the or operator behaving as explained above 11 2 7 Mixed Logical Conditions Operator Precedence The building blocks discussed in the first four
141. a look at the structure of the GAMS language and its components It should be emphasized again that GAMS is a programming language and that programs must be written in the language to use it A GAMS program is contained in a disk file which is normally constructed with a text editor of choice When GAMS is run the file containing the program the input file is submitted to be processed After this processing has finished the results which are in the output file s can be inspected with a text editor On many machines a few terse lines appear on the screen while GAMS runs keeping the user informed about progress and error detection But it is the responsibility of the user to inspect the output file carefully to see the results and to diagnose any errors The first time or casual reader can skip this chapter the discussion of specific parts of the language in the next Chapters does not assume an understanding of this chapter 3 2 The Structure of GAMS Programs GAMS programs consist of one or more statements sentences that define data structures initial values data modifications and symbolic relationships equations While there is no fixed order in which statements have to be arranged the order in which data modifications are carried out is important Symbols must be declared as to type before they are used and must have values assigned before they can be referenced in assignment statements Each statement is followed by a semicolon e
142. ade The next two sub sections provide examples illustrating the use of the linear form of the lag and lead operators for reference and assignment Section 13 5 3 will illustrate the use of the circular form of the lag and lead operator 13 5 1 Linear Lag and Lead Operators Reference Consider the following example where two parameters a and b are used to illustrate the linear lag and lead operators for reference set t time sequence y 1987 y 1991 parameter a t b t a t 1986 ord t b t 1 b t a t 1 option decimals 0 display a b The option statement suppresses the decimal places from the display The results are shown below Sass 6 PARAMETER A Y 1987 1987 Y 1988 1988 Y 1989 1989 Y 1990 1990 Y 1991 1991 eon 6 PARAMETER B Y 1988 1987 Y 1989 1988 Y 1990 1989 Y 1991 1990 For a as expected the values 1987 1988 up to 1991 are obtained corresponding to the labels y 1987 y 1988 and so on b is initialized to 1 For b the assignment is done over all members of t and for each the value of a from the previous period is assigned to the current member of b If no previous period as with y 1987 zero is used and b y 1987 becomes zero replacing the previous value of 1 13 5 2 Linear Lag and Lead Operators Assignment Consider the following example where two parameters a and c are used to illustrate the assignment of linear lag and lead operators set t time sequence y 1987 y
143. ain the following unique element reference reports ELEMENT REFERENCES ONE DECLARED 2 INDEX 6 THREE DECLARED 2 TWO DECLARED 2 on off upper offupper This option controls the upper casing of input lines when echoed to the listing file Consider the following slice of code D 3 Detailed Description of Dollar Control Options 211 onupper now we list everything in upper case offupper now we are back to list lines as entered The resulting listing file is as follows 2 NOW WE LIST EVERYTHING IN UPPER CASE 4 x now we are back to list lines as entered Note that all the characters in the lines between onupper and offupper are capitalized onjoff warning offwarning Switch for data domain checking In some cases it may be useful to accept domain errors in data statements that are imported from other systems and report warnings instead of errors Data will be accepted and stored even though it is outside the domain t This switch affects three types of domain errors usually referred to as error numbers 116 170 and 171 t This can have serious side affects and one has to exercise great care when using this feature Consider the following slice of code set i one two three onwarning j i four five parameter x i Messed up Data one 1 0 five 2 0 x six 6 x j 10 x two x seven offwarning display i j x Note that the set j although specified as a subset of i contains el
144. al failure during problem set up time ERROR SOLVER FAILURE The solver encountered a fatal error ERROR INTERNAL SOLVER FAILURE The solver encountered an internal fatal error 12 SOLVE PROCESSING SKIPPED The entire solve step has been skipped This happens if execution errors were encountered and the GAMS parameter ExeErr has been set to a nonzero value or the property MaxExecError has a nonzero value ERROR SYSTEM FAILURE This indicates a completely unknown or unexpected error condition 10 5 5 Solver Report The next section in the listing file is the part of the solve summary that is particular to the solver program that has been used This section normally begins with a message identifying the solver and its authors MINOS was used in the example here There will also be diagnostic messages in plain language if anything unusual was detected and specific performance details as well some of them probably technical The Solver Manual will help explain these In case of serious trouble the GAMS listing file will contain additional messages printed by the solver This may help identify the cause of the difficulty If the solver messages do not help a perusal of the solver documentation or help from a more experienced user is recommended The solver report from our example follows GAMS MINOS B A Murtagh University of New South Wales and P E Gill W Murray M A Saunders and M H Wright Systems Optimization Laboratory Stanford U
145. al hub Parameter congestfac j newyork 1 5 detroit 0 7 losangeles 1 2 atlanta 0 9 Congestfac is a parameter used to model the congestion at each regional hub The unit cost of shipment is then computed as follows 110 Conditional Expressions Assignments and Equations shipcost i j ij i j factor congestfac j distance i j This cannot be re written as shipcost ij factor congestfac j distance ij The above representation has the index j on the right hand side but not on the left hand side As explained before GAMS will flag this assignment as an error However the following representation will work shipcost ij i j factor congestfac j distance ij In the above assignment ij is specifically denoted as a tuple of i and j which then appear on the left hand side 11 5 Conditional Indexed Operations Another important use of the dollar condition is to control the domain of operation of indexed operations This is conceptually similar to the dollar on the left described in Section 11 3 1 Consider the following example adapted from GTM tsubc sum i supc i ne inf supc i This statement evaluates the sum of the finite values in supc t A common use of dollar controlled index operations is where the control is itself a set This importance of this concept will become apparent with the discussion of dynamic sets A set has been used to define the mapping between mines and ports in Ch
146. all GAMS systems along with a database to help users locate examples that cover countries sectors or topics of interest to them The syntax used to introduce features in the various chapters are presented using the Backus Naur form BNF notation where 1 3 Organization of the Book 3 denotes that the enclosed construct is optional denotes that the enclosed construct may be repeated zero or more times and denotes that there is an or operator across the arguments on both sides of the symbol 1 3 Organization of the Book Some introductions to software systems are like reference manuals they describe each command in detail Others take you step by step through a small number of examples This book uses elements of both approaches The text is divided into three parts The first part Chapters 1 and 2 is introductory Chapter 2 is a self contained tutorial that guides you through a single example a small transportation model in some detail you can quickly investigate the flavor of GAMS by reading it The second part Chapters 3 to 17 comprises the meat of the book The components of the GAMS language are introduced in an ordered way interspersed with detailed examples that are often drawn from the model library All models from the model library are enclosed in square parenthesis for example TRNSPORT Some specialized material has deliberately been omitted in this process because the primary aim is to make GAMS accessible
147. alues it computes for the primal and dual variables are placed in the database in the 1 and m fields We can then read these results and transform and display them with GAMS statements For example in the transportation problem suppose we wish to know the percentage of each market s demand that is filled by each plant After the solve statement we would enter parameter pctx i j perc of market j s demand filled by plant i petx i j 100 0 x 1 i j b j display pctx Appending these commands to the original transportation problem input results in the following output pctx percent of market j s demand filled by plant I new york chicago topeka seattle 15 385 100 000 san diego 84 615 100 000 For an example involving marginal we briefly consider the ratio constraints that commonly appear in blending and refining problems These linear programming models are concerned with determining the optimal amount of each of several available raw materials to put into each of several desired finished products Let y i j be the variable for the number of tons of raw material put into finished product j Suppose the ratio constraint is that no product can consist of more than 25 percent of one ingredient that is y i j j 1 25 for all i j To keep the model linear the constraint is written as ratio i j y i j 25 q j l 0 0 rather than explicitly as a ratio The problem here is that ratio m i j the marginal va
148. ame with the scratch directory and the scratch extension composes the file name The default is no compilation error messages This option can be used when GAMS is being integrated into other environments like Visual Basic The error messages that are reported in the listing file can be extracted through this option and their display can be controlled from the environment that is calling GAMS To illustrate the option consider the following slice of GAMS code used to explain the errmsg option Calling GAMS on this code with ferr myfile err will result in a file called myfile err being created in the scratch directory This file contains the following lines 0 0 0 O D GAMS NEW LST 1 1 170 31 D GAMS NEW GMS 2 2 120 14 D GAMS NEW GMS The first column refers to the global row number of the error in the listing file The second column refers to the row number of the error in the individual file where the problem occurs This will be different from the first column only if the error occurs in an include file In this case the second column will contain the line number in the include file where the error occurs while the first number will contain the global line number as reported in the listing file where the error occurs The number in the third column refers to the error number of the error The fourth number refers to the column number of the error in the source file The fifth column contains the individual file in which the error occurred f
149. an bratio times the size of the basis Setting bratio to 1 will cause all existing basis information to be discarded which is sometimes needed with nonlinear problems A bratio of 0 accepts any basis and a bratio of 1 always rejects the basis Setting bratio to 0 forces GAMS to construct a basis using whatever information is available If bratio has been set to 0 and there was no previous solve an all slack sometimes called all logical basis will be provided This option is not useful for MIP solvers Range 0 1 cns default The default cns solver is set during installation The user can change this default by setting this option to the required solver The list of cns solvers available with your system can be obtained by reading the gamscomp txt file that is present in the GAMS system directory A value of default will change the cns solver back to the default one as specified in gamscomp txt decimals 3 Number of decimals printed for symbols not having a specific print format attached Range 0 8 dnlp default This option controls the solver used to solve dnlp models For details cf option cns domlim 0 This controls the number of domain errors undefined operations like division by zero a nonlinear solver will perform while calculating function and derivative values before it terminates the run Nonlinear solvers have difficulty recovering after attempting an undefined operation eject Advances output in the list
150. an have only one Grid Directory By default the grid directory is assumed to be the scratch directory This can be overwritten by using the GAMS parameter GridDir or short GDir For example gt gams myprogram GDir gridpath If gridpath is not a fully qualified name the name will be completed using the current directory If the grid path does not exist an error will be issued and the GAMS job will be terminated A related GAMS parameter is the DerDir SDir for short Recall the following default mechanism When a GAMS job starts a unique process directory is created in the current job submitting directory These directories are named 225a to 225z When a GAMS job terminates it will remove the process directory at the completion of a GAMS job Any file that has not been created by the GAMS core system will be flagged Using the program gamskeep instead of gams will call another exit script which the default script will do nothing and the process directory will not be removed If we do not specify a scratch directory the scratch directory will be the same as the process directory If we do not specify a grid directory the grid directory will be the same as the scratch directory If there is a danger that some of the model instances may fail or we want to break the GAMS program into several pieces to run as separate jobs we need to be careful not to remove the model instance we have not completely processed In such cases we have to
151. an identifier count sum i j a i j emp sum t 1 t m t The equivalent mathematical forms are count 5 SN Ay and emp 5 ILM i j t The smin and smax operations are used to find the largest and smallest values over the domain of the index set or sets The index for the smin and smax operators is specified in the same manner as in the index for the sum operator Consider the following example to find the largest capacity lrgunit smax i m capacity i m 6 3 3 Functions Functions play an important part in the GAMS language especially for non linear models Similar to other programming languages GAMS provides a number of built in intrinsic functions However GAMS is used in an extremely diverse set of application areas and this creates frequent requests for the addition of new and often sophisticated and specialized functions There is a trade off between satisfying these requests and avoiding complexity not needed by most users The GAMS Function Library Facility 6 3 3 provides the means for managing that trade off Intrinsic Functions GAMS provides commonly used standard functions such as exponentiation and logarithmic and trigonometric functions The complete list of available functions is given in table 6 1 There are cautions to be taken when functions appear in equations these are dealt with in Section 8 4 page 74 In table 6 1 the Endogenous Classification second column specifies in which models t
152. and continue without waiting for the completion of the solution step There is a new model attribute handle which provides a unique identification of the submitted solution request We need to store those handle values in this case in the parameter h to be used later to collect the solutions once completed This is then done with a collection loop 13 A First Example 239 loop pp handlecollect h pp xres i pp x 1 i report pp i inc xi 1 i report pp i dec xd 1 i The function handlecollect interrogates the solution process If the solution process has been completed the results will be retrieved and the function returns a value of 1 If the solution is not ready to be retrieved the value zero will be returned The above collection loop has one big flaw If a solution was not ready it will not be retrieved We need to call this loop several times until all solutions have been retrieved or we get tired of it and quit We will use a repeat until construct and the handle parameter h to control the loop to look only for the not yet loaded solutions as shown below Repeat loop pp handlecollect h pp xres i pp x 1 i report pp i inc xi 1 i report pp i dec xd 1 i display handledelete h pp trouble deleting handles h pp 0 display sleep card h 0 2 sleep some time until card h O or timeelapsed gt 100 xres i pp h pp na Once we have extracted a
153. and is discussed in detail later The user distinguishes between these suffix numbers when necessary by appending a suffix to the variable name 7 3 1 Bounds on Variables All default bounds set at declaration time can be changed using assignment statements ts For binary and integer variable types the consequences of the type declaration cannot be completely undone Bounds on variables are the responsibility of the user After variables have been declared default bounds have already been assigned for many purposes especially in linear models the default bounds are sufficient In nonlinear models on the other hand bounds play a far more important role It may be necessary to provide bounds to prevent undefined operations such as division by zero It is also often necessary to define a reasonable solution space that will help to make the nonlinear programming problem be solved more efficiently ts The lower bound cannot be greater than the upper if you happen to impose such a condition GAMS will exit with an error condition 7 3 2 Fixing Variables GAMS allows the user to set variables through the fx variable suffix This is equivalent to the lower bound and upper bound being equal to the fixed value Fixed variables can subsequently be freed by changing the lower and upper bounds 68 Variables 7 3 3 Activity Levels of Variables GAMS allows the user to fix the activity levels of variables through the 1 variable suf
154. and the solution is ready for retrieval e 3 the solution process signaled completion but the solu tion cannot be retrieved An execution error is triggered if GAMS cannot retrieve the status of the handle handleSubmit HANDLE none resubmits a previously created instance of the model identified by the HANDLE for solution A numerical indication of the result is returned as follows e 0 the model instance has been resubmitted for solution e 1 if the argument HANDLE is not a legal handle e 2 if a model associated with the HANDLE is not known to the system e 3 the completion signal could not be removed e 4 the resubmit procedure could not be found e 5 the resubmit process could not be started In case of a nonzero return an execution error is triggered heapFree none allocated memory which is no more in use but not freed yet heapLimit none interrogates the current heap limit maximum allowable mem ory use in Mb and allows it to be reset heapSize none returns the current heap size in Mb jobHandle none returns the Process ID PID of the last job started jobKill PID none sends a kill signal to the running job with Process ID PID the return value is one if this was succesful otherwise it is zero jobStatus PID none checks for the status of the job with the Process ID PID pos sible return values are e 0 error input is not a valid PID or access is denied e 1 process is still running e 2 process is finished with return code which could
155. aps Maps are most often turned on or off at the beginning of the program and left as initially set but it is possible to produce maps of part of the program by using a on map directive followed later by an off map The symlist lists all the symbols in the model The symxref shows a complete cross reference list of symbols by number Both these maps are suppressed by default offuelxref offuellist onuelxref onuellist These four directives are used to control the production of Unique Element maps which show set membership labels Maps are most often turned on or off at the beginning of the program and left as initially set but it is possible to produce maps of part of the program by using a on map directive followed later by an off map The uellist lists all labels in both GAMS entry and alphabetical order The uelxref shows a complete cross reference list by number These label maps are suppressed by default offupper onupper This directive causes the echo print of the portion of the GAMS program following the directive to appear on the output file in the case that it has been entered in This is the default on newer GAMS systems It is necessary if case conventions have been used in the program for example to distinguish between variables and equations onupper will cause all echo print to be in upper case ontext Sofftext ontext offtext pairs are used to create block comments that are ignored by GAMS Every ontext must have a matc
156. apter 4 Another typical example is a set to set mapping defining the relationship between states and regions used for aggregating data obtained by state to the models requirements by region sets r west east s florida texas vermont maine corr r s north vermont maine south florida texas parameter y r income s income of each state florida 4 5 vermont 4 2 texas 6 4 maine 4 1 The set corr provides a correspondence to show which states belong to which regions The parameter income is the income of each state Y r can be calculated with this assignment statement y r sum s corr r s income s For each region r the summation over s is only over those pairs of r s for which corr r s exists Concep tually set existence is analogous to the Boolean value True or the arithmetic value not zero The effect is that only the contributions for vermont and maine are included in the total for north and south includes only texas and florida Note that the summation above can also be written as sum s income s corr r s but this form is not as easy to read as controlling the index of summation 11 6 Conditional Equations 111 11 5 1 Filtering Controlling Indices in Indexed Operations The controlling indices can in certain cases be filtered through the conditional set without the use of the dollar operator Consider the example described in that section The total
157. ar programming Characteristics are the same as for RMINLP but the discrete requirements are enforced MPEC Mathematical Programs with Equilibrium Constraints MCP Mixed Complementarity Problem CNS Constrained Nonlinear System Each of these model types will be discussed in detail in later chapters 9 2 3 Model Attributes Various model attributes can be set and accessed by the user through a list of model suffixes The complete list of model suffixes is shown below 9 3 The Solve Statement 79 Attributes Controlled by the User bratio basis acceptance test domlim maximum number of domain violations holdfixed substitution of fixed variables iterlim iteration limit limcol number of columns displayed for each block of variables limrow number of rows displayed for each block of equations optca absolute termination criterion for MIP optcr relative termination criterion for MIP optfile option file usage reslim time limit for solver Usually in CPU seconds scaleopt scale option cf Section 17 3 solprint solution print option solveopt merge or replace option for solution data sysout subsystem print option workspace size of work array in MB Attributes Controlled by the Solver domusd number of domain violations iterusd number of iterations used modelstat model status cf Section 10 5 4 numequ number of single equations generated numinfes number of infeasibilities numnopt number of non optimalities numnz nu
158. aracters are encountered Consider running the following slice of code oninline the default comment symbols are now active These comments can continue to additional lines till the closing comments are found t inlinecom automatically sets oninline Consider running the following slice of code inlinecom lt lt gt gt lt lt the in line comment characters have been changed from the default gt gt t Nested in line comments are illegal unless onnestcom is set onjoff listing onlisting Controls the echoing of input lines to the listing file Note that suppressed input lines do not generate entries in the symbol and reference sections appearing at the end of the compilation listing Lines with errors will always be listed Consider running the following slice of code set i 0234 0237 j a b c table x i j very long table a b c 0234 1 23 offlisting 0235 4 5 6 0236 5 6 7 onlisting 0237 1 1 1 208 Dollar Control Options The resulting listing file looks as follows 1 set i 0234 0237 2 j a b c 3 table x i j very long table 4 a b c 5 0234 1 2 3 10 0237 1 1 1 Note that the lines in the source file between the offlisting and onlisting settings are not echoed to the listing file onjoff margin offmargin Controls the margin marking The margins are set with mincol and maxcol Consider running the following slice of code onmargin mincol 20 maxcol 45 Now we hav
159. are ready to make some test runs similar to those we expect to be defined by the target user We will define three scenarios to be solved in a loop and name the file u1 gms set s one two three parameter sbeta s one 1 25 two 1 5 three 2 0 sf s one 85 two 75 three 50 G 6 Limitations and Future Requirements 231 parameter report summary report loop s beta sbeta s f sf s solve getc using cns solve newtrans using nlp minmizing Z solve rep using cns report i j s delta 1 i j report beta s beta report f s f report obj z s 2 10 display report When executing the above GAMS code together with the original transport model from the GAMS model library we will get the following results gt gams ul r p1 a 109 PARAMETER report summary report one two three seattle new york 4 050 6 967 8 083 seattle chicago 18 797 27 202 31 550 seattle topeka 233 958 348 468 404 187 san diego new york 3 605 6 201 7 194 san diego chicago 28 138 40 719 47 228 san diego topeka 15 512 23 104 26 799 beta 1 250 1 500 2 000 of 85 000 75 000 50 000 obj Z 526 912 1652 963 13988 774 Note that all symbols are still completely exposed We need to add access controls to the model pl gms before we can ship it to the target client The information to be protected is the original distance matrix and derived information We start out by hiding everything and th
160. ared before the model statement is entered For most simple applications this is all you need to know about the model statement 9 2 1 The Syntax In general the syntax in GAMS for a model declaration is model s model_name text all eqn_name eqn_name model_name text all eqn_name eqn_name Model_name is the internal name of the model also called an identifier in GAMS The accompanying text is used to describe the set or element immediately preceding it Eqn_name is the name of an equation that has been declared prior to the model statement As with all identifiers model_name has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long Explanatory text must not exceed 80 characters and must all be contained on the same line as the identifier or label it describes An example of a model definition in GAMS is shown below Model transport a transportation model all The model is called transport and the keyword all is a shorthand for all known declared equations Several models can be declared and defined in one model statement This is useful when experimenting with different ways of writing a model or if one has different models that draw on the same data Consider the following example adapted from PROLOG in which different groups of the equations are used in alternative versions of the problem Three versio
161. assigned between the solves and thus apply only to the second one t The values associated with an option can be changed as often as necessary with the new value replacing the older one each time An example of a list of option statements is shown below 216 The Option Statement option profit 0 3 2 option eject iterlim 100 solprint off solve mymodel using lp maximizing profit display profit 1 input vali 5 3 option iterlim 50 solve mymodel using lp maximizing profit The option statement in the second line affects the display format of the identifier profit More details on this option can be found under the heading lt identifier gt in the following section The option on the second line has no value associated with it and serves to advance the output in the listing file to the next page The third line contains two options iterlim and solprint The values associated with the two options on the fourth line are of different types iterlim has an integer value while solprint requires a character string as a value Note also that the end of line and the comma serve as legal separators between two options The option iterlim serves to limit the number of iterations taken by the solver while attempting to solve the lp model mymodel After mymodel is solved for the first time some of the input data is changed and the model is solved again However before the second solve statement the option iterlim is change
162. ation 116 117 direction 164 of optimization 80 94 discontinuous 164 derivate 74 functions 78 discrete 164 variables 66 78 display controls local 130 example 127 generating data in list format 131 global controls 130 introduction 127 label order 128 syntax 127 distributions beta 249 binomial 250 cauchy 249 chiSquare 249 exponential 249 f 249 gamma 249 geometric 250 gumbel 249 hyperGeo 250 invGaussian 249 INDEX 259 laplace 249 logarithmic 250 logistic 249 logNormal 249 negBinomial 250 normal 249 pareto 249 poisson 250 rayleigh 249 student T 249 triangular 249 uniform 249 uniformInt 250 weibull 249 div function 55 divO function 55 dnlp GAMS call parameter 174 GAMS option 217 DNLP model type 15 78 dollar dollar control option 197 dollar condition control over the domain of definition 111 example 106 in equations 111 116 in indexed operations 116 nested 106 on the left 107 on the right 108 with dynamic sets 115 within indexed operations 110 within the algebra 111 dollar control option 164 Introduction 193 Syntax 193 dollar operator 106 164 domain checking 38 164 domain definition 164 domain restriction condition 164 domlim GAMS option 217 model attribute 79 option 94 101 domusd model attribute 79 dot in equation definitions 72 in level and marginal listings 98 in many to many mappings 40 in
163. ax for flow control statements Endloop endif endfor and endwhile are introduced as key words with the use of the onend option that then serves the purpose of closing the loop if for and while language constructs respectively The following example provides the alternate syntax for the four language constructs mentioned above standard syntax as eolcomment set i 1 3 scalar cond 0 parameter a i 1 1 23 2 2 65 3 1 34 maxcol 40 onend loop i do loop i display a display a endloop J if cond then if cond display a display a else else a i a i 2 a i a i 2 display a display a endif J for cond 1 to 5 do for cond 1 to 5 a i 2 a i a i 2 a i endfor while cond lt 2 do while cond lt 2 206 Dollar Control Options a i a i 2 a i a i 2 endwhile Note that the alternate syntax is more in line with syntax used in some of the popular programming languages t Both forms of the syntax will never be valid simultaneously Setting the onend option will make the alternate syntax valid but makes the standard syntax invalid onjoff eolcom offeolcom Switch to control the use of end of line comments By default the end of line comments are set to 7 but the processing is disabled Consider running the following slice of code oneolcom set i 1 2 1 set declaration parameter a i parameter declaration Note that comments can now be
164. ber ESROTALOTS gt cc na ce oe e a a a AA 250 Tistibunon MUCHOS oe aaa A A a e OR whe 250 TOSORODIE HAS DIBCUOBS 00 a hg ae a Soba A A 251 Introduction 1 1 Motivation Substantial progress was made in the 1950s and 1960s with the development of algorithms and computer codes to solve large mathematical programming problems The number of applications of these tools in the 1970s was less then expected however because the solution procedures formed only a small part of the overall modeling effort A large part of the time required to develop a model involved data preparation and transformation and report preparation Each model required many hours of analyst and programming time to organize the data and write the programs that would transform the data into the form required by the mathematical programming optimizers Furthermore it was difficult to detect and eliminate errors because the programs that performed the data operations were only accessible to the specialist who wrote them and not to the analysts in charge of the project GAMS was developed to improve on this situation by gt Providing a high level language for the compact representation of large and complex models gt Allowing changes to be made in model specifications simply and safely gt Allowing unambiguous statements of algebraic relationships gt Permitting model descriptions that are independent of solution algorithms 1 2 Basic Features of GAMS 1 2 1 General Princip
165. between the elements in different sets GAMS also uses a domain checking capability to help catch labeling inconsistencies and typographical errors made during the definition of related sets The discussion here has been limited to sets whose members are all specified as the set is being declared For many models this is all you need to know about sets Later we will discuss more complicated concepts such as sets whose membership changes in different parts of the model assignment to sets and other set operations such as unions complements and intersections 42 Set Definitions 9 Data Entry Parameters Scalars amp Tables 5 1 Introduction One of the basic design paradigms of the GAMS language has been to use data in its most basic form which may be scalar list oriented or tables of two or more dimensions Based on this criterion three data types are introduced in this chapter Scalar Single scalar data entry Parameter List oriented data Table Table oriented data Must involve two or more dimensions Each of these data types will be explained in detail in the following sections ts Initialization of data can only be done once for parameters thereafter data must be modified with assignment statements 5 2 Scalars The scalar statement is used to declare and optionally initialize a GAMS parameter of dimensionality zero That means there are no associated sets and that there is therefore exactly one number associat
166. but it is necessary to allow for exceptions of one sort or another For example heavy trucks may not be able use a particular route because of a weak bridge or some sectors in an economy may not produce exportable product The use of a subset in an indexed expression has already been shown to provide some ability to handle exceptions 11 2 Logical Conditions Logical conditions are special expressions that evaluate to a value of True or False Numerical Expressions can also serve as logical conditions Additionally GAMS provides for numerical relationship and logical operators that can be used to generate logical conditions The next four sub sections discuss these various building blocks that can be used to develop complex logical conditions 11 2 1 Numerical Expressions as Logical Conditions ts Numerical expressions can also serve as logical conditions a result of zero is treated as a logical value of False and a non zero result is treated as a logical value of True The following numerical expression can be used to illustrate this point 2 a 4 This expression results in a logical value of False when a is 2 because the expression numerically evaluates to 0 For all other values of a the expression results in a non zero value and therefore is equivalent to a logical value of True 11 2 2 Numerical Relationship Operators Numerical relationship operators compare two numerical expressions For completeness all numerical relationship
167. by the following directive FuncLibIn lt InternalLibName gt stodclib Function Description SetSeed SEED defines the seed for random number generator Continous distributions beta SHAPE 1 SHAPE_2 cauchy LOCATION SCALE ChiSquare DF exponential LAMBDA f DF_1 DF_2 gamma SHAPE SCALE gumbel LOCATION SCALE invGaussian MEAN SHAPE laplace MEAN SCALE logistic LOCATION SCALE logNormal MEAN STD_DEV normal MEAN STDDEV pareto SCALE SHAPE rayleigh SIGMA studentT DF triangular LOW MID HIGH uniform LOW HIGH weibull SHAPE SCALE Beta distribution with shape parameters SHAPE_1 and SHAPE_2 see MathWorld Cauchy distribution with location parameter LOCATION and scale param eter SCALE see MathWorld Chi squared distribution with degrees of freedom DF see MathWorld Exponential distribution with rate of changes LAMBDA see MathWorld F distribution with degrees of freedom DG_1 and DG_2 see MathWorld Gamma ditribution with shape parameter SHAPE and scale parameter SCALE see MathWorld Gumbel distribution with location parameter LOCATION and scale param eter SCALE see MathWorld Inverse Gaussian distribution with mean MEAN and scaling parameter SHAPE see MathWorld Laplace distribution with mean MEAN and scale parameter SCALE see MathWorld Logistic distribution with location parameter LOCATION and scale param eter SCALE see MathWorld Log Normal distribution
168. cal item formatting 142 parmfile put paging control GAMS call parameter 185 lp 146 phantom ws 146 dollar control option 211 putdir pi function 55 251 poisson distribution 250 poly function 55 power function 54 55 precision fixed 98 priorities for branching example 158 introduction 158 problem type 78 166 prod operator 54 88 PRODSCH example from GAMSLIB 71 profile GAMS call parameter 185 GAMS option 218 profiletol GAMS option 218 program 166 PROLOG example from GAMSLIB 77 81 put additional numeric control 143 appending to a file 136 assigning files 135 closing a file 136 cursor control 144 database database application 147 defining files 135 errors 146 example 134 143 exception handling 146 global item formatting 141 introduction 133 local item formatting 142 numeric items 141 output items 139 page format 136 page sections 137 paging 138 paging control 146 positioning the cursor on a page 138 set value items 141 syntax 133 system suffices 139 text items 140 put current cursor control cc 144 cr 145 hdcr 145 tler 145 put cursor control GAMS call parameter 186 pwpFunc function 248 qcp GAMS call parameter 186 GAMS option 218 QCP model type 15 quoted labels 31 names of sets 36 text 31 quotes 31 36 RAMSEY example from GAMSLIB 65 74 randBinomial function 55 randLinear function 55 randTriangle function 55 range of numbers
169. ce of code call dir This command makes a directory listing on a PC The command string can be passed to the system and executed directly without using a command processor by prefixing the command with an sign Compilation errors are issued if the command or the command processor cannot be loaded and executed properly call gams trnsport call gams trnsport The first call runs TRNSPORT in a new command shell The DOS command shell does not send any return codes from the run back to GAMS Therefore any errors in the run are not reported back The second call however sends the command directly to the system The return codes from the system are intercepted correctly and available to the GAMS system through the errorlevel DOS batch function t Some commands like copy on a PC and cd in Unix are shell commands and cannot be spawned off to the system Using these in a system call will create a compilation error Consider the following slice of code call copy myfile txt mycopy txt call copy myfile txt mycopy txt The first call will work on a PC but the second will not The copy command can only be used from a command line shell The system is not aware of this command Try this command after clicking Run under the Start menu in Windows You will find that it does not work clear This option resets all data for an identifier to its default values clear id1 id2 D 3 Detailed Description of Dollar Control O
170. ced before it is declared to exist 2 GAMS statements may be laid out typographically in almost any style that is appealing to the user Multiple lines per statement embedded blank lines and multiple statements per line are allowed You will get a good idea of what is allowed from the examples in this tutorial but precise rules of the road are given in the next Chapter 3 When you are a beginning GAMS user you should terminate every statement with a semicolon as in our examples The GAMS compiler does not distinguish between upper and lowercase letters so you are free to use either 4 Documentation is crucial to the usefulness of mathematical models Tt is more useful and most likely to be accurate if it is embedded within the model itself rather than written up separately There are at least two ways to insert documentation within a GAMS model First any line that starts with an asterisk in column 1 is disregarded as a comment line by the GAMS compiler Second perhaps more important documentary text can be inserted within specific GAMS statements All the lowercase words in the transportation model are examples of the second form of documentation 8 A GAMS Tutorial by Richard E Rosenthal Inputs Outputs e Sets e Echo Print Declaration e Reference Maps Assignment of members Equation Listings e Data Parameters Tables Scalars Status Reports Declaration Results Assignment of values e Variables Declarat
171. ces between the GAMS format and the usual mathematical format for listing the elements of a set GAMS uses slashes rather than curly braces to delineate the set simply 2 4 Data 9 because not all computer keyboards have keys for curly braces Note also that multiword names like New York are not allowed so hyphens are inserted The lowercase words in the sets statement above are called text Text is optional It is there only for internal documentation serving no formal purpose in the model The GAMS compiler makes no attempt to interpret the text but it saves the text and parrots it back to you at various times for your convenience It was not necessary to combine the creation of sets i and j in one statement We could have put them into separate statements as follows Set i canning plants seattle san diego Set j markets new york chicago topeka The placement of blank spaces and lines as well as the choice of upper or lowercase is up to you Each GAMS user tends to develop individual stylistic conventions The use of the singular set is also up to you Using set in a statement that makes a single declaration and sets in one that makes several is good English but GAMS treats the singular and plural synonymously A convenient feature to use when you are assigning members to a set is the asterisk It applies to cases when the elements follow a sequence For example the following are valid set sta
172. cessing of the input file s The syntax is similar to the IF statement of the DOS Batch language if not exist filename string1 string2 new_input_line The syntax allows for negating the conditional with a not operator followed either of two types of conditional expressions a file operation or a string comparison The result of the conditional test is used to determine whether to read the remainder of the line which can be any valid GAMS input line 200 Dollar Control Options The exist file operator can be used to check for the existence of the given file name specification The string compare consists of two strings quoted or unquoted for which the comparison result is true only if the strings match exactly Null empty strings can be indicated by an empty quote t The case of the strings provided either explicitly or more likely through a parameter substitution is preserved and therefore will effect the string comparison t Quoted strings with leading and trailing blanks are not trimmed and the blanks are considered part of the string ts If the string to be compared is a possibly empty parameter the parameter operator must be quoted New_input_line is the remainder of the line containing the if option and could be any valid GAMS input line t The first non blank character on the line following the conditional expression is considered to be the first column position of the GAMS input line Therefore if the
173. changed safely and this statement will always fix c for the last one 13 4 Lag and Lead Operators The lag and lead operators are used to relate the current to the next or previous member of a set In order to use these operators the set in question must of course be ordered GAMS provides two forms of lag and lead operators gt Linear Lag and Lead Operators gt Circular Lag and Lead Operators The difference between these two types of operators involves the handling of endpoints in the sequence GAMS provides some built in facilities to deal with this issue but in any work involving sequences the user must think carefully about the treatment of endpoints and all models will need special exception handling logic to deal with them In the linear case the members of the set that are endpoints are left hanging In other words there are no members preceding the first member or following the last one This may cause the use of non existent elements The next section will describe how this is handled in GAMS This form of the lag and lead operators is useful for modeling time periods that do not repeat A set of years say 1990 to 1997 is an example The operators are and GAMS is able to distinguish linear lag and lead operators from arithmetic operators by context In the circular case the first and last members of the set are assumed to be adjacent so as to form a circular sequence of members The notion i
174. check for xxx symbols This option affects the result of the check for xxx symbols Values O no substitution if symbol undefined 1 error if symbol undefined 2 remove xxx if symbol undefined subsys subsys text configuration file name This option is only to be used by advanced users attempting to override internal sub system information The file name is used as given The default sub systems file is gamscomp txt in the GAMS system directory suppress suppress 0 compiler listing option This option suppresses the echoing of the contents of the input file s to the listing file This parameter is similar in functionality to the 0fflisting dollar control option Values O standard compiler listing 1 suppress compiler listing ts The offlisting and onlisting dollar control options effect the listing file only if suppress is set to 0 If suppress is set to 1 the input file s is not echoed to the listing file and these dollar control options have no effect on the listing file symbol symbol tezt symbol file name Writes a partial symbol table to be used in conjunction with reference files C 3 Detailed Description of Command Line Parameters 189 sysdir sysdir text system directory This option sets the GAMS system directory This option is useful if there are multiple systems installed on the machine or when GAMS is called from an external system like Visual Basic sysincdir sdir texwt system library search directory
175. cost of shipment is obtained through the following equation variable shipped i j totcost equation costequ cost totcost e sum i j ij i j shipcost i j shipped i j where shipped is the amount of material shipped from i to j and totcost is the total cost of all shipment The equation above can be written as cost totcost e sum ij shipcost ij shipped ij However if the original equation is expressed as cost totcost e sum i j ij i j factor congestfac j distance i j shipped i j Index j appears separately from i in congestfac j The equation then needs to be simplified as cost totcost e sum ij i j factor congestfac j distance ij shipped ij Note that the presence of j separately in the indexed expression necessitated the use of ij i j rather than ij 11 6 Conditional Equations The dollar operator is also used for exception handling in equations The next two subsections discuss the two main uses of dollar operators within equations within the body of an equation and over the domain of definition 11 6 1 Dollar Operators within the Algebra A dollar operator within an equation is analogous to the dollar control on the right of assignments as discussed in Section 11 4 2 and if one thinks of on the right as meaning on the right of the then the analogy is even closer An if else operation is implied as it was with assignments It is used to exclude parts of the defi
176. countries is set c countries jamaica haiti guyana brazil and the set of ports is set P ports kingston s domingo georgetown belem Then a set can be created to associate each port with its country viz set ptoc p c port to country relationship 40 Set Definitions kingston jamaica s domingo haiti georgetown guyana belem brazil The dot between kingston and jamaica is used to create one such pair Blanks may be used freely around the dot for readability The set ptoc has four elements and each element consists of a port country pair The notation p c after the set name ptoc indicates that the first member of each pair must be a member of the set p of ports and that the second must be in the set c of countries This is a second example of domain checking GAMS will check the set elements to ensure that all members belong to the appropriate sets 4 5 2 Many to many Mapping A many to many mapping is needed in certain cases Consider the following set set i a b j c d e ijidi j a c a d ij2 i j a c b c ij3 i j a c b c a d b d ijl represents a one to many mapping where one element of i maps onto many elements of j ij2 represents a many to one mapping where many elements of i map onto one element of j ij3 is the most general case where many elements of i map on to many elements of j These sets can be written compactly as set i a b j c d e ij1 i j a c d ij
177. d This option will cause GAMS to search for a line starting with label id and then continue reading from there This option can be used to skip over or repeat sections of the input files In batch include files the target labels or label arguments can be passed as parameters because of the manner in which parameter substitution occurs in such files In order to avoid infinite loops one can only jump a maximum of 100 times to the same label Consider the following example scalar a a 5 display a goto next a at5 display a label next a a 10 display a On reaching the goto next option GAMS continues from label next All lines in between are ignored On running the example a finally takes a value of 15 ts The goto and label have to be in the same file If the target label is not found in the current file and error is issued hidden This line will be ignored and will not be echoed to the listing file This option is used to enter information only relevant to the person manipulating the file Consider the following example hidden You need to edit the following lines if you want to hidden hidden 1 Change form a to b hidden 2 Expand the set The lines above serve as comments to the person who wrote the file However these comments will not be visible in the listing file and is therefore hidden from view The if dollar control option provides the greatest amount of control over conditional pro
178. d Solve Statements s oc ke a EEE a A Display Statements s lt ae Ree ee we a ee Ae ew Pw er A The Io ly A DE DAS ce a Ae ee RRS REG De ee Eee Ee 2 10 1 Assignment of Variable Bounds and or Initial Values o o 2 10 2 Transformation and Display of Optimal Values gt s sea oa ses sead neau a dua CPS COMPE E a Se a he a a E AAA a A a 2AL Ee PINS ees sa ga A AAA a a Ek A e aA Ede oe 211 2 Error Messages rato A a a ea a a A SUL AORTA pi sas noda ea ea da BS ak RIA a eee a a 2 114 Equation Listings oe 22024 ee oa a a oa E a aean A at a BUS Model Staol ra ise A A a a G o la da a e a 2110 Statua Repais e peca wa a ee Bee A aoa a ha E a ek ee ZAS Ola REPOTI re du A a kA a E AA A A ie ea es he ee ee oe ee we ae EO wh ree Ge es 3 GAMS Programs 3 1 a2 Tatro iGO 6 oes a Bek ee ho ee Gee Be es A ee a eee Be Go The Structure of GAMS Programs 2 66 44 A RA Oe RE iriri SN ee ee S20 Format or CAMS DOUE oc ek ee A ee Be Re a ee eee ees 32 2 Classification of GAMS Statements o arada na ea EE EnG TABLE OF CONTENTS 3 3 3 4 3 5 3 2 3 Organization of GAMS Programs Data Types and Definitions Language tems occ Re a Oe Bal Characters os ns a eo hae ee 8 3 4 2 Reserved Words 343 Identifiers eee Ra nai 34d Labels sc cae bee ae ea ee E eee aoe oe Oe a me ow A Pe oe 340 Numbers o oe cece cee eRe age a oA Delumtels vos ica be ees S08 COMES lt lt cde eine pea kha hes D
179. d by a label tuple for higher dimensions The elements in the n tuple are separated by dots just like in the case of multi dimensional sets The following example illustrates the use of parameter data for higher dimensions parameter salaries employee manager department anderson murphy toy 6000 hendry smith toy 9000 hoffman morgan cosmetics 8000 All the mechanisms using asterisks and parenthesized lists that we introduced in our discussion of sets are available here as well Below is an artificial example in which a very small fraction of the total data points are initialized GAMS will mark an error if the same label combination or label tuple appears more than once in a data list Set row rowi row10 col colix col10 parameter a row col rowl row4 cl2 col7 12 row10 col10 17 rowl row7 col10 33 23 In this example the twelve elements row1 co12 to row1 co17 and row4 col2 to row4 col7 are all initialized at 12 the single element row10 co110 at 17 and the seven elements rows1 col10 to row7 col10 at 33 The other 80 elements out of a total of 100 remain at their default value which is 0 This example shows the ability of GAMS to provide a concise initialization or definition for a sparse data structure 5 4 Tables Tabular data can be declared and initialized in GAMS using a table statement For 2 and higher dimensional parameters this provides a more concise and easier method of data entry
180. d into GAMS using the parameter statement 5 3 1 The Syntax In general the syntax in GAMS for a parameter declaration is parameter s param_name text element signed_num element signed num param_name text element signed_num element signed num Param_name is the internal name of the parameter also called an identifier in GAMS The accompanying text is used to describe the parameter immediately preceding it Signed_num is a signed number and is declared to be the value of the entry associated with the corresponding element As with all identifiers param_name has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 long Explanatory text must not exceed 254 characters and must all be contained on the same line as the identifier or label it describes A parameter may be indexed over one or more sets the maximum number being 20 The elements in the data should belong to the set that the parameter is indexed over t The default value of a parameter is 0 Parameter initialization requires a list of data elements each consisting of a label and a value Slashes must be used at the beginning and end of the list and commas must separate data elements entered more than one to a line An equals sign or a blank may be used to separate the label tuple from its associated value A parameter can be defined in a similar syntax to that used
181. d parameter Consider the following slice of code parameter a a 0 include file2 inc include file2 inc The content of the include file file2 inc is shown below a ati display a Running the model with the command line flag expand myfile fil results in the creation of the file myfile fil The content of this file is provided below 1 INPUT 0 0 0 1 7 E TEMP FILE1 GMS 2 INCLUDE 1 1 2 2 4 E TEMP FILE2 INC 3 INCLUDE 1 1 3 5 7 E TEMP FILE2 INC The first column gives the sequence number of the input files encountered The first row always refers the parent file called by the GAMS call The second column refers to the type of file being referenced The various types of files are 178 The GAMS Call O INPUT 1 INCLUDE 2 BATINCLUDE 3 LIBINCLUDE 4 SYSINCLUDE The third column provides the sequence number of the parent file for the file being referenced The fifth column gives the local line number in the parent file where the include appeared The sixth column gives the global expanded line number which contained the include statement The seventh column provides the total number of lines in the file after it is processed The eighth and last column provides the name of the file In the example listed above the include files file1 inc and file2 inc were included on lines 1 and 4 of the parent file test1 gms ferr ferr text compilation error message file Instructs GAMS to write error messages into a file Completing the n
182. d to 50 The effect of the sequence above is to limit the first solve to less than 100 iterations and the second to less than 50 E 2 List of Options The options available through the option statement are grouped into the following functional categories affecting output detail solver specific parameters input program control choice of solver Table E 1 briefly describes the various options in each of the categories Section E 3 contains a reference list of all options available through the option statement in alphabetical order with detailed description for each Options controlling output detail lt identifier gt controls print format profile lists program execution profile decimals global control of print format profiletol sets tolerance for execution profile eject advances output to next page solprint controls printing of solution limcol number of columns listed solslack controls type of equation information limrow number of rows listed sysout controls printing of solver status file Options controlling solver specific parameters bratio use of advanced basis optca sets absolute optimality tolerance domlim limits number of domain errors optcr sets relative optimality tolerance iterlim limits number of solver iterations reslim limits amount of solver time Options controlling choice of solver cns sets solver for cns model type mip sets solver for mip model type dnlp sets solver for dnlp model type mpec sets solver for mpec model t
183. d with any sets parameters variables or equations A simple assignment is written in the style associated with many other computer languages GAMS uses the traditional symbols for addition subtraction multiplication and division We will use them in the examples that follow and give more details in Section 6 3 page 53 6 2 1 Scalar Assignments Consider the following artificial sequence scalar x 1 5 x 1 2 x 2 x The scalar x is initialized to be 1 5 The second statement changes the value to 1 2 and the third changes it to 3 2 The second and third statement assignments have the effect of replacing the previous value of x if any with a new one Note that the same symbol can be used on the left and right of the sign The new value is not available until the calculation is complete and the operation gives the expected result rt An assignment cannot start with a reserved word A semicolon is therefore required as a delimiter before all assignments 6 2 2 Indexed Assignments The syntax in GAMS for performing indexed assignments is extremely powerful This operation offers what may be thought of as simultaneous or parallel assignment and it provides a concise way of specifying large amounts of data Consider the mathematical statement DJa 2 75D Ag for all d 52 Data Manipulations with Parameters This means that for every member of the set d a value is assigned to DJ This can be written in GAMS a
184. dd a eee ad 215 ELI The Stee cs tor a ma eh ne OR de ee hw Boe aoe eo ea ee OR a G 215 E2 Dish er Options 2 244 444 da Pee es Abobo se Gent bbad ib daa a eee wea 216 E3 Detailed Description of Options s oo scs esaa mameta iea radaas Ganap ea 216 F The Save and Restart Feature 221 Pal Tatroduction iii a ae a a dt e de a eee E a a a Oe a 221 F 2 The Save and Restart Feature o ee 221 F21 Saving The Work File s e races eS errors a A 222 F222 Restarting fromthe Works File 2 40554 css ER he g ees 222 F 3 Ways in which a Work File is Useful c scac coroada taged pa e eee eee 223 F31 Separation of Model and Date o co se crase RR ee Re Re 223 F 3 2 Incremental Program Development ee 224 F 3 3 Tacking Sequences of Difficult Solves o 0 220 ee eee ee ee 225 Fae Multiple SESUAPOS se ierd re bee ered eee a baw Pees 225 F35 The GAMS Runtime License osco eek a eRe EERE SR BE eee 225 G Secure Work Files 227 Col Tarroduehioi a eh ke AE EER Oe ee Be A ee ed 227 G2 A First Example oos o a ci maca aii a ae ae ee ed EGA a hae eee 228 Go Secure Work Files s s 245 Se be ta ae p PAA eA DR a A OR De a e 229 G 4 Access Control Commands s o e c sos e s e eot oeta ea ee eee G 229 G 5 Advanced Use of Access Control o ss s caos a 045 wR RRR OR REE RAR ee e e a 230 G6 Limitations and Future Requirements 231 H Compressed and Encrypted Input Files 233 BE Sara igo es cias a A e A He a o a A A 233 HS
185. de file could look as follows Batch Include File inclproc bch Process and INCLUDE an unknown number of input files label nextfile if fla a goto end if exist 1 include 1 name might have blanks shift goto nextfile label end The call to this file in the parent file could look like batinclude inclproc bch fili inc f112 inc fi13 inc fil4 inc include The include option inserts the contents of a specified text file at the location of the call The name of the file to be included which follows immediately the keyword include may be quoted or unquoted Include files can be nested The include file names are processed in the same way as the input file is handled The names are expanded using the working directory If the file cannot be found and no extension is given the standard GAMS input extension is tried However if an incomplete path is given the file name is completed using the include directory By default the library include directory is set to the working directory The default directory can be reset with the idir command line parameter The start of the include file is marked in the compiler listing This reference to the include file can be omitted by using the 0ffinclude option The following example illustrates the use of an include statement include myfile include myfile Both statements above are equivalent and the search order for the include file is as follows 1 myfile
186. del suffixes set values Represent existence of set elements and carry the values yes or no only The methods for identifying and using each of these different types of output items are described in the following sub sections 140 The Put Writing Facility 15 9 1 Text Items Output items which are quoted text are any combination of characters or numbers set apart by a pair of single or double quotes However the length of quoted text as well as any output item has a limit No portion of the output item can be placed outside of the page margin When the page width is exceeded several asterisks are placed at the end of the line and a put error is recorded in the program listing In addition to quoted text the output of other text items is possible through the use of system and identifier suffixes The identifier suffixes are identifier symbol text ts Displays the text associated with any identifier set element labels t1 Displays the individual element labels of a set set element text te index Displays the text associated with an element of a set Notice that the te suffix requires a driving index This driving index controls the set which will be displayed and does not necessarily have to be the same as the controlled set Often a subset of indices of the controlled set is used text fill tf Used to control the display of missing text for set elements 0 no fill 1 fill existing only 2 default fill always The fo
187. der which less than eight equations might be produced will be discussed in later chapters It is certainly true however that no more than eight equations will be produced 8 3 Equation Definitions The definitions are the mathematical specification of the equations in the GAMS language The next sub section explain the syntax for an equation definition and this is followed by an illustrative example The rest of this section is devoted to discussions about some of the key components of equation definitions 8 3 1 The Syntax The syntax in GAMS for defining an equation is as follows eqn_name domain_list expression eqn_type expression Eqn _name is the name of the equation as in the equation declaration The two dots are always required between the equation name and start of the algebra The expressions in the equation definition can be of the forms discussed in the Chapters before but can involve variables as well Eqn_type refers to the symbol between the two expressions that form the equation and can be of the following types e Equality rhs must equal lhs g Greater than lhs must be greater than or equal to rhs 1 Less than lhs must be less than or equal to rhs n No relationships enforced between lhs and rhs This equation type is rarely used x External equation Only supported by selected solvers c Coaen constraint Only supported by selected solvers ts As with the assignment statement equation definition
188. directory and the standard output file extension is applied If the output parameter is given as a file name without an absolute path using the current directory composes the final name If the absolute path is included in the file name then the name is used as given Consider the following examples gams trnsport gams trnsport o trnsport out gams trnsport o c test trnsport out The first call will create an output file called trnsport 1st for PC and Unix platforms in the current directory The second call will create a file called trnsport out in the current directory The last call will create the file as listed If the directory c test does not exist GAMS will exit with a parameter error pagecontr pc 3 page control This option affects the page control in the listing file Values O no page control with padding 1 Fortran style line printer format 2 no page control no padding 3 Form feed character for new page C 3 Detailed Description of Command Line Parameters 185 pagesize ps 58 page size This is the number of lines that are used on a page for printing the listing file If value of the option is set to less than 30 it will be reset to the default of 58 Note that the total number of lines on a page are ps 2 bm The botmargin lines are only added if padding is requested pc 0 pagewidth pw 255 print width This option sets the print width on a page in the listing file If the value is outside the range the default
189. dle collects loads the solution if ready 0 the model instance was not ready or could not be loaded 1 the model instance solution has been loaded HandleStatus handle returns the status of the solve identified by handle An execution error is triggered if GAMS cannot retrieve the status of the handle 0 the model instance is not known to the system 1 the model instance exists but no solution process is complete 2 the solution process has terminated and the solution is ready for retrieval 3 the solution process signaled completion but the solution cannot be retrieved HandleDelete handle returns the status of the deletion of the handle model instance In case of a nonzero return an execution error is triggered 0 the model instance has been removed 1 the argument is not a legal handle 2 the model instance is not known to the system 3 the deletion of the model instance encountered errors HandleSubmit handle resubmits a previously created instance for solution In case of a nonzero return an execution error is triggered 0 the model instance has been resubmitted for solution the argument is not a legal handle the model instance is not known to the system the completion signal could not be removed the resubmit procedure could not be found oF WN Fe the resubmit process could not be started In addition GAMS will issue execution errors which will give additional information that may help to identify the source of problems The pro
190. ds Transport is the name of the model 1p is the model type minimizing is the direction of optimization and cost is the objective variable The opposite of minimizing is maximizing both reserved words Note that an objective variable is used instead of an objective row or function ts The objective variable must be scalar and type free and must appear in the least one of the equations in the model The next two sub sections will describe briefly below what happens when a solve statement is processed and more details on how the resulting output is to be interpreted will be given in the next chapter After that sequences of solve statements will be discussed The final section will describe options that are important in controlling solve statements 9 3 2 Requirements for a Valid Solve Statement When GAMS encounters a solve statement the following are verified 1 All symbolic equations have been defined and the objective variable is used in at least one of the equations 2 The objective variable is scalar and of type free 3 Each equation fits into the specified problem class linearity for 1p continuous derivatives for nlp as we outlined above 4 All sets and parameters in the equations have values assigned 9 3 3 Actions Triggered by the Solve Statement The solve statement triggers a sequence of steps that are as follows 1 The model is translated into the representation required by the solution system to be used 2 Debu
191. e Grid Directory and to restart the problem we will have to create a save file The first job will then look a follows gt gams qsubmit s submit gdir c test grid The solution of all the model instances may take hours From time to time I can then run a quick inquiry job to learn about the stats The following program qcheck gms will list the current status parameter status pp scalar handle acronym BadHandle Waiting Ready loop pp handle handlestatus h pp if handle 0 handle BadHandle elseif handle 2 handle Ready minvar handle h pp execute_loadhandle minvar status pp solvestat minvar solvestat I 5 Summary of Grid Features 241 status pp modelstat minvar modelstat status pp seconds minvar resusd else handle Waiting status pp status handle display status To run the above program we will restart from the previous save file by using the restart or r parameter gt gams qcheck r submit gdir c test grid The output may then look like 2 173 PARAMETER status solvestat modelstat seconds status pl 1 000 1 000 0 328 Ready p2 1 000 1 000 0 171 Ready p3 Waiting p4 Waiting pd 1 000 1 000 0 046 Ready You may want to do some more detailed analysis on one of the solved model instances Then we may have a qanalyze gms program that may look like and be called using the double dash option which sets a GAMS environment variable if not set instance abort
192. e See a ah A 97 TWA Report SUE eee ho oe a Bae ae ds a He Re eA al ee a 98 WAS File uy ss ee RA A BA A A OO de Pd 98 Io Error e ac ad Sie eh oe ee ee oe Ee Gel Ee Se RB 98 106 1 Compilation Errors ss o as ee eh ee RED ee A ee ae eS 99 106 2 Compilation Time Errors lt sa soe 04 5244 eRe A aR eee A RR 100 WAS Ezecuton Errors o s e ace A Be ee a ee we Se A A 101 HUG A Salve EMOS i 2 at a Re Aas Bonde Slee Wane ae Se me Rk Ra Ew REGS AR 101 ER a A ee a OE ae Sa oe ae he oe SASS 102 11 Conditional Expressions Assignments and Equations 103 LLI AGRO AI es Rd we hl ee ae a A OS a we el Ale Aas 103 11 2 Degieal conditions cee na a PS Ge ee ee oe BS Oe ee a we BL a ok GE 103 11 2 1 Numerical Expressions as Logical Conditions o 103 11 2 2 Numerical Relationship Operators e 103 11 2 3 Logloal Op rators scoa i baa he debe a a a a ea ee 104 24 Seb Members 220 oo bu dee Rob a a a a oY ee 104 11 2 5 Logical Conditions Involving Acronyms e 105 11 2 6 Numerical Values of Logical Conditions eee eee 105 11 2 7 Mixed Logical Conditions Operator Precedence o o e 105 11 2 8 Mixed Logical Conditions Examples e 106 IES The Dollar Conditio lt o s soea a eee re ee ee eee ED Pee oe PA Oe ee 106 LRM An ERG oe o A ee Dee OE Se a ED a A RY 106 1132 Nested Dolar Conditions cio be Re ee ee BR he ee Re we 106 14 Com
193. e comment to a single character which follows immediately th command keyword This should be used with great care and one should reset it quickly to the default symbol ts The case of the start of line comment character does not matter when being used Consider the following example comment c c now we use a FORTRAN style comment symbol C case doesn t matter comment now we are back how it should be dollar This option changes the current symbol to a single character which follows immediately the dollar keyword When the include file is inserted all dollar control options are inherited and the current symbol may not be known The special substitution symbol can be used to get the correct symbol see batinclude Consider the following example dollar hidden now we can use tt as the symbol double The lines following the double statement will be echoed double spaced to the listing file Consider the following example 198 Dollar Control Options set i 1 2 scalar a 1 double set j 10 15 scalar b 2 The resulting listing file looks as follows 1 set i 1 2 2 scalar a 1 4 set j 10 15 5 scalar b 2 Note that lines before the double option are listed singly spaced while the lines after the option are listed with double space echo The echo option allows to write text to a file echo text gt file echo text gt gt file These
194. e display to the screen of a PC system at the location of this statement if the console had been the output device 15 17 Simple Spreadsheet Database Application This last section provides a simple example of the preparation of output for spreadsheets databases or other software packages which allow importation of delimited files As mentioned in Section 15 3 output items can be prepared with comma delimiters and text items in quotes This is implemented by using pc suffix value 5 Delimited files are different than normal put files All output items are written with variable field widths and separated by delimiters Consequently all global and local format specifications for field widths and justification are ignored by GAMS Note that the number of decimals for numeric items can still be specified with the nd file suffix Each item is written immediately following the previous delimiter on the same line unless the cursor is reset t Avoid horizontal cursor relocations in a program which creates a delimited file Horizontally relocating the cursor in a delimited file is potentially damaging since a delimiter could be overwritten While the comma is the most common delimiting character for spreadsheets other delimiters like blank space and tab characters can also be used 15 17 1 An Example In the following example the capacity sub table of the MEXSS report program is prepared as a delimited file The following program segment demonst
195. e labels vary slowest for the first index position and 14 5 Display Controls 129 quickest for the highest Within each index position the order is the GAMS entry order of the labels The order of the indices is always as in the declaration statement for the symbol One can declare them in the order that is found appealing or make an assignment to a new identifier with a different order t The only way to change the order in which the labels for each index position appear on display output is to change the order of appearance of the labels in the GAMS program This is most easily done by declaring a set whose only purpose is to list all the labels in the order that is needed Make this set the very first declaration in the GAMS program 14 4 1 Example Consider the following example X has four dimensions or index positions It is initialized using parameter format and then displayed as shown below set i first index first second j second index one two three k third index Ja b 1 fourth index Icaro 3 parameter x i j k 1 a four dimensional structure second one a i inf first three b i 6 3161 first one b i 5 63559 second two b i 19 8350 second one b ii 17 29948 first two b ii 10 3457 first two a ii 0 02873 second one a ii 1 0037 second two a ii inf first two a i 2 9393 first one a ii 0 00000 FS display x This code fragment produces the following output a 12 PARAMETER X a four dimensional str
196. e ml using lp minimizing 1p else if ml modelstat ne 1 abort error solving model ml The following GAMS code is illegal since one cannot define equations inside an if statement if s gt O eq sum i x i g 2 The following GAMS code is illegal since one cannot make declarations inside an if statement if s gt 0 scalar y y 5 152 Programming Flow Control Features 16 4 The While Statement The while statement is used in order to loop over a block of statements 16 4 1 The Syntax The syntax of the while statement is while condition statements e t One cannot make declarations or define equations inside a while statement 16 4 2 Examples One can use while statements to control the solve statement For instance consider the following bit of GAMS code that randomly searches for a global optimum of a non convex model scalar count count 1 scalar globmin globmin inf option bratio 1 while count le 1000 x 1 j uniform 0 1 solve ml using nlp minimizing obj if obj 1 le globmin globmin obj 1 globinit j x 1 j Y count count 1 In this example a non convex model is solved from 1000 random starting points and the global solution is tracked The model PRIME from the model library illustrates the use of the while statement through an example where the set of prime numbers less than 200 are generated The following GAMS code is illegal sinc
197. e name class2 and it corresponds to the defined external file report txt Lastly the special internal file name con is defined to write output to the console screen for a PC systems Writing to the screen can be useful to advise the user of various aspects of the model during the model s execution 15 4 2 Assigning Files The put statement is used both to assign the current file and to write output items to that file The complete syntax for using the put statement is put fname item s fname item s As indicated by this syntax multiple files can be sequentially written using a single put statement Note that only one file is current at a time After the output items following an internal file name are written the current file is reassigned based on the next internal file name in the statement The last internal file name used in a put statement remains as the current file until a subsequent put statement uses an internal file name 136 The Put Writing Facility 15 4 3 Closing a File The keyword putclose is used to close a file during the execution of a GAMS program The syntax is as follows putclose myfile item s where myfile is the internal name of the file to be closed and item s are the final entries into the file before it is closed If the internal file name is omitted from the putclose statement the current put file is closed Note that after using the putclose command the file does not have to be redefined in orde
198. e name provided for the restart file follows the same convention as that of the save file see command line parameter save rminlp rminlp tezt default RMINLP solver rmip rmip text default RMIP solver save s tezt save file name The final name is composed by completing the save file name with the current directory and the standard workfile extension Eight save files are generated so the name provided by the user for the save file should be such that GAMS can generate eight names from it GAMS distinguishes file names from their extensions If no extension is provided by the user GAMS adds the extensions g01 through g08 to name the eight saved work files The presence of a character in the save file name is used by GAMS to substitute the numbers 1 through 8 in its place The following table illustrates through examples the generation of names for the save files by GAMS from the name provided through the save parameter C 3 Detailed Description of Command Line Parameters 187 myfile myfile g01 myfile g02 myfile g08 myfile myfile1 g01 myfile2 g02 myfile8 g08 myfile wrk myfilel wrk myfile2 wrk myfile8 wrk myfile 00 myfile 001 myfile 002 myfile 008 myfile myfile1 111 myfile2 222 Mmyfile8 888 gt On Unix platforms the character is a special character and may require a backslash character 1 in front of it in order to be interpreted correctly The name myfile should be written on this platform as
199. e one cannot define equations inside a while statement while s gt 0 eq sum i x i g 2 The following GAMS code is illegal since one cannot make declarations inside a while statement while s gt 0 scalar y y 5 16 5 The For Statement The for statement is used in order to loop over a block of statements 16 5 The For Statement 153 16 5 1 The Syntax The syntax is for i start toldownto end by incr statements Note that i is not a set but a parameter Start and end are the start and end and incr is the increment by which i is changed after every pass of the loop One cannot make declarations or define equations inside a for statement t The values of start end and incr need not be integer The start and end values can be positive or negative real numbers The value of incr has to be a positive real number 16 5 2 Examples One can use for statements to control the solve statement For instance consider the following bit of GAMS code that randomly searches for a global optimum of a non convex model scalar i scalar globmin globmin inf option bratio 1 for i 1 to 1000 x 1 j uniform 0 1 solve ml using nlp minimizing obj if obj 1 le globmin globmin obj 1 globinit j x 1 j In this example a non convex model is solved from 1000 random starting points and the global solution is tracked The use of real numbers as start end and incr can be u
200. e rewrite the example above using this second method 7 3 Variable Attributes 67 free variables phi total cost mill us phipsi raw material cost mill us positive variables u c i purchase of domestic materials mill units per yr v c j imports mill typ e c i exports mill typ The choice between the two approaches is best based on clarity 7 3 Variable Attributes Another important difference between parameters and variables is that an additional set of keywords can be used to specify various attributes of variables A GAMS parameter has one number associated with each unique label combination A variable on the other hand has seven They represent lo The lower bound for the variable Set by the user either explicitly or through default values up The upper bound for the variable Set by the user either explicitly or through default values fx The fixed value for the variable 1 The activity level for the variable This is also equivalent to the current value of the variable Receives new values when a model is solved m The marginal value also called dual value for the variable Receives new values when a model is solved scale This is the scaling factor on the variable This is normally an issue with nonlinear programming problems and is discussed in detail in Section 17 3 prior This is the branching priority value of a variable This parameter is used in mixed integer programming models only
201. e set i plant US UK This defines I turned on the scalar x 3 145 A scalar example margin marking parameter a b Define some parameters offmargin Any statements between columns 1 and 19 and anything beyond column 45 are treated as comments onjoff multi offmulti Controls multiple data statements or tables By default GAMS does not allow data statements to be redefined If this option is enabled the second or subsequent data statements are merged with entries of the previous ones Note that all multiple data statements are executed before any other statement is executed Consider running the following slice of code eolcom set i 1 10 parameter x i 1 3 1 1 1 2 1 3 1 onmulti parameter x i 7 9 parameter x i 2 6 parameter x i 3 5 display x 2 9 2 OWN Nx kk ou ou PRR N NN iow ou Owe O ww Momo UR NBN ow N OWN an A NWN OD oO fowl NWN a I N 00 This would have been illegal without the presence of the onmulti option The result of the display statement in the listing file is as follows 8 PARAMETER X 1 1 000 2 3 000 6 3 000 7 2 000 8 2 000 9 2 000 Note that x 1 has a value of 1 after the first data statement since none of the subsequent data statements affect it x 2 on the other hand is reset to 3 by the third data statement ts The two pass processing of a GAMS file can lead to seemingly unexpected results Both the dollar control options and t
202. e variable is INF and if above you also would display v up for example you will see A 203 VARIABLE V UP imports mill tpy C ALL INF If any of the bounds have been changed from the default value then only the entries for the changed elements will be shown This sounds confusing but since few users display bounds it has not proved troublesome in practice 7 5 Summary Remember that wherever a parameter can appear in a display or an assignment statement a variable can also appear provided that it is qualified with one of the four suffixes The only places where a variable name can appear without a suffix is in a variable declaration as shown here or in an equation definition which is discussed in the next chapter 70 Variables 8 Equations 8 1 Introduction Equations are the GAMS names for the symbolic algebraic relationships that will be used to generate the constraints in the model As with variables one GAMS equation will map into arbitrarily many individual constraints depending on the membership of the defining sets 8 2 Equation Declarations A GAMS equation like all identifiers must be declared before it can be used 8 2 1 The Syntax The declaration of an equation is similar to a set or parameter declaration in that domain lists and explanatory text are allowed and recommended and several equations can be declared in one statement Equation s eqn_name text eqn_name text Eqn_name is t
203. echo encrypt trnsport gms t1 gms gt s1 gms call gams si license DEMO plicense LICENSE lo gams lof if errorlevel 1 abort encryption failed eolcom if NOT errorfree abort pending errors decompress t1 gms t1 org this has to fail if errorfree abort decompress did not fail clearerror execute original and encrypted model call gams trnsport gdx trnsport lo gams lo if errorlevel 1 abort model trnsport failed Although this reads license DEMO this license file is the one specified with plicense from the si call call gams t1 license DEMO gdx t1 lo gams lo if errorlevel 1 abort model t1 failed call gdxdiff trnsport t1 system redirlog 236 Compressed and Encrypted Input Files if errorlevel 1 abort results for trnsport and ti are not equal use the encrypted file as an include file onecho gt t2 gms offlisting this is hidden option limrow 0 limcol 0 solprint off include t1 gms onlisting this will show o0ffecho call gams t2 license DEMO lo gams lo if errorlevel 1 abort model t2 failed protect against viewing now we will show how to protect parts of an input file from viewing and extracting original source via the gams DUMPOPT parameter We just need to encrypt again encrypt new model call rm f t3 gms echo encrypt t2 gms t3 gms gt s1 gms call gams si license DEMO plicense LICENSE lo gams 1o if errorlevel 1 abort encryption
204. ecurity violation H 3 The CEFILES Gamslib Model The CEFILES model from the GAMS Model Library contains a more elaborate example that can be easily modified to test the use of compressed files This example will also show how to use the PLICENSE LICENSE parameter to test the creation and use without having a target license file available title Compressed Input Files CEFILES SEQ 317 ontext This model demonstrates the use of compressed input files Remember if the file names contain spaces you need to use single or double quotes around the file names o0fftext get model ondollar call gamslib q trnsport g q P compress and run model compress trnsport gms t1 gms decompress t1 gms ti org call diff trnsport gms tl org gt system nullfilef if errorlevel 1 abort files trsnport and t1 are different check to see if we get the same result H 4 The ENCRYPT GAMSLIB Model 235 call gams trnsport gdx trnsport lo gams lo if errorlevel 1 abort model trnsport failed call gams t1 gdx t1 lo gams 1o if errorlevel 1 abort model t1 failed call gdxdiff trnsport t1 system redirlog if errorlevel 1 abort results for trnsport and ti are not equal also works with include files echo include ti gms gt t2 gms call gams t2 gdx t2 lo gams lof if errorlevel 1 abort model t2 failed call gdxdiff trnsport t2 system redirlog if errorlevel 1 abort results for trnsport and t2
205. ed on a page of the document Can be reset by the user at any place in the program However an error will result if set to a value less than the number of rows which have already been written to the current page Maximum value is 130 The default value is 60 page width pw Used to specify the number of columns characters which can be placed on a single row of the page Can be reset by the user at any place in the program However an error will result if set to a value less than the number of rows or columns which have already been written to the current page The default value is 255 top margin tm Number of blank lines to be placed at the top margin of the page These lines are in addition to the number of lines specified in the ps file suffix Default value is 0 bottom margin bm Number of blank lines to be placed in the bottom margin of the page These lines are in addition to the number of lines specified in the ps file suffix This is functional with pc option 0 only Default value is 0 alphabetic case case Used to specify the case in which alphabetic characters are displayed in the output file 0 default Causes mixed case to be displayed 1 Causes the output to be displayed in upper case regardless of the case used for the input To illustrate the use of these file suffixes the following example involves formatting report txt so that the pages are 72 spaces wide with 58 lines of output an additional top margin of 6 l
206. ed with the parameter 5 2 1 The Syntax In general the syntax in GAMS for a scalar declaration is scalar s scalar_name text signed_num scalar_name text signed_num Scalar_name is the internal name of the scalar also called an identifier in GAMS The accompanying text is used to describe the element immediately preceding it Signed_num is a signed number and is assigned to be the value of scalar_name As with all identifiers scalar_name has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long Explanatory text must not exceed 254 characters and must all be contained on the same line as the identifier or label it describes 44 Data Entry Parameters Scalars amp Tables 5 2 2 An Illustrative Example An example of a scalar definition in GAMS is shown below Scalars rho discount rate 15 irr internal rate of return life financial lifetime of productive units 20 The statement above initializes rho and life but not irr Later on another scalar statement can be used to initialize irr or looking ahead to a notion that will be developed later an assignment statement could be used to provide the value irr 0 07 5 3 Parameters While parameter is a data type that encompasses scalars and tables the discussion in this chapter will focus on the use of parameters in data entry List oriented data can be rea
207. ee specific variables for each generic variable This listing would be particularly useful for verifying a GAMS model that was previously implemented in MPS format To change the default number of specific column printouts per generic variable the above command can be extended option limrow r limcol c where c is the desired number of columns Setting limrow and limcol to 0 is a good way to save paper after your model has been debugged In nonlinear models the GAMS equation listing shows first order Taylor approximations of the nonlinear equa tions The approximations are taken at the starting values of the variables 2 11 5 Model Statistics The last section of output that GAMS produces before invoking the solver is a group of statistics about the model s size as shown below for the transportation example MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 6 BLOCKS OF VARIABLES 2 SINGLE VARIABLES 7 NON ZERO ELEMENTS 19 The BLOCK counts refer to the number of generic equations and variables The SINGLE counts refer to individual rows and columns in the specific model instance being generated For nonlinear models some other statistics are given to describe the degree of non linearity in the problem 2 11 6 Status Reports After the solver executes GAMS prints out a brief solve summary whose two most important entries are SOLVER STATUS and the MODEL STATUS For our transportation problem the solve summary is as follows
208. efault 12 maximum 20 tw text field width default 0 The field width is specified with the number of spaces to be allocated to the field Variable length field widths are possible by using a suffix value of 0 This forces the field width to match the exact size of the item being displayed If a textual output item does not fit within the specified field truncation occurs to the right For numeric output items the decimal portion of a number is rounded or scientific notation used to fit the number within the given field If a number is still too large asterisks replace the value in the output file As an example to set the global numeric field width to four spaces from its default of 12 in the file out put we would use the following statement out nw 4 15 11 Local Item Formatting It is often useful to format only specific put items For this we use the local format feature which overrides global format settings The syntax of this feature is as follows item lt gt width decimals The item is followed by a justification symbol the field width and the number of decimals to be displayed The specification of the number of decimals is only valid for numeric output The following local justification symbols are applicable gt right justified lt left justified lt gt center justified Omitting any of the components causes their corresponding global format settings to be used As with global formatting when the field
209. efault LP solver mcp mcp text default MCP solver minlp minlp tezt default MINLP solver miqcp miqcp tezt default MIQCP solver mpec mpec text default MPEC solver multipass mp 0 Multipass facility This option allows slices of GAMS code to be independently checked for syntax errors This option is useful when a large model is being put together from smaller pieces Values O standard compilation 1 check out compilation As an example consider the following example a i b i b i 5 c j By default running a file containing just the two statements shown above results in the following listing file 1 a i b i 5 k 140 120 140 2 bi c j OK 140 120 149 120 Unknown identifier entered as set 140 Unknown symbol 149 Uncontrolled set entered as constant xo 6 ERROR S 0 WARNING S C 3 Detailed Description of Command Line Parameters 183 None of the sets i or j have been defined or initialized and the identifiers a b and c have not been defined Further an assignment cannot be made without the right hand side of the assignment being known In both the assignments in the example above there is no data available for the right hand side Running the model with the setting mp 1 results in the following listing file 1 a i b i 5 2 bi c j AK 149 Error Messages 149 Uncontrolled set entered as constant xx 1 ERROR S 0 WARNING S Note that the statements in the example have now been p
210. efault value alongside marginal Often called reduced costs or dual values The values which are meaningful only for non basic rows or columns in optimal solutions contain information about the rate at which the objective value will change of if the associated bound or right hand side is changed matrix element See nonzero element model generation The initial phase of processing a solve statement preparing a problem description for the solver model list A list of equations used in a model as specified in a model statement nonbasic A column that is not basic and in nonlinear problems not superbasic Its value will be the same as the one of the finite bounds or zero if there are no finite bounds if the solution is feasible nonlinear nonzero In a linear programming problem the nonzero elements are constant In a nonlinear problem one or more of them vary because their values depend on that of one or more columns The ratio of nonlinear varying to linear constant non linear zero elements is a good indicator of the pervasiveness of non linearities in the problem nonoptimal There are two contexts First describing a variable a non basic variable that would improve the objective value if made basic The sign of the marginal value is normally used to test for non optimality Second for a solution other solutions exists with better objective values nonsmooth A classification of function that does not have continuous first deriva
211. egin on or after column 31 Any changes in the margins via maxcol or mincol will be reported in the listing file with the message that gives the valid range of input columns For example the dollar control option mincol 20 maxcol 110 will trigger the message NEW MARGIN 20 110 204 Dollar Control Options tw GAMS requires that the right margin set by maxcol is greater than 15 te GAMS requires that the right margin set by maxcol is greater than the left margin set by mincol mincol n 1 Sets the left margin for the input file All valid data is after and including column n in the input file All text before column n is treated as comment and ignored Consider the following example mincol 30 set definition set i vienna rome scalar definition scalar a 2 3 The text strings set definition and scalar definition are treated as comments and ignored since they begin before column 30 Any changes in the margins via maxcol or mincol will be reported in the listing file with the message that gives the valid range of input columns For example the dollar control option mincol 20 maxcol 110 will trigger the message NEW MARGIN 20 110 GAMS requires that the left margin set by mincol is smaller than the right margin set by maxcol onloff digit ondigit Controls the precision check on numbers Computers work with different internal precision Sometimes a GAMS problem has to be moved from a machine with hi
212. eir paths are specified by libincdir and sysincdir respectively Consider the following illustration gams myfile idir mydir mydir2 The search order for the file myfile or myfile gms and all included files in PC systems is as follows current di rectory directories specified by inputdir mydir and mydir2 directories in order under Unix the corresponding command is gams myfile idir mydir mydir2 inputdirl to inputdir18 idirl tezt idir18 tezt Input search path The same information as in inputdir can be transferred to GAMS by entering the individual directories separately A maximum of 18 directories can be passed on in this manner The number appended to inputdir is important because the earlier inputdir directories are searched first The example used to illustrate the inputdir option can also be equivalently called as gams myfile idiri mydiri idir2 mydir2 Note that the search order in this case is as follows 1 current directory 180 The GAMS Call 2 mydirt 3 mydir2 However if the command was altered to be gams myfile idir3 mydiri idir2 mydir2 then the search order is altered to be as follows 1 current directory 2 mydir2 3 mydirl Note that it is not the order in which they are specified that matters but the number of the inputdir that they have been assigned to keep keep 0 keep flag internal use only Values O delete all files 1 keep intermediate files leftmargin lm 0 left margin
213. ement Finally the model is solved and the results are displayed A second style emphasizes the model by placing it before the data This is a particularly useful order when the model may be solved repeatedly with different data sets There is a separation between declaration and definition For example sets and parameters may be declared first with the statements set c crops parameter yield crop yield and then defined later with a statement set c wheat clover beans parameter yield wheat 1 5 clover 6 5 beans 1 0 73 3 3 Data Types and Definitions 29 Style 1 Style 2 Data Set declarations and definitions Parameter declarations and definitions Variable declarations Equation declaration Equation definition Model definition Model Set declarations Parameter declarations Assignments Variable declarations Displays Equation declaration Model Equation definition Model definition Data Set definitions Parameter definitions Solution Assignments Solve Displays Displays Solution Solve Displays Table 3 1 Organization of GAMS programs The first statement declares that the identifier c is a set and the second defines the elements in the set tx Sets and parameters used in the equations must be declared before the equations are specified they can be defined however after the equation specifications but before a
214. ements not belonging to its domain Similarly the parameter x contains data elements outside its domain The skeleton listing file that results from running this code is as follows 1 set i one two three 3 j i four five kkk 170 170 4 parameter x i Messed up Data one 1 0 five 2 0 kkk 170 5 xOsix 6 x j 10 x two x seven kkk 170 116 170 7 display i j x Error Messages 116 Label is unknown 170 Domain violation for element xk O ERROR S 6 WARNING S Execution icy 7 SET I one two three 7 SET J four five secre 7 PARAMETER X Messed up Data one 1 000 four 10 000 five 10 000 six 6 000 The domain violations are marked like normal compilation errors but are only treated as warnings and one can execute the code phantom id Used to designate id as a phantom set element Syntactically a phantom element is handled like any other set element Semantically however it is handled like it does not exist This is sometimes used to specify a data template that initializes the phantom records to default values Consider the following example 212 Dollar Control Options phantom null set i null j a b null display i j The resulting section of the listing file is shown below 4 SET I EMPTY 4 SET J a b Note that null does not appear in the listing file t Assignment statements on the phantom label are ignored Consider the follow
215. en give access to selected parts of the model We collect the access control information in the file s1 gms shown below and save the secure work file under the name s1 g00 Since we are still testing we use our own license as target user This will allows us to test the system the same way the target user will use it hide all expose getc newtrans rep expose i j z delta expose f beta a b gt gams si r pi s si plicense license To test the new secure file we run again the problem ul gms When doing so you will observe that equation variable and solution listings related to the hidden variables are not shown any more Any attempt to reference a hidden variable will case a compilation error gt gams ul r s1 Before we can ship a secure work file we need a copy of the target user license file We then will restart again from p1 gms zip the resulting secure files and we are ready to distribute the model gt gams si r p1 plicense target txt s target gt zip target target g00 G 6 Limitations and Future Requirements One of the design goals for secure work files has been to minimize the impact on other components of the GAMS system Solvers used out of a secure environment should work as if called out of a normal environment This 232 Secure Work Files implies that in principle certain information could be recovered if one has knowledge of GAMS solvers internals and is willing to expand considerable programming effort In th
216. en the bottom of the page is reached a page can also be written to file early The keyword putpage is used to do this Putpage forces the current page to immediately be written to file making a new page available for put statements In its simplest form the keyword putpage is used by itself to eject the current page Additionally it can be used with output items When it is used with output items the page is written to file including the output items contained in the putpage statement The putpage statement is in fact another variation of the put statement In the following statement the quoted text is placed in the current page which is then written to the file out put putpage out This text is placed in window and the page ends Two additional file suffixes that can help the user in determining when to page a file are last page 1p Indicates the number of pages that are already in the document Note that setting this to 0 does not erase the pages that have previously been written to the file window size ws Shows the number of rows which can be placed in the window considering the number of lines that are in the title and header blocks of the current page and the existing page size The ws file suffix value is calculated by GAMS and is not changeable by the user This suffix is useful for manual pagination when used in conjunction with the 11 file suffix 15 15 Exception Handling In this section the topic of exception ha
217. eneralized binomial coefficient for n k gt 0 ceil x DNLP returns the smallest integer number greater than or equal to x centropy x y Z NLP Centropy x 2 default setting Z 0 cos x NLP returns the cosine of the argument x where x must be in radi ans see MathWorld cosh x NLP returns the hyperbolic cosine of x where x must be in radians see MathWorld cvPower X y NLP returns XY for X gt 0 another possible command is X y div dividend divisor NLP returns dividend undefined for divisor 0 div0 dividend divisor NLP returns vidend returns 12 for divisor 0 eDist x1 x2 x3 x4 x5 x6 NLP Euclidean or L 2 Norm y1i 23 default setting T2 T3 T4 T5 Lg 0 entropy x NLP Entropy 2 ln x errorf x NLP calculates the integral of the standard normal distribution from T a negative infinity to x error f x Tz f e dt oo execSeed none reads or writes the seed for the random number generator exp x NLP returns the exponential function e of an expression or term x see MathWorld fact X any returns the factorial of X where X is an integer floor x DNLP returns the greatest integer number less than or equal to x frac x DNLP returns the fractional part of x co gamma x DNLP gamma function y x f t te dt see MathWorld 0 gammaReg x a NLP regularized gamma function see MathWorld log x NLP returns the natural logarithm logarithm base e see Math World logBeta x y NLP log beta functi
218. ent GAMS would fail to discern a valid interpretation so it would send you a terse but helpful error message The effects of the first statement above are to declare the parameter c to specify the domain i j and to provide some documentary text The second statement assigns to c i j the product of the values of the parameters f and d i j Naturally this is legal in GAMS only if you have already assigned values to f and d i j in previous statements The direct assignment above applies to all i j pairs in the domain of c If you wish to make assignments for specific elements in the domain you enclose the element names in quotes For example c Seattle New York 0 40 is a valid GAMS assignment statement The same parameter can be assigned a value more than once Each assignment statement takes effect immediately and overrides any previous values In contrast the same parameter may not be declared more than once This is a GAMS error check to keep you from accidentally using the same name for two different things The right hand side of an assignment statement can contain a great variety of mathematical expressions and built in functions If you are familiar with a scientific programming language such as FORTRAN or C you will have no trouble in becoming comfortable writing assignment statements in GAMS Notice however that GAMS has some efficiencies shared by neither FORTRAN nor C For example we were able to assig
219. entered on the same line as GAMS code t feolcom automatically sets oneolcom Consider the following example eolcom gt set i 1 2 gt set declaration parameter a i gt parameter declaration The character set gt serves as the end of line comment indicator onjoff eps offeps This option is used to treat a zero as an EPS in a parameter or table data statement This can be useful if one overloads the value zero with existence interpolation Consider running the following slice of code set i one two three four parameter a i oneps one 0 offeps two 0 three EPS 73 display a The result of the display statement in the listing file is as follows 8 PARAMETER A one EPS three EPS Note that only those entries specifically entered as 0 are treated as EPS onjoff global offglobal When an include file is inserted it inherits the dollar control options from the higher level file However the dollar control option settings specified in the include file do not affect the higher level file This convention is common among most scripting languages or command processing shells In some cases it may be desirable to break this convention This option allows an include file to change options of the parent file as well Consider running the following slice of code include inc inc hidden after first call to include file onglobal include inc inc hidden after second call to include f
220. entities First comes the keyword Equations in this case followed by the name domain and text of one or more groups of equations or inequalities being declared Our transportation model contains the following equation declaration Equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j Keep in mind that the word Equation has a broad meaning in GAMS It encompasses both equality and inequality relationships and a GAMS equation with a single name can refer to one or several of these relationships For example cost has no domain so it is a single equation but supply refers to a set of inequalities defined over the domain i 2 6 2 GAMS Summation and Product Notation Before going into equation definition we describe the summation notation in GAMS Remember that GAMS is designed for standard keyboards and line by line input readers so it is not possible nor would it be convenient for the user to employ the standard mathematical notation for summations The summation notation in GAMS can be used for simple and complex expressions The format is based on the idea of always thinking of a summation as an operator with two arguments Sum index of summation summand A comma separates the two arguments and if the first argument requires a comma then it should be in parentheses The second argument can be any mathematical expression including another summation As a simple example
221. ents below produce very different results In the first case the lower bound for c 1985 will be 0 01 but in the second the lower bound is 1 c x 1985 1 c lo t 0 01 c lo t 0 01 c fx 19857 1 Everything works as described in the previous chapter including the various mechanisms described there of indexed operations dollar operations subset assignments and so on 7 4 2 Variable Attributes in Assignments Using variable attributes on the right hand side of assignment statements is important for a variety of reasons Two common uses are for generating reports and for generating initial values for some variables based on the values of other variables The following examples adapted from CHENERY illustrate the use of variable attributes on the right hand side of assignment statements scalar cva total value added at current prices rva real value added cli cost of living index sum i v 1 i x 1 1 sum i p 1 i ynot i sum i ynot i cva cli cva cli rva display cli cva rva 7 5 Summary 69 As with parameters a variable must have some non default data values associated with it before one can use it in a display statement or on the right hand side of an assignment statement After a solve statement to be discussed later has been processed or if non default values have been set with an assignment statement this condition is satisfied ts The fx suffix is really
222. ents of n The log file that results from running TRNSPORT with the option 11 0 is shown below Starting compilation Starting execution Generating model TRANSPORT EA 6 rows 7 columns and 19 non zeroes Executing BDMLP GAMS BDMLP 1 1 Aug 1 1994 001 049 030 033 030 386 486 DOS W READING DATA Work space allocated 0 03 Mb Iter Sinf Objective Status Num Freq 1 2 25000000E 02 infeas 1 1 182 The GAMS Call 4 1 53675000E 02 nopt 0 SOLVER STATUS 1 NORMAL COMPLETION MODEL STATUS 1 OPTIMAL OBJECTIVE VALUE 153 67500 Restarting execution Reading solution for model TRANSPORT All done Comparing this output to the one shown in the example of option logfile one can see that the line numbers are absent from the log file logoption lo 1 log file option This option controls the location of the output log of a GAMS run By default GAMS directs the log of the run to the screen console If lo 2 the log is redirected to a file With 1o 3 all the output goes to the standard output If no file name is provided for the log through the 1f option the file name will be the input file name with the extension log Values no log output 0 1 log output to screen console 2 log output to file 3 log output to stdout To illustrate the use of the 1o option run TRNSPORT with the options 10 2 The resulting log file trnsport 1og looks exactly as shown in the example of option logfile Ip lp tezt d
223. er Text can be quoted or unquoted Quoted text can contain any character except the quote character used Single or double quotes can be used but must match Text has to fit on one line and cannot exceed 80 characters in length Text used in unquoted form must follow a number of mild restrictions Unquoted text cannot start with a reserved word or and must not include semicolon commas or slashes End of lines terminate a text These restrictions are a direct consequence of the GAMS syntax and are usually followed naturally by the user Some examples are 32 GAMS Programs this is text final product shipment tpy quoted text containing otherwise illegal characters use single quotes to put a double quote in text 3 4 6 Numbers Numeric values are entered in a style similar to that used in other computer languages t Blanks can not be used in a number GAMS treats a blank as a separator The common distinction between real and integer data types does not exist in GAMS If a number is used without a decimal point it is still stored as a real number In addition GAMS uses an extended range arithmetic that contains special symbols for infinity INF negative infinity INF undefined UNDF epsilon EPS and not available NA One cannot enter UNDF it is only produced by an operation that does not have a proper result such as division by zero All the other special symbols can
224. errors found while analyzing solve statements is more complicated than for normal compilation errors mainly because many things must be checked All identifiers referenced must be defined or assigned the mathematics in the equations must match the model class and so on More elaborate reporting is required to accurately describe any problems found The solve statement is only checked if the model has been found to be error free up to this point This is not only because the check is comparatively expensive but also because many erroneous and confusing messages can be produced while checking a solve in a program containing other errors ts Solve error messages are reported in two places and in two formats First they are shown immediately below the solve statement with a short text including the name of any offending identifier and the type of model involved This will be sufficient in most cases Second a longer message with some hints appears with the rest of the error messages at the end of the compilation The example below illustrates how the general reporting format for compiler errors associated with a solve statement 1 variables x y Z 2 equations eqi eq2 3 4 eqi x 2 y e Z 5 eq2 min x y 1 20 6 7 model silly all 8 solve silly using lp maximizing z CK 54 51 256 x amp THE FOLLOWING LP ERRORS WERE DETECTED IN MODEL SILLY xk 54 IN EQUATION EQ1 ENDOG OPERANDS FOR xkk 51 IN EQUATION EQ2
225. erse lines describing the progress GAMS is making including the name of the file onto which the output is being written When GAMS has finished examine this file and if all has gone well the optimal shipments will be displayed at the bottom as follows new york chicago topeka seattle 50 000 300 000 san diego 275 000 275 000 You will also receive the marginal costs simplex multipliers below chicago topeka seattle 0 036 san diego 0 009 These results indicate for example that it is optimal to send nothing from Seattle to Topeka but if you insist on sending one case it will add 036 K or 36 00 to the optimal cost Can you prove that this figure is correct from the optimal shipments and the given data 2 2 Structure of a GAMS Model For the remainder of the tutorial we will discuss the basic components of a GAMS model with reference to the example above The basic components are listed in table 2 2 There are optional input components such as edit checks for bad data and requests for customized reports of results Other optional advanced features include saving and restoring old models and creating multiple models in a single run but this tutorial will discuss only the basic components Before treating the individual components we give a few general remarks 1 A GAMS model is a collection of statements in the GAMS Language The only rule governing the ordering of statements is that an entity of the model cannot be referen
226. ess and the layout of displays They are processed at execution time unlike the dollar control options discussed in Appendix D They are provided to give flexibility to the user who would like to change the way GAMS would normally do things GAMS does provide default values that are adequate for the most purposes but there are always cases when the user would like to maintain control of aspects of the run E 1 1 The Syntax The general form of an option statement is option keyword1 valuel EOL keyword2 value2 where the keyword1 and keyword2 are recognized option names but not reserved words and the value1 and value2 are valid values for each of the respective options Note that commas or end of line characters are both legal separators between options t Option names are not reserved words and therefore do not conflict with other uses of their name There are five possible formats 1 a display specifier 2 a recognized name number following sign or value a recognized name number following an sign then an unsigned integer value a recognized name number following an sign then an unsigned real number Cu a ee a recognized name number following an sign then either of two recognized words t An option statement is executed by GAMS in sequence with other instructions Therefore if an option statement comes between two solve statements the new values are
227. failure 95 unknown 94 errorf function 55 errorLevel function 59 errorlog GAMS call parameter 177 evaluation error limit 95 exception handling 89 handling in equations 111 execerr GAMS call parameter 177 execError function 59 execSeed function 55 execution 164 errors 101 execution statements 164 exit dollar control option 199 exogenous 164 exp function 55 expand GAMS call parameter 177 explanatory text 66 77 164 exponent 54 164 exponential distribution 249 extended value 98 extended arithmetic 164 Extrinsic Functions Fitpack Library 247 Introduction 247 Piecewise Polynomial Library 248 Stochastic Library 249 Trigonometric Library 250 f distribution 249 fact function 55 feasible 164 feasible solution 165 ferr GAMS call parameter 178 FERTD example from GAMSLIB 108 FERTS example from GAMSLIB 112 file GAMS statement 133 defining 135 summary 98 fitFunc function 247 fitParam function 247 floor function 55 for example 153 statement 152 syntax 153 forcework GAMS call parameter 178 frac function 55 fsave GAMS call parameter 178 functions abs 55 arccos 55 arcsin 55 arctan 55 arctan2 55 Beta 55 betaReg 55 binomial 55 bool_and 58 bool_eqv 58 bool_imp 58 bool_not x 58 bool_or 58 bool_xor 58 ceil 55 centropy 55 cos 55 cosh 55 cosine 251 cvPower 55 div 55 divO 55 eDist 55 entropy 55 errorf 55 errorLevel 59 exec
228. ference being the choice of put keyword This is illustrated by writing to the title block of our report dat file puttl class2 GAMS Put Example In this case the text GAMS Put Example has been placed in the first column of the first row of the title block Any subsequent pages in the report dat file will now start with this information ts If the title block was modified or the header block was started after the window of the current page has been written to these modifications would appear in the next page and not the current page 15 6 2 Paging Paging occurs automatically whenever a page is full However note that the window must be used in order for the page to be written to the output file When a page has no output in its window the page is not written to file regardless of whether there are output items in the title or header blocks To force a page that has an empty window out to file simply write something innocuous to the window such as put Now the window of the page has been initiated and it will be written 15 7 Positioning the Cursor on a Page The cursor is positioned at the space immediately following the last character written unless the cursor is specif ically moved using one of the following cursor control characters n Move cursor position to row n of current page 15 8 System Suffixes 139 On Move cursor position to column n of current line Move cursor to first column of next line
229. first character encountered is a comment character the rest of the line is treated as a comment line Likewise if the first character encountered is the dollar control character the line is treated as a dollar control line An alternative to placing new_input_line on the same line as the conditional is to leave the remainder of the line blank and place new_input_line on the line immediately following the if line If the conditional is found to be false either the remainder of the line if any is skipped or the next line is not read Consider the following example if exist myfile dat include myfile dat The statement above includes the file myfile dat if the file exists Note that the character at the beginning of the include option is the first non blank character after the conditional expression if exist myfile dat and is therefore treated as the first column position The above statement can also be written as if exist myfile dat include myfile dat Consider the following additional examples if not 1a a goto labelname if not exist 41 display file 1 not found The first statement illustrates the use of the if option inside a batch include file where parameters are passed through the batinclude call from the parent file The if condition checks if the parameter is empty and if not processes the goto option Note that the string comparison attempted la a can also be done using 1 The second statement
230. fix These activity levels of the variables prior to the solve statement serve as initial values for the solver This is particularly important for nonlinear programming problems 7 4 Variables in Display and Assignment Statements GAMS allows the modeler to use the values associated with the various attributes of each variable in assignment and display statements The next two sub sections explain the use of variables in the left and right hand sides of assignment statements respectively Later we will explain the use of variables in display statements 7 4 1 Assigning Values to Variable Attributes Assignment statements operate on one variable attribute at a time and require the suffix to specify which attribute is being used Any index list comes after the suffix The following example illustrates the use of assignment statements to set upper bounds for variables x up c i j 1000 phi lo inf p fx pellets ahmsa mexico df 200 c l t 4xcinit t Note that in the first statement the index set covering the domain of x appears after the suffix The first assignment puts an upper bound on all variables associated with the identifier x The statement on the second line bounds one particular entry The statement on the last line sets the level values of the variables in c to four times the values in the parameter cinit Remember that the order is important in assignments and notice that the two pairs of statem
231. for listing file This option controls the width of the left margin of the text in the listing file If 1m is greater than 0 the output is shifted 1m positions to the right libincdir Idir text library include directory Used to complete a file name for libinclude If the 1dir option is not set the sub directory inclib in the GAMS system directory is searched t Unlike idir additional directories cannot be set with ldir The string passed will be treated as one directory Passing additional directories will cause errors t Note that if the ldir parameter is set the default library include directory is not searched Consider the following illustration gams myfile ldir mydir GAMS searches for any referenced libinclude file in the directory mydir license license text license file name This option is only to be used by advanced users attempting to override internal license information The file name is used as given The default license file is gamslice txt in the GAMS system directory limcol limcol 3 default column listing Values n first n columns listed C 3 Detailed Description of Command Line Parameters 181 limrow limrow 3 default row listing Values n first n rows listed logfile lf text log file name This option is used in conjunction with the lo option If lo is set to 2 then this option will specify the name of the log file name The name provided by the option is completed using the current direct
232. forms This option allows for recognizing these Control M characters and interpreting them as blanks Values O Ctrl M is not a valid input 1 Ctrl M will be interpreted as blank ctrlz ctrlz 0 control Z indicator The Control Z character appears as the end of file character when files have been incorrectly transferred from PC to Unix platforms This option allows for recognizing these Control Z characters and interpreting them as blanks Values O Ctrl Z is not a valid input 1 Ctrl Z will be interpreted as blank curdir curdir text set current directory This option sets the current directory This option is useful when GAMS is called from an external system like Visual Basic If not specified it will be set to the directory the GAMS module is called from 174 The GAMS Call dformat df 0 date format This option controls the date format in the listing file The three date formats correspond to the various con ventions used around the world For example the date December 2 1996 will be written as 12 02 96 with the default df value of 0 as 02 12 96 with df 1 and as 96 12 02 with df 2 Values 0 mm dd yy 1 dd mm yy 2 yy mm dd dnlp dnlp tezt default DNLP solver dumpopt dumpopt 0 workfile dump option Extracts selected portions of the workfile and writes it in GAMS source format to another file that has the extension dmp Values no dumpfile use original element names use new element names and change text use
233. ge and must be entered on separate lines recognized by a symbol in the first column A dollar control option line may be placed anywhere within a GAMS program and it is processed during the compilation of the program The symbol is followed by one or more options identified by spaced Since the dollar control options are not part of the GAMS language they do not appear on the compiler listing unless an error had been detected Dollar control option lines are not case sensitive and a continued compilation uses the previous settings D 1 1 Syntax In general the syntax in GAMS for dollar control options is as follows option_name argument_list option_name argument_list where option_name is the name of the dollar control option while argument_list is the list of arguments for the option Depending on the particular option the number of arguments required can vary from 0 to many t No blank space is permitted between the character and the first option that follows ts In most cases multiple dollar control options can be processed on a line However some dollar control options require that they be the first option on a line ts The effect of the dollar control option is felt immediately after the option is processed An example of a list of dollar control options is shown below title Example to illustrate dollar control options onsymxref onsymlist Note that there is no blank space between the character and the option that fol
234. gging and comprehension aids are produced and written to the output file EQUATION LISTING etc 3 GAMS verifies that there are no inconsistent bounds or unacceptable values for example NA or UNDF in the problem 4 Any errors detected at this stage cause termination with as much explanation as possible using the GAMS names for the identifiers causing the trouble 5 GAMS passes control to the solution subsystem and waits while the problem is solved 9 4 Programs with Several Solve Statements 81 6 GAMS reports on the status of the solution process and loads solution values back into the GAMS database This causes new values to be assigned to the 1 and m fields for all individual equations and variables in the model A row by row and column by column listing of the solution is provided by default Any apparent difficulty with the solution process will cause explanatory messages to be displayed Errors caused by forbidden nonlinear operations are reported at this stage The outputs from these steps including any possible error messages are discussed in detail in the next chapter 9 4 Programs with Several Solve Statements Several solve statements can be processed in the same program If you have to solve sequences of expensive or difficult models you should read the chapter on workfiles to find out how to interrupt and continue program execution The next few sub sections discuss various instances where several solve statements may
235. gher precision to one with lower precision Instead of changing numbers with too much precision the offdigit tells GAMS to use as much precision as possible and ignore the rest of the number If the stated precision of a number exceeds the machine precision an error will be reported For most machines the precision is 16 digits Consider running the following slice of code parameter y toolarge 12345678901234 5678 offdigit ignored 12345678901234 5678 The resulting listing file contains 1 parameter y toolarge 12345678901234 5678 HK 103 3 ignored 12345678901234 5678 Error Messages 103 Too many digits in number offdigit can be used to ignore trailing digits Note that the error occurs in the 17th significant digit of y toolarge However after the offdigit line y ignored is accepted without any errors even though there are more than 16 significant digits onjoff dollar offdollar This option controls the echoing of dollar control option lines in the listing file Consider running the following slice of code hidden this line will not be displayed ondollar hidden this line will be displayed offdollar hidden this line will not be displayed The listing file that results looks like 2 ondollar 3 hidden this line will be displayed Note that all lines between the ondollar and offdollar are echoed in the listing file Also note that this action of this option is immediate i e the ondollar line i
236. grams instead of modifying the path as described above C shell users can use the following commands on the command line or in their cshrc file alias gams usr gams 23 3 gams alias gamslib usr gams 23 3 gamslib alias gamsbatch usr gams 23 3 gamsbatch The correct Bourne or Korn shell syntax either command line or profile is 256 Installation and System Notes alias gams usr gams 23 3 gams alias gamslib usr gams 23 3 gamslib alias gamsbatch usr gams 23 3 gamsbatch Again you should log out and log in in order to put the alias settings in cshrc or profile into effect 4 Casual users can always type the absolute path names of the GAMS programs e g usr gams 23 3 gams trnsport Index circular operator 121 circular operator 121 After equation name 72 cursor control 138 Cn cursor control 138 n cursor control 138 abort dollar control option 195 abs function 55 acronym 28 163 action GAMS call parameter 172 activity level 1 or L 67 68 81 91 ALAN example from GAMSLIB 85 87 algorithm 163 Implementation of non standard 82 alias 28 163 statement 38 all defining a model 92 ALUM example from GAMSLIB 39 and relational operator 104 ANDEAN example from GAMSLIB 54 appendlog GAMS call parameter 172 appendout GAMS call parameter 172 arccos function 55 arcsin function 55 arctan function 55 arctan2 function 55 arithmetic operations 53 62 101 add
237. have 10 kk constraints defining the relationship between the 11 k capital values The other interesting point in the RAMSEY excerpt is that the constraint tc is explicitly defined only for the final period because of the assignment to the set tlast Notice the use of dynamic sets to control the domain of the two equations The set tfirst is also used in other parts of the model to set initial conditions particularly the capital stock in the first period k 1990 13 6 2 Linear Lag and Lead Operators Reference In the example discussed in Section 13 6 1 equation kk can be rewritten with equivalent effect as kk t mot tfirst t k t 1 e k t it The dollar condition will cause one of the individual equations to be suppressed However note that using lags and leads in the equation domain will always cause one or more individual equations to be suppressed and this may not be desirable in every case Consider the following modified set of constraints to the one discussed in the previous example It is expressed with the lag and lead operators being used to control the domain of the equation definition kk t 1 k t 1 e k t i t kfirst tfirst k tfirst e k0 Here the important boundary is the one at the beginning of the set rather than at the end This can be expressed more compactly as kk t k t e k t 1 kO tfirst t i t 1 In general the choice between using lag and lead operators as reference or in
238. have been only defined and have not been initialized or assigned The result of the ki11 statement above is equivalent to i and a being defined as follows set i scalar a Unlike the clear a display statement for i and a after they are killed will trigger an error label id This option marks a line to be jumped to by a goto statement Any number of labels can be used in files and not all of them need to be referenced Re declaration of a label identifier will not generate an error and only the first occurrence encountered by the GAMS compiler will be used for future goto references Consider the following example scalar a a 5_ display a goto next a at5 display a label next a a 10 display a On reaching the goto next option GAMS continues from label next All lines in between are ignored On running the example a finally takes a value of 15 The label statement has to be the first dollar control option of multiple dollar control options that appear on the same line libinclude Equivalent to batinclude libinclude file argl arg2 However if an incomplete path is given the file name is completed using the library include directory By default the library include directory is set to the inclib directory in the GAMS system directory The default directory can be reset with the 1dir command line parameter Consider the following example libinclude abc x y This call first looks for the
239. he target user specified with the PLICENSE parameter The target user can if licensed add access controls to an existing secure file by using the PLICENSE LICENSE parameter but cannot change the original information about source and target users Secure work files can be tested on any GAMS system by specifying a non default license file with the LI CENSE target parameter G 4 Access Control Commands There are four Access Control Commands ACC that are processed during the compilation phase These com mands can be inserted anywhere and are processed in chronological order and have the following syntax acc ident1 ident2 acc ALL 230 Secure Work Files Where ace is one of the four ACC s PURGE remove the objects and all data associated HIDE hide the objects but allow them to be used in model calculations PROTECT the objects cannot be modified but used in model calculations EXPOSE removes all restrictions The keyword ALL applies the ACC to all identifiers defined up to this point in the GAMS source code ACC s can be changed and redefined within the same GAMS program Identifiers inherited from a restart file cannot be changed however G 5 Advanced Use of Access Control We will again use the transport model to show how to hide input data and results from the target user The target user is only allowed to view percentage changes from an unknown base case In addition to the original model we will introduce a data init
240. he actual number will depend on the page width and the number and length of your labels Using the same example as in the previous sections the following extension option x 5 0 1 display x changes the output to look like below 12 PARAMETER X first one b i 5 63559 first two a i 2 93930 first two a ii 0 02873 first two b ii 10 34570 first three b i 6 31610 second one a i INF second one a ii 1 00370 second one b ii 17 29948 second two a ii INF second two b i 19 83500 a four dimensional structure This output nicely illustrates the label order used The first index varies the slowest the last the fastest and each one runs from beginning to end before the next one to the left advances This ordering scheme is also used on equation and column lists and on the solution report all produced by the solve statement 132 The Display Statement 15 The Put Writing Facility 15 1 Introduction In this chapter the put writing facility of the GAMS language is introduced The purpose of this writing facility is to output individual items under format control onto different files Unlike the display statement the entire set of values for indexed identifiers cannot be output using a single put statement identifiers are the names given to data entities such as the names for parameters sets variables equations models etc While its structure is more complex and requires more programming than is required
241. he data initialization is done in the first pass and assignments in the second irrespective of their relative locations This is an issue particularly with onmulti since it allows data initializations to be performed more than once Consider the following example scalar a 12 a at1 onmulti scalar a 20 display a The two scalar data initialization statements and the onmulti option are processed before the assignment statement a a 1 In the order that it is processed the example above is read by GAMS as compilation step scalar a 12 onmulti scalar a 20 execution step a at1 display a D 3 Detailed Description of Dollar Control Options 209 The example results in a taking a value of 21 The display statement in the resulting listing file is as follows 5 PARAMETER A 21 000 onjoffF nestcom offnestcom Controls nested in line comments Make sure that the open comment and close comment characters have to match Consider running the following slice of code inlinecom onnestcom nesting is now possible in comments braces have to match onjoffF symlist offsymlist Controls the complete listing of all symbols that have been defined and their text including pre defined functions and symbols in alphabetical order grouped by symbol type The symbol listing in the listing file generated by running TRNSPORT with onsymlist is as follows Symbol Listing FUNCTIONS FA RK ABS
242. he function can legally appear with endogenous non constant arguments In order of least to most restrictive the choices are any NLP DNLP or none see Section 9 2 2 for details The following conventions are used for the function arguments Lower case indicates that an endogenous variable is allowed Upper case indicates that a constant argument is required The arguments in square brackets can be omitted and default values will be used Those default values are specified in the function description provided in the last column Function Endogenous Description Classifica tion Mathematical functions abs x DNLP returns the absolute value of an expression or term x arccos x NLP returns the inverse cosine of the argument x where x is a real number between 1 and 1 and the output is in radians see MathWorld 56 Data Manipulations with Parameters arcsin x NLP returns the inverse sine of the argument x where x is a real number between 1 and 1 and the output is in radians see MathWorld arctan x NLP returns the inverse tangent of the argument x where x is a real number and the output is in radians see Math World arctan2 y x NLP four quadrant arctan function yielding arctangent y x which is the angle the vector x y makes with 1 0 in radians Beta x y DNLP beta function B x y w see MathWorld betaReg x y Zz NLP regularized beta function see MathWorld binomial n k NLP returns the g
243. he internal name of the equation an identifier in GAMS An identifier has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long The accompanying text is used to describe the set or element immediately preceding it This must not exceed 254 characters and must all be contained on the same line as the identifier it describes There are no modifying keywords as there are with variables and no initializing data list as there may be with parameters or sets 8 2 2 An Illustrative Example The example is adapted from PRODSCH an inventory and production management problem The relevant set definitions are also shown sets q quarters summer fall winter spring s shifts first second equations cost total cost definition invb q inventory balance sbal q s shift employment balance R 72 Equations The declaration of the first equation follows the keyword equations This declaration begins with the name of the equation in this case cost and is followed by the text namely Total cost definition The equation cost above is a scalar equation which will produce at most one equation in the associated optimization problem By contrast the equation sbal is declared over the sets q 4 members and s 2 members and is thus likely to produce eight individual equations one for each unique combination of labels The circumstances un
244. he local line number in the parent file where the include appeared In the example listed above the include files file1 inc and file2 inc were included on lines 1 and 4 of the parent file test1 gms inlinecom This option redefines the in line comment symbols which are a pair of one or two character sequence By default the system is initialized to and but is not active The oninline option is used to activate the in line comments The inlinecom option sets the oninline automatically 202 Dollar Control Options kill Consider the following example inlinecom set this is an inline comment i 1 2 The character pair serves as the indicator for in line comments te GAMS requires that one not reset the inlinecom option to an existing symbol The following code is illegal since inlinecom is being reset to the same symbol as it is currently inlinecom inlinecom t The onnestcom enables the use of nested comments Removes all data for an identifier and resets the identifier only the type and dimension are retained Note that this is carried out during compile time and not when the GAMS program executes Not all data types can be killed only set parameter equation and variable types can be reset Consider the following example set i 1 20 scalar a 2 kill ia Note that this is different from clear in that after setting ki11 i and a are treated as though they
245. hing offtext in the same file The 0fftext must be on a line by itself title text The text can have up to 80 characters This causes every page of the output to have the title specified t In all dollar control directives the symbol must be in the first character position on the line t Dollar control directives are dynamic they affect only what happens after they are encountered and they can be set and reset wherever appropriate They are remembered in continued compilations started from work files The directives that do not have following text can be entered many to a line as shown below for the map controls 10 4 Execution Output The only output to the listing file while GAMS is executing performing data manipulations is from the display statement All the user controls available to change the format will be discussed in detail later The output from the display statement on line 41 of the example is shown below Note the wrap of the explanatory text FREF 32 PARAMETER LOWYIELD 7 000 yield of lowest yielding security 10 000 variance of highest security risk PARAMETER HIGHRISK If errors are detected because of illegal data operations a brief message indicating the cause and the line number of the offending statement will appear 10 5 Output Produced by a Solve Statement 91 10 5 Output Produced by a Solve Statement In this section the content of the output produced when a solve statement is executed will be e
246. i j supply i sum j x i j 1 a i demand j sum i x i j g b j Here are some points to remember gt The power to create multiple equations with a single GAMS statement is controlled by the domain For example the definition for the demand constraint will result in the creation of one constraint for each element of the domain j as shown in the following excerpt from the GAMS output DEMAND new york X seattle new york X san diego new york G 325 DEMAND chicago X seattle chicago X san diego chicago G 300 DEMAND topeka X seattle topeka X san diego topeka G 275 The key idea here is that the definition of the demand constraints is exactly the same whether we are solving the toy sized example above or a 20 000 node real world problem In either case the user enters just one generic equation algebraically and GAMS creates the specific equations that are appropriate for the model instance at hand Using some other optimization packages something like the extract above would be part of the input not the output In many real world problems some of the members of an equation domain need to be omitted or differentiated from the pattern of the others because of an exception of some kind GAMS can readily accommodate this loss of structure using a powerful feature known as the dollar or such that operator which is not illustrated here The domain restriction feature can be absolutely essent
247. ial for keeping the size of a real world model within the range of solvability The relational operators have the following meanings 1 less than or equal to g greater than or equal to e equal to It is important to understand the difference between the symbols and e The symbol is used only in direct assignments and the e symbol is used only in equation definitions These two contexts are very different A direct assignment gives a desired value to a parameter before the solver is called An equation definition also describes a desired relationship but it cannot be satisfied until after the solver is called It follows that equation definitions must contain variables and direct assignments must not 2 7 Objective Function 15 gt Variables can appear on the left or right hand side of an equation or both The same variable can appear in an equation more than once The GAMS processor will automatically convert the equation to its equivalent standard form variables on the left no duplicate appearances before calling the solver gt An equation definition can appear anywhere in the GAMS input provided the equation and all variables and parameters to which it refers are previously declared Note that it is permissible for a parameter appearing in the equation to be assigned or reassigned a value after the definition This is useful when doing multiple model runs with one GAMS input The equations need not
248. ialization and a report model First we will define a new model to calculate input data The previous parameter c is now the variable newc and the model getc does the calculations include trnsport gms variable newc i j new tansport data equation defnewc i j definition of new transport data model getc compute new transport data defnewc defnewc i j newc i j e f d i j 1000 solve getc using cns Next we change the objective function of the original model to a more complicated nonlinear function Fur thermore we will compute a base case value to be used later in the reporting model Note the reference to newc 1 i j since nexc is a variable we have to specify that we only want the level value scalar beta scale coefficient 1 1 equation newcost definition of new objective function model newtrans newcost supply demand newcost z e sum i j newc 1 i j x i j beta solve newtrans using nlp minimizing z parameter basex i j base values of x basex i j x 1 i j Finally we transform the result by using a third model variable delta i j percentage change from base values equation defdelta i j definition of delta model rep defdelta defdelta i j basex i j delta i j e 100 x 1 i j basex i j basex i j solve rep using cns We will save the above GAMS code under the name p1 gms execute and make a save restart file with the name p1 g00 as follows gt gams pl s p1 Now we
249. ibrary gt gams trnsport The output goes by default to the file trnsport 1st C 1 1 Specifying Options through the Command Line GAMS allows for certain options to be passed through the command line The syntax of the simple GAMS call described in Section C 2 is extended to look as follows gt gams myfile keyi valuei key2 value2 where key1 is the name of the option that is being set on the command line and valuel is the value to which the option is set Depending on the option value1 could be a character string or an integer number For example consider the following commands to run TRNSPORT from the GAMS model library gams trnsport o myrun lst lo 2 gams trnsport o myrun 1lst lo 2 gams trnsport o myrun lst lo 2 gams trnsport o myrun lst lo 2 All the four commands above are equivalent and each directs the output listing to the file myrun 1st o is the name of the option and it is set to myfile 1st In addition in each case the log of the run is redirected to the file myrun log 172 The GAMS Call C 2 List of Command Line Parameters The options available through the command line are grouped into the following functional categories affecting the specific GAMS run input file processing other files system settings output in listing file Table C 1 briefly describes the various options in each of the categories Section C 3 contains a reference list of all options available through the command line with detailed
250. ile where the file inc inc contains the lines ondollar hidden text inside include file The resulting listing file is as follows D 3 Detailed Description of Dollar Control Options 207 INCLUDE D GAMS INC INC 2 ondollar 3 hidden text inside include file INCLUDE D GAMS INC INC 7 ondollar 8 hidden text inside include file 9 hidden after second call to include file Note that the effect of the ondollar dollar control option inside the include file does not affect the parent file until onglobal is turned on The hidden text is then echoed to the listing file on off include oninclude Controls the listing of the expanded include file name in the listing file Consider running the following slice of code include inc inc offinclude include inc inc where the file inc inc contains the line ondollar hidden text inside include file The resulting listing file is as follows INCLUDE D GAMS INC INC 2 ondollar 3 hidden text inside include file 6 ondollar 7 hidden text inside include file Note that the include file name is echoed the first time the include file is used However the include file name is not echoed after offinclude is set on off inline offinline Switch to control the use of in line comments By default the in line comments are set to the two character pairs and but the processing is disabled These comments can span lines till the end of comment ch
251. illustrates using standard GAMS statements if the conditional is valid If the file name passed as a parameter through the batinclude call does not exist the GAMS display statement is processed ts In line and end of line comments are stripped out of the input file before processing for new_input_line If either of these forms of comments appears it will be treated as blanks Consider the following example parameter a a 10 eolcom inlinecom if exist myfile dat in line comments end of line comments a 4 display a The fourth line is ignored and the fifth line involving an assignment setting a to 4 will be treated as the result of the conditional So the result of the display statement would be the listing of a with a value of 4 if the file myfile dat exists and a value of 10 if the file does not exist ts It is suggested that a label not appear as part of the conditional input line The result is that if the label appears on the if line a goto to this label will re scan the entire line thus causing a reevaluation of the conditional expression On the other hand if the label appears on the next line the condition will not be reevaluated on subsequent gotos to the label D 3 Detailed Description of Dollar Control Options 201 The following example illustrates how an unknown number of file specifications can be passed on to a batch include file that will include each of them if they exist The batch inclu
252. in current working directory 2 myfile gms in current working directory 3 myfile and myfile gms in that order in directories specified by idir parameter ts The current settings of the dollar control options are passed on to the lower level include files However the dollar control options set in the lower level include file are passed on to the parent file only if the onglobal option is set Compiler errors in include files have additional information about the name of the include file and the local line number At the end of the compiler listing an include file summary shows the context and type of include files The line number where an include file has been called is given For example in the Include File Summary below we see that SEQ GLOBAL TYPE PARENT LOCAL FILENAME 1 1 INPUT 0 0 C TEST TEST1 GMS 2 1 INCLUDE 1 1 C TEST FILE1 INC 3 6 INCLUDE 1 4 C TEST FILE2 INC The first column named SEQ gives the sequence number of the input files encountered The first row always refers the parent file called by the GAMS call The second column named GLOBAL gives the global expanded line number which contained the include statement The third column named TYPE refers to the type of file being referenced The various types of files are INPUT INCLUDE BATINCLUDE LIBINCLUDE and SYSINCLUDE The fourth column named PARENT provides the sequence number of the parent file for the file being referenced The fifth column named LOCAL gives t
253. in the following section that corresponds to the display statement 128 The Display Statement lo Up Variable positive 0 INF free INF INF negative INF 0 integer 0 100 binary 0 1 Equation g 0 INF n INF INF c 0 INF l INF 0 e 0 0 Table 14 1 Default values for lo and up subtypes Sas 5 first a set 5 SET S si 82 3 s4 a5 5 then a parameter gt 5 PARAMETER P si 0 330 S3 0 670 sess 5 then the activity level of a variable Sass 5 VARIABLE V L T5 T7 S1 0 109 0 221 s3 0 221 0 449 Note that the only the non zero values are displayed In the case of multi dimensional identifiers the data is reported in a tabular form that is easy to read 14 4 The Label Order in Displays The default layout of a display for identifiers of different dimensionality is summarized in table 14 2 The figures in the table refer to the index position in the domain list of the identifier As an example if we display c where c has been declared as c i j k 1 then the i labels the first index will be associated with the planes or individual sub tables the j and k with the row labels and the 1 the fourth and last index with the column headings Numbers of Indices Plane Index Position s on the Row Column 1 List Format 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 Table 14 2 Default layout of display output For 7 to 10 indices the natural progression is followed Th
254. include file GAMS System Directory inclib abc and if this file does not exist GAMS looks for the file GAMS System Directory inclib abc gms The arguments x and y are passed on to the include file to interpret as explained for the batinclude option Consider the following example libinclude c abc myinc inc x y D 3 Detailed Description of Dollar Control Options 203 This call first looks specifically for the include file c abc myfile inc The arguments x and y are passed on to the include file to interpret as explained for the batinclude option lines n log This option starts a new page in the listing file if less than n lines are available on the current page Consider the following example hidden Never split the first few lines of the following table lines 5 table io i j Transaction matrix This will ensure that the if there are less than five lines available on the current page in the listing file before the next statement in this case the table statement is echoed to it the contents of this statement are echoed to a new page This option will send a message to the log file By default the log file is the console The default log file can be reset with the lo and 1f command line parameters t Leading blanks are ignored when the text is written out to the log file using the log option t All special symbols will be substituted out before the text passed through the log option is sent to the log file
255. index set In the example above the set element labels are identified using their set identifier and the suffix t1 As can be seen the set element labels are located starting in the third column and the parameter a at column 15 The example continues with the display of another quoted textual item followed by the parameter b When executed the factors dat file will look like Transportation Model Factors Freight cost 90 00 Plant capacity seattle 350 00 san diego 600 00 Market demand new york 325 00 chicago 300 00 topeka 275 00 This output has been formatted using the default file format values The methods to change these defaults will be described later in this chapter In the last two lines of the example the file results dat is made current and the values associated with the variable x along with their corresponding set element index labels are written line by line The output results of 15 4 Output Files 135 the variable x are formatted by specifying a field width of eight spaces with four of these spaces reserved for the decimal Notice that the local formatting options are delimited with colons The results dat file will look like Transportation Model Results seattle new york 0 0000 seattle chicago 300 0000 seattle topeka 0 0000 san diego new york 325 0000 san diego chicago 0 0000 san diego topeka 275 0000 With just this brief introduction to the put writing facility it is easy to envision its many uses such as re
256. ines using ASCII page control characters inserted every 64 lines and with the output displayed in upper case file class2 report txt class2 pw 72 class2 ps 58 class2 tm 6 class2 pc 3 class2 case 1 t Using a value of 4 5 or 6 for the print control suffix pc will cause data to be squeezed and therefore will ignore spacing information provided by the user through the character However these values can be used to pass data on to be read by spreadsheets 15 6 Page Sections There are three independent writing areas on each page of a document These areas are the title block the header block and the window This is quite useful when there are sections of a page which remain relatively constant throughout a document Title and header blocks are often used to provide organizational information in a document with the window being used for specific reporting These writing areas are always sequentially located on the page in the order shown on the following diagram It is important to note that the title and header blocks are essentially the same as the window and use exactly the same syntax rules However the window is required in each page of your document while the title and headers are optional Also note that once the window is written to any further modifications of the title or header blocks will be shown on subsequent pages and not the current page Writing to the window is what ultimately forces a page to be writ
257. ing convention as other identifiers like names of sets parameters or tables 5 5 2 Illustrative Example Consider the following example set machines m 1 m 5 acronyms monday tuesday wednesday thursday friday parameter shutdown machines m 1 tuesday 5 6 Summary 49 m 2 wednesday m 3 friday m 4 monday m 5 thursday 3 In the example above data entries are in the form of strings like monday and tuesday By declaring each of those character strings as acronyms this kind of data entry can be used by GAMS Sections 6 2 7 and 11 2 5 will explain the further use of acronyms once entered in this form 5 6 Summary In this chapter the declaration and initialization of parameters with the parameter scalar and the table statement have been discussed The next chapter will describe how this data can be changed with assignment statements 50 Data Entry Parameters Scalars amp Tables 6 Data Manipulations with Parameters 6 1 Introduction Data once initialized may require manipulation in order to bring it to the form required in the model The first part of this chapter will deal explicitly with parameter manipulation The rest of the chapter will be devoted to explaining the ramifications indexed assignment functions index operations 6 2 The Assignment Statement The assignment statement is the fundamental data manipulation statement in GAMS It may be used to define or alter values associate
258. ing extension to the previous example Parameter p j a 1 null 23 display p The resulting section of the listing file is shown below 6 PARAMETER P a 1 000 shift The shift option is similar to the DOS batch shift operator It shifts the order of all parameters passed once to the left This effectively drops the lowest numbered parameter in the list Consider the following example scalar a b c a 1 batinclude inc inc abc display a b c where the batch include file inc inc is as follows 12 1 1 shift 12 11 1 The resulting listing file is 1 scalar a b c a 1 BATINCLUDE C PROGRAM FILES GAMSIDE INC INC 3 b atti 5 c bt1 6 display a b c In the first statement in the include file 1 is the first argument in the batinclude call and is interpreted in this case as a 2 is the second argument in the batinclude call and is interpreted as b This leads to the overall assignment being interpreted as b at1 The shift option shifts the arguments to the left So now 41 is interpreted as b and 2 is interpreted as c This leads to the second assignment being interpreted as c b 1 The result of the display statement in the input file is therefore RE 6 PARAMETER A 1 000 PARAMETER B 2 000 PARAMETER C 3 000 single The lines following a single option will be echoed single spaced on the compiler listing This option is the default and is only useful as a switch to turn
259. ing file to the next page iterlim 1000 This option will cause the solver to interrupt the solution process after iterlim iterations and return the current solution values to GAMS limcol 3 This controls the number of columns that are listed for each variable in the COLUMN LISTING section of the listing file Specify zero to suppress the COLUMN LISTING altogether limrow 3 This controls the number of rows that are listed for each equation in the EQUATION LISTING section of the listing file Specify zero to suppress the EQUATION LISTING altogether lp default This option controls the solver used to solve 1p models For details cf option cns mcp default This option controls the solver used to solve mcp models For details cf option cns 218 The Option Statement minlp default This option controls the solver used to solve minlp models For details cf option cns mip default This option controls the solver used to solve mip models For details cf option cns miqcp default This option controls the solver used to solve miqcp models For details cf option cns nlp default This option controls the solver used to solve nlp models For details cf option cns optca 0 0 This option is only used with problems containing discrete variables i e the GAMS model type mip General mixed integer problems are often extremely difficult to solve and proving that a solution found is the best possible can use enormous
260. inued Tables If a table has too many columns to fit nicely on a single line then the columns that don t fit can be continued on additional lines We use the same example to illustrate 5 4 Tables 47 table ka m i initial cap of productive units 100 tons per yr inchon ulsan atmos dist 3702 12910 steam cr 517 aromatics 181 hydrodeal 180 yosu atmos dist 9875 steam cr 1207 aromatics 148 SC The crucial item is the plus sign above the row labels and to the left of the column labels in the continued part of the table The row labels have been duplicated except that hydroreal has been left out not having associated data Tables can be continued as many times as necessary 5 4 4 Tables with more than Two Dimensions A table can have up to 20 dimensions Dots are again used to separate adjacent labels and can be used in the row or column position The label on the left of the row corresponds to the first set in the domain list and that on the right of each column header to the last Obviously there must be the same number of labels associated with each number in the table as there are sets in the domain list The actual layout chosen will depend on the size of the controlling sets and the amount of data and the ideal choice should be the one that provides the most intuitively satisfactory way of organizing and inspecting the data Most people can more easily look down a column of numbers than across a row but to put extr
261. ion Assignment of type e Assignment of bounds and or initial values optional e Equations Declaration Definition e Model and Solve statements e Display statement optional Table 2 2 The basic components of a GAMS model 5 As you can see from the list of input components above the creation of GAMS entities involves two steps a declaration and an assignment or definition Declaration means declaring the existence of something and giving it a name Assignment or definition means giving something a specific value or form In the case of equations you must make the declaration and definition in separate GAMS statements For all other GAMS entities however you have the option of making declarations and assignments in the same statement or separately 6 The names given to the entities of the model must start with a letter and can be followed by up to thirty more letters or digits 2 3 Sets Sets are the basic building blocks of a GAMS model corresponding exactly to the indices in the algebraic representations of models The Transportation example above contains just one Set statement Sets i canning plants seattle san diego j markets new york chicago topeka The effect of this statement is probably self evident We declared two sets and gave them the names i and j We also assigned members to the sets as follows i Seattle San Diego j New York Chicago Topeka You should note the typographical differen
262. ioned above is to start a line with an asterisk in the first character position The remaining characters on the line are ignored but printed on the output file The second is to use special block delimiters that cause GAMS to ignore an entire section of the program The symbol must be in the first character position The choice between the two ways is a matter of individual taste or utility The example below illustrates the use of the block comment 3 5 Summary 33 ontext Following a ontext directive in column 1 all lines are ignored by GAMS but printed on the output file until the matching offtext is encountered also in column 1 This facility is often used to logically remove parts of programs that are not used every time such as statements producing voluminous reports Every ontext must have a matching offtext in the same file Sofftext The third style of comment allows embedding a comment within a line It must be enabled with the compiler option inlinecom or eolcom as in the following example eolcom inlinecom x 1 this is a comment y 2 this is also a comment z 3 3 5 Summary This completes the discussion of the components of the GAMS language Many unfamiliar terms used in this chapter have been further explained in the Glossary 34 GAMS Programs 4 Set Definitions 4 1 Introduction Sets are fundamental building blocks in any GAMS model They allow the model to be s
263. ions The controlling indices can in certain cases be filtered through the conditional set without the use of the dollar operator Consider the example described in that section The total cost of shipment is obtained through the following equation variable shipped i j totcost equation costequ cost totcost e sum i j ij i j shipcost i j shipped i j where shipped is the amount of material shipped from i to j and totcost is the total cost of all shipment The equation above can be written as cost totcost e sum ij shipcost ij shipped ij However if the original equation is expressed as cost totcost e sum i j ij i j factor congestfac j distance i j shipped i j Index j appears separately from i in congestfac j The equation then needs to be simplified as cost totcost e sum ij i j factor congestfac j distance ij shipped ij Note that the presence of j separately in the indexed expression necessitated the use of ij i j rather than ij 11 4 Conditional Assignments 109 11 4 4 Filtering Sets in Assignments Consider the following statement u k s k a k where k and s k are sets while u and a are parameters This can be rewritten as u s a s Note that the assignment has been filtered through the conditionality without the use of the dollar operator This is a cleaner and more understable representation of the assignment This feature gets more useful when dea
264. is a scalar quantity Every GAMS optimization model must contain one such variable to serve as the quantity to be minimized or maximized Once declared every variable must be assigned a type The permissible types are given in table 2 3 Variable Type Allowed Range of Variable free default oo to 00 positive 0 to 00 negative oo to 0 binary 0 or 1 integer 0 1 100 default Table 2 3 Permissible variable types The variable that serves as the quantity to be optimized must be a scalar and must be of the free type In our transportation example z is kept free by default but x i j is constrained to non negativity by the following statement Positive variable x Note that the domain of x should not be repeated in the type assignment All entries in the domain automatically have the same variable type Section 2 10 describes how to assign lower bounds upper bounds and initial values to variables 2 6 Equations The power of algebraic modeling languages like GAMS is most apparent in the creation of the equations and inequalities that comprise the model under construction This is because whenever a group of equations or inequalities has the same algebraic structure all the members of the group are created simultaneously not individually 2 6 Equations 13 2 6 1 Equation Declaration Equations must be declared and defined in separate statements The format of the declaration is the same as for other GAMS
265. is section we will discuss current limitations and possible extension to the security features The following limitations exist gt Solvers are not security aware and it would be possible to write a special GAMS solver that extracts information about a specific model instance Primal and duals values as well as first partial derivatives could be extracted and displayed gt The names and explanatory text of all GAMS symbols are retained in the work file and could be accessed by a special GAMS solver gt The source and target license files locked to the secure work file cannot be changed If the target user upgrades the GAMS system and receives a new license file the secure work file cannot be read any more H Compressed and Encrypted Input Files H 1 Introduction When models are distributed to users other than the original developers issues of privacy security data integrity and ownership arise Besides using secure work files one can compress and encrypt GAMS input files The compression and decompression of files is available to any GAMS user The encryption follows the work file security model and requires special licensing Three new Dollar Control Options have been introduced Encrypt lt source gt lt target gt Encrypts into a GAMS system file Compress lt source gt lt target gt Compresses into a GAMS system file Decompress lt source gt lt target gt Decompresses a GAMS system file Encryption is only available
266. isfy demand at market j supply observe supply limit at plant i models transport 2 11 4 Equation Listings Once you succeed in building an input file devoid of compilation errors GAMS is able to generate a model The question remains and only you can answer it does GAMS generate the model you intended The equation listing is probably the best device for studying this extremely important question A product of the solve command the equation listing shows the specific instance of the model that is created when the current values of the sets and parameters are plugged into the general algebraic form of the model For example the generic demand constraint given in the input file for the transportation model is demand j sum i x i j g b j while the equation listing of specific constraints is A demand g satisfy demand at market j demand new york x seattle new york x san diego new york g 325 demand chicago x seattle chicago x san diego chicago g 300 demand topeka x seattle topeka x san diego topeka g 275 The default output is a maximum of three specific equations for each generic equation To change the default insert an input statement prior to the solve statement option limrow r 2 11 GAMS Output 23 where r is the desired number The default output also contains a section called the column listing analogous to the equation listing which shows the coefficients of thr
267. isplayed which is more common especially for the marginal m The meanings of the attributes 1o 1 and up will be described with respect to an individual constraint rather than the symbolic equation After a solution has been obtained there is a value associated with the unknown terms on the left and this is by definition 1 The meaning of 1o and up are shown in table 8 2 in terms of the constant right hand side rhs and the variable left hand side 1 for each of the equation types The relationship between rhs and 1 is satisfied only if the constraint is feasible at the solution point Type lo up l e rhs rhs rhs 1 inf rhs rhs g rhs inf rhs n inf inf any Table 8 2 Subfield definitions for equations The meaning of the marginal value m in terms of the objective value is discussed in detail in most texts on mathematical programming The crude but useful definition is that it is the amount by which the objective function would change if the equation level were moved one unit 76 Equations 9 Model and Solve Statements 9 1 Introduction This chapter brings together all the concepts discussed in previous chapters by explaining how to specify a model and solve it 9 2 The Model Statement The model statement is used to collect equations into groups and to label them so that they can be solved The simplest form of the model statement uses the keyword all the model consists of all equations decl
268. itioenal Assia lt eet sa a DR Ree bw ea SG See Pade eae EY 107 1141 Dollar om the Left o cca bb bone tod ee eR ee Ee ea bd a e a 107 11 42 Dollar pa the Right ceire aea a ie ee ee de a ae ae 108 11 4 3 Filtering Controlling Indices in Indexed Operations 0 0 108 11 44 Filtering Sets in Assignments 0 ee 109 11 5 Gonditional Indexed Operations o gt se 4 445226 082 se eae tee Ree ea tee aes ae 110 11 5 1 Filtering Controlling Indices in Indexed Operations 111 11 6 Conditional Equations oos e sos es ae eea aos PDE eee ee ee ee ee EEA we eS 111 11 6 1 Dollar Operators within the Algebra ee eee 111 11 6 2 Dollar Control over the Domain of Definition 111 11 6 3 Filtering the Domain of Definition gt lt e q qo oc eaaa aceros ss 112 TABLE OF CONTENTS 12 Dynamic Sets 12 1 12 2 12 5 ir A II Assigning Membership to Dynamic Sets e e e 1221 The Synta oo omita oe ee AR A a eas 122 2 Mustr tiv Exampl ooo e md a a bebe e eean 12 2 3 Dynamic Sets with Multiple Indices gt oroc oea a e eaea nea da eia p Ei a 12 2 4 Assignments over the Domain of Dynamic Sets aoao a 12 2 5 Equations Defined over the Domain of Dynamic Sets aaa oaaae a Using Dollar Controls with Dynamic Sets o een o IL Assi os ek ee A a A AA 1332 enc Operations ascii A E A a A as Oe Ms a AI 12 34 Filtermg through
269. ition 53 division 53 exponentiation 53 multiplication 53 prod 54 smax 54 smin 54 subtraction 53 sum 54 assigned reference type 88 assignment 68 163 conditional 107 indexed 51 issues with controlling indices 52 over subsets 52 scalar 51 statement 51 to dynamic sets 114 using labels explicitly 52 asterisk in set definitions 37 marking errors 92 99 use in comments 32 basic 163 batinclude dollar control option 195 beta distribution 249 Beta function 55 betaReg function 55 binary operator 105 128 binding 163 binomial distribution 250 binomial function 55 bool_and function 58 bool_eqv function 58 bool_imp function 58 bool_not x function 58 bool or function 58 bool_xor function 58 boolean operations 110 botmargin GAMS call parameter 172 bounds 163 on variables 67 branching priority value prior 67 bratio GAMS option 217 model attribute 79 call dollar control option 196 card operator on sets 121 case GAMS call parameter 173 cauchy distribution 249 ceil function 55 74 centropy function 55 cerr GAMS call parameter 173 character set valid 35 charset GAMS call parameter 173 258 INDEX CHENERY example from GAMSLIB 68 74 111 chiSquare distribution 249 clear dollar control option 196 cns GAMS call parameter 173 GAMS option 217 CNS model type 16 78 codex GAMS call parameter 173 column 163
270. ive function discontinuous A classification of a function A plot of the function values will be a line with breaks in it discrete A discrete variable type binary or integer may not assume any value between the bounds but must assume integer values dollar control option Directives or options used to control input or output detail associated with the GAMS compiler dollar operator An operator used for exceptions handling in assignment statements and in equation definitions domain checking The check that ensures that only legal label combination are used on every assignment to or reference of an identifier domain definition The label combinations whose data will be updated in an assignment statement or that will generate an individual constraint in an equation definition domain restriction condition The alteration to the domain of definition caused when a dollar operator is used on the left of the in an assignment or of the in an equation definition driving set The set that determine the domain of definition or that control and index operation such as sum dynamic set A set is dynamic if it has been changed with an assignment statement Dynamic sets cannot be used with lag operations or in domain definitions endogenous Data values that change when a solve statement is processed In GAMS most often associated with variables equation The GAMS data type used to specify required relationships between activity
271. just a shorthand for 1o and up and can therefore only be used only on the left hand side of an assignment statement 7 4 3 Displaying Variable Attributes When variables are used in display statements you must specify which of the six value fields should be displayed Appending the appropriate suffix to the variable name does this As before no domain specification can appear As an example we show how to display the level of phi and the level and the marginal values of v from MEXSS display phi 1 v l v m The output looks similar except that of course the listing shows which of the values is being displayed Because zeroes and especially all zero rows or columns are suppressed the patterns seen in the level and marginal displays will be quite different since non zero marginal values are often associated with activity levels of zero Mexico Steel Small Static MEXSS SEQ 15 Execution aso 203 VARIABLE PHI L 538 811 total cost mill us a 203 VARIABLE V L imports mill tpy C ALL 0 000 Sane 203 VARIABLE V M imports mill tpy mexico df monterrey guadalaja steel 7 018 18 822 6 606 We should mention here a clarification of our previous discussion of displays It is actually the default values that are suppressed on display output For parameters and variable levels the default is zero and so zero entries are not shown For bounds however the defaults can be non zero The default value for the upper bound of a positiv
272. lar condition All the dollar control machinery is available for use with dynamic sets In fact the full power of dynamic sets can be exploited using these dollar controls Note that the dynamic set has values of yes and no only and can therefore be treated as a logical statement The only operations that can be performed on dynamic sets inside the dollar operator are therefore not and or or xor as well as the set operations described in Section 12 4 page 116 The main uses of dynamic sets inside dollar conditions are in assignments indexed operations and in equations Each of these will be discussed in detail in the following subsections Examples will be used to illustrate its use in each of the three cases 12 3 1 Assignments Dynamic sets can be used inside dollar conditions within assignments defining other dynamic sets or parameters As an illustration of its use in defining other dynamic sets the two statements in the example from Section 12 2 4 can be written with equivalent effect as subitemi item yes subitem2 item which is a terse form of the following statement subitemi item yes subitem2 item no not subitem2 item The value used in the implied else that goes with dollar on the right is no in a set assignment rather than zero which is used with normal data The second example from Section 12 2 4 can be rewritten as follows to illustrate the use of dynamic sets in defining parameters invento
273. le below shows how two sets can be declared together Note that the semicolon is used only after the last set is declared sets s Sector manuf agri services government r regions north eastcoast midwest sunbelt Fo 4 3 The Alias Statement Multiple Names for a Set It is sometimes necessary to have more than one name for the same set In input output models for example each commodity may be used in the production of all other commodities and it is necessary to have two names for the set of commodities to specify the problem without ambiguity In the general equilibrium model ORANI the set of commodities is written set c commodities food clothing and a second name for the set c is established with either of the following statements alias c cp alias cp c where cp is the new set that can be used instead of the original set c t The newly introduced set can be used as an alternative name for the original set and will always contain only the same elements as the original set The alias statement can be used to introduce more than one new name for the original set alias c cp cpp cppp where the new sets cp cpp cppp are all new names for the original set c t The order of the sets in the alias statement does not matter The only restriction set by GAMS is that exactly one of the sets in the statement be defined earlier All the other sets are introduced by the alias statement We will n
274. les The design of GAMS has incorporated ideas drawn from relational database theory and mathematical program ming and has attempted to merge these ideas to suit the needs of strategic modelers Relational database theory provides a structured framework for developing general data organization and transformation capabilities Math ematical programming provides a way of describing a problem and a variety of methods for solving it The following principles were used in designing the system 1 All existing algorithmic methods should be available without changing the user s model representation Introduction of new methods or of new implementations of existing methods should be possible without requiring changes in existing models Linear nonlinear mixed integer mixed integer nonlinear optimizations and mixed complementarity problems can currently be accommodated 2 The optimization problem should be expressible independently of the data it uses This separation of logic and data allows a problem to be increased in size without causing an increase in the complexity of the representation 2 Introduction 3 The use of the relational data model requires that the allocation of computer resources be automated This means that large and complex models can be constructed without the user having to worry about details such as array sizes and scratch storage 1 2 2 Documentation The GAMS model representation is in a form that can be easily read b
275. levels of variables execution The second phase of GAMS processing when GAMS is actually carrying out data transformations or generating a model execution statements Instructions to carry out actions such as data transformations model solutions and report generation Some examples are the assignment and the option display loop and solve statements exogenous Data values known before a solve statement is processed and not changed by the solve In GAMS most often parameters explanatory text See text exponent A scale factor used to conveniently represent very large or small numbers extended arithmetic The usual computer arithmetic is extended to include plus and minus infinity inf and inf and a special value for an arbitrarily a small number i e one which is close to zero known as epsilon eps Also not available na can be used to indicate missing data and undefined undf is the result of illegal operation GAMS allows extended arithmetic for all operations and functions The library problem CRAZY demonstrates extended arithmetic by showing the results for all operations and functions e format The representation of numbers when an exponent is used explicitly For example 1 1E 07 feasible Often used to describe a model that has at least one feasible solution see below 165 feasible solution A solution to a model in which all column activity levels are within the bounds and all the constraints are satisfied
276. line numbers whereas comments starting with asterisks have line numbers shown Line numbers always refer to the physical line number in your input file t Dollar control directives are only listed if a directive to list them is enabled or if they contain errors Here is the rest of the echo print 10 11 Set i securities hardware software show biz t bills alias i j 10 3 Compilation Output 87 12 13 Scalar target target mean annual return on portfolio 10 14 lowyield yield of lowest yielding security 15 highrisk variance of highest security risk 16 17 Parameters mean i mean annual returns on individual securities 4 18 19 hardware 8 20 software 9 21 show biz 12 22 t bills 7 23 24 Table v i j variance covariance array squared annual return 25 26 hardware software show biz t bills 27 28 hardware 4 3 1 0 29 software 3 6 1 0 30 show biz t 1 10 0 31 t bills 0 o 0 0 32 33 lowyield smin i mean i 34 highrisk smax i v i i 35 display lowyield highrisk 36 37 Variables x i fraction of portfolio invested in asset i 38 variance variance of portfolio 39 40 Positive Variable x 41 42 Equations fsum fractions must add to 1 0 43 dmean definition of mean return on portfolio 44 dvar definition of variance 45 46 fsum sum i x i e 1 0 47 dmean sum i mean i x i e target 48 dvar sum i x i sum j v i j x j e variance 49 50 Model portfo
277. ling with tuples sets with multiple indices Consider the following example for calculating the travel cost for a fictional parcel delivery service between collection sites i and regional transportation hubs j set i miami boston chicago houston sandiego phoenix baltimore j newyork detroit losangeles atlanta set ij i j boston newyork baltimore newyork miami atlanta houston atlanta chicago detroit sandiego losangeles phoenix losangeles table distance i j distance in miles newyork detroit losangeles atlanta miami 1327 1387 2737 665 boston 216 699 3052 1068 chicago 843 275 2095 695 houston 1636 1337 1553 814 sandiego 206 phoenix 2459 1977 398 1810 parameter factor shipcost i j factor 0 009 The set ij denotes the regional transportation hub for each collection site Factor is the cost estimate per unit mile The cost of transporting parcels shipcost from a local collection site i to a regional hub j is then provided by the following assignment shipcost i j ij i j factor distance i j Note that i and j do not appear separately in the assignment for shipcost The assignment can then be simply written as shipcost ij factor distance ij If i or j appear separately in any assignment the above simplification cannot be made For example consider that travelcost depended not only on factor and the distance between collection sites and regional hubs but also the load on the region
278. lio fsum dmean dvar 51 52 Solve portfolio using nlp minimizing variance That is the end of the echo of the input file If errors had been detected the explanatory messages would be found in this section of the listing file All discussion of error messages have been grouped in the section 10 6 page 98 10 3 2 The Symbol Reference Map The maps are extremely useful if one is looking into a model written by someone else or if trying to make some changes in one s own model after spending time away from it The first map is the Symbol Cross Reference which lists the identifiers symbols from the model in alphabetical order identifies them as to type shows the line numbers where the symbols appear and classifies each appearance The symbol reference map can be turned on by entering a line containing onsymxref at the beginning of the program The map that resulted from ALAN is shown Symbol Listing SYMBOL TYPE REFERENCES DMEAN EQU DECLARED 43 DEFINED 47 IMPL ASN REF 50 DVAR EQU DECLARED 44 DEFINED 48 IMPL ASN REF 50 FSUM EQU DECLARED 42 DEFINED 46 IMPL ASN 52 52 52 88 GAMS Output REF 50 HIGHRISK PARAM DECLARED 15 ASSIGNED 34 REF 35 I SET DECLARED 11 DEFINED 11 REF 11 17 24 33 2 34 37 46 2 47 2 48 CONTROL 33 34 46 47 48 J SET DECLARED 11 REF 24 2 48 CONTROL 48 LOWYIELD PARAM DECLARED 14 ASSIGNED 33 REF 35 MEAN PARAM DECLARED 17 DEFINED 19 REF 33 47 PORTFOLIO MODEL DECLARED 50 DEFINED 50 IM
279. llowing example illustrates these ideas file out put out set i master set of sites il Seattle i2 Portland i3 San Francisco i4 Los Angeles i5 j subset of sites i3 id put j ts loop j put j tl i te j The resulting file out put will look like subset of sites i3 San Francisco i4 Los Angeles i5 i5 In this example the symbol text for the identifier of the subset j is written first This is followed with the labels for the subset j and the associated element text found in its domain that is the set i Notice the driving set j is used for the element text specification of the set i Since there was no set element text associated with the i5 element of set i the set element label was displayed again By placing the following before the last line out tf 0 The missing element text is now no longer replaced with the label text The resulting file out put file would now look like subset of sites i3 San Francisco i4 Los Angeles i5 15 10 Global Item Formatting 141 15 9 2 Numeric Items The syntax used for the display of numeric items is generally easier to work with To output a parameter only the identifier along with its index set as appropriate has to be used To output a variable or equation value the identifier is combined with one of the variable and equation suffixes The variable and equation suffixes are 1 level or marginal value lo lower bound m marginal or dual value prior
280. lows The first dollar control option title sets the title of the pages in the listing file to the text that follows the option name In the second line of the example above two options are set onsymxref and onsymlist Both these options turn of the echoing of the symbol reference table and listings to the listing file D 2 List of Dollar Control Options The Dollar Control Options are grouped into five major functional categories affecting 194 Dollar Control Options input comment format input data format output format reference maps program control Table D 1 briefly describes the various options in each of the categories Section D 3 contains a reference list of all dollar control options in alphabetical order with detailed description for each Non default settings are reported before the file summary at the end of a GAMS listing as a reminder for future continued compilations This is only relevant if a restart file has been requested with the GAMS call Options affecting input comment format comment sets the comment character offnestcom turn off nested comments eolcom sets end of line comment character offtext off text mode inlinecom sets in line comment character oneolcom turn on end of line comments maxcol sets right hand margin of input file oninline turn on in line comments mincol sets left hand margin of input file onmargin on margin marking offeolcom turn off end of line comments onnestcom turn on nested comments
281. luated need to be defined and stored in a GDX file like it is done in the GAMS Test Library model pwp1ib01 Define two piecewise polynomial functions Table pwpdata 1st index function number 2nd index segment number 3rd index degree leftBound 0 1 2 Lol 1 2 4 2 7 0 3 1 2 4 5 6 4 3 0 5 2 1 0 0 6 3333 0 2 2 0 3333 1 0370 12 5554 9 3333 2 3 0 6667 9 7792 38 7791 29 Write pwp data to gdx file read by external library gdxout pwp gdx unload pwpdata gdxout On each row of the Table pwpdata we have FuncInd SegInd leftBound Coef0 Coef1 Coef2 FuncInd sets the function index SegInd defines the index of the segment or interval which is decribed here LeftBound gives the lower bound of the segment The upper bound is the lower bound on the next row or the upper bound for the variable if this is the last segment CoefX defines the Xth degree coefficient of the polynomial corresponding to this segment This library is made available by the following directive FuncLibIn lt InternalLibName gt pwpcclib Function Endogenous Description Classifica tion pwpFunc FUNIND x DNLP Piecewise Polynomials Table J 2 Piecewise polynomial functions J 4 Stochastic Library 249 J 4 Stochastic Library The stochastic library provides random deviates probability density functions cumulative density functions and inverse cumulative density functions for certain distributions This library is made available
282. lude which is described in Appendix D 3 2 2 Classification of GAMS Statements Each statement in GAMS is classified into one of two groups gt declaration and definition statements or gt execution statements A declaration statement describes the class of symbol Often initial values are provided in a declaration and then it may be called a definition The specification of symbolic relationships for an equation is a definition The declaration and definition statements are acronym parameter equation declaration set scalar equation definition alias table model variable Execution statements are instructions to carry out actions such as data transformation model solution and report generation The execution statements are option display solve assignment abort loop for while repeat execute Although there is great freedom about the order in which statements can be placed in a GAMS program certain orders are commonly used The two most common arrangements are discussed in the next sub section 3 2 3 Organization of GAMS Programs The two most common ways of organizing GAMS programs are shown in table 3 1 The first style places the data first followed by the model and then the solution statements In this style of organization the sets are placed first Then the data are specified with parameter scalar and table statements Next the model is defined with the variable equation declaration equation definition and model stat
283. lue associated with the linear form of the constraint has no intrinsic meaning At optimality it tells us by at most how much we can benefit from relaxing the linear constraint to y i j 25 q j l 1 0 18 A GAMS Tutorial by Richard E Rosenthal Unfortunately this relaxed constraint has no realistic significance The constraint we are interested in relaxing or tightening is the nonlinear form of the ration constraint For example we would like to know the marginal benefit arising from changing the ratio constraint to y i j a 3 1 26 We can in fact obtain the desired marginals by entering the following transformation on the undesired marginals parameter amr i j appropriate marginal for ratio constraint amr i j ratio m i j 0 01 q 1 j display amr Notice that the assignment statement for amr accesses both m and 1 records from the database The idea behind the transformation is to notice that ydi p q j 1 26 is equivalent to y i j 25 q j 1 0 01 q j 2 11 GAMS Output The default output of a GAMS run is extensive and informative For a complete discussion see Chapter 10 page 85 This tutorial discusses output partially as follows Echo Print Reference Maps Status Reports Error Messages Model Statistics Solution Reports A great deal of unnecessary anxiety has been caused by textbooks and users manuals that give the reader the false impression that flawless use of advanced software sho
284. lution Reports If the solver status and model status are acceptable then you will be interested in examining the results of the optimization The results are first presented in as standard mathematical programming output format with the added feature that rows and columns are grouped and labeled according to names that are appropriate for the specific model just solved In this format there is a line of printout for each row and column giving the lower limit level upper limit and marginal Generic equation block and the column output group the row output by generic variable block Set element names are embedded in the output for easy reading In the transportation example the solver outputs for supply i demand j and x i j are as follows EQU SUPPLY observe supply limit at plant i LOWER LEVEL UPPER MARGINAL seattle INF 350 000 350 000 EPS san diego INF 550 000 600 000 EQU DEMAND satisfy demand at market j LOWER LEVEL UPPER MARGINAL new york 325 000 325 000 INF 0 225 chicago 300 000 300 000 INF 0 153 topeka 275 000 275 000 INF 0 126 VAR X shipment quantities in cases LOWER LEVEL UPPER MARGINAL seattle new york a 50 000 INF seattle chicago k 300 000 INF seattle topeka s INF 0 036 san diego new york E 275 000 INF san diego chicago A INF 0 009 san diego topeka 275 000 INF The single dots in the output represent zeroes The entry EPS which stands for epsilon mean very small but nonze
285. mber of non zero entries in the coefficient matrix numvar number of single variables generated resusd resource units in CPU seconds used to solve model solvestat solver status cf Section 10 5 4 The following example illustrates the use of model suffixes Model transport all transport reslim 60 This sets the solver an upper limit of 60 seconds to attempt to solve the problem to optimality 9 3 The Solve Statement Once the model has been put together through the model statement one can now attempt to solve it using the solve statement On seeing this statement GAMS calls one of the available solvers for the particular model type ts It is important to remember that GAMS itself does not solve your problem but passes the problem definition to one of a number of separate solver programs The next few sub sections discuss the solve statement in detail 80 Model and Solve Statements 9 3 1 The Syntax In general the syntax in GAMS for a model declaration is solve model_name using model_type maximizing minimizing var_name solve model_name maximizing minimizing var_name using model_type Model_name is the name of the model as defined by a model statement Var_name is the name of the objective variable that is being optimized Model_type is one of the model types described before An example of a solve statement in GAMS is shown below Solve transport using lp minimizing cost Solve and using are reserved wor
286. me periods spring sum fall wtr results in the echo 1 set q quarterly time periods spring sum fall wtr CK 160 In this case the GAMS compiler indicates that something is wrong with the set element sum At the bottom of the echo print we see the interpretation of error code 160 20 A GAMS Tutorial by Richard E Rosenthal Error Message 160 UNIQUE ELEMENT EXPECTED The problem is that sum is a reserved word denoting summation so our set element must have a unique name like summer This is a common beginner s error The complete list of reserved words is shown in the next chapter Example 2 Another common error is the omission of a semicolon preceding a direct assignment or equation definition In our transportation example suppose we omit the semicolon prior to the assignment of c i j as follows parameter c i j transport cost in 1000s of dollars per case c i j f d i j 1000 Here is the resulting output 16 parameter c i j transport cost in 1000s of dollars per case 17 c i j f d i j 1000 OK 97 195 96 194 1 Error Message 1 REAL NUMBER EXPECTED 96 BLANK NEEDED BETWEEN IDENTIFIER AND TEXT OR ILLEGAL CHARACTER IN IDENTIFIER OR CHECK FOR MISSING ON PREVIOUS LINE 97 EXPLANATORY TEXT CAN NOT START WITH or OR CHECK FOR MISSING ON PREVIOUS LINE 194 SYMBOL REDEFINED 195 SYMBOL REDEFINED WITH A DIFFERENT TYPE It is not uncommon for one little
287. mit the label which may begin with and or include any legal character Either single or double quotes can be used but the closing quote has to match the opening one A label quoted with double quotes can contain a single quote and vice versa Most experienced users avoid quoted labels because they can be tedious to enter and confusing to read There are a couple of special circumstances If one wants to make a label stand out then one can for instance put asterisks in it and indent it A more subtle example is that GAMS keywords can be used as labels if they are quoted If one needs to use labels like no ne or sum then they will have to be quoted Examples of quoted labels are gt TOTAL MATCH gt 104 INCR 12 FOOT LINE 1 t Labels do not have a value The label 1986 does not have the numerical value 1986 and the label 01 is different from the label 1 The rules for constructing identifiers and labels are shown in table 3 4 Identifiers Unquoted Labels Quoted Labels Number of Characters 63 63 63 Must Begin With A letter A letter or a number Any character Permitted Special Characters None or characters Any but the starting quote Table 3 4 Rules for constructing identifiers and labels 3 4 5 Text Identifiers and simple labels can also be associated with a line of descriptive text This text is more than a comment it is retained by GAMS and is displayed whenever results are written for the identifi
288. mount the DVD using the appropriate command The correct arguments for the mount command vary from machine to machine After mounting the DVD view the README TXT file on it to find the subdirectory containing the GAMS system for your machine 255 10 If you transferred the distribution file via the web check that it has the execute permission set If you are not sure how to do this just type in the command e g chmod 755 linux_x86_32_sfx exe Check if the file gamslice txt exists in the GAMS system directory The license files is nowadays sent via email If no license file is present GAMS will still function in the demonstration mode but can only solve small problems Student and demonstration systems do not include a license file A license file can easily be added later so if you cannot find a license file you can safely proceed without one Run the program gamsinst This will unpack files if necessary It will also prompt you for default solvers to be used for each class of models If possible choose solvers you have licensed since unlicensed solvers will only run in demonstration mode These solver defaults can be changed or overridden by a rerunning gamsinst and resetting the default values b setting a command line default e g gams trnsport l1p bdmlp c an option statement in the GAMS model e g option 1p bdmlp Add the GAMS system directory to your path see ACCESS TO GAMS below To test the installatio
289. myfile scrdir sd text scratch directory This option sets the scratch directory where the intermediate files generated by GAMS and the various solvers The files in the scratch directory are used by GAMS and the various solvers to communicate with each other The scratch directory and all its contents are usually deleted at the end of a GAMS run If not specified the scratch directory will be set to the default one generated by GAMS scriptexit sl gamsexit program or script executed at the end of a GAMS run scriptfrst sf tezt first line to be written to gamsnext file The default is an empty string and the first line is not written scriptnext script gamsnext script mailbox file name scrnam sn tezt scratch name Name stem used to complete the names of intermediate work files This name stem has to have at least one Name will be completed with the scratch directory and the standard scratch name extension solvercntr scntr text solver control file name default name override Name completed with scratch directory and scratch extension solverdict sdict text solver dictionary file name default name override Name completed with scratch directory and scratch extension solverdopt sdopt 0 solver dictionary file name override Values O no override 1 use this option for all solvers solverinst sinst tezt solver instruction file name default name override Name completed with scratch directory and scratch exten
290. n log in as a normal user and run a few models from your home directory but not the GAMS system directory LP trnsport objective value 153 675 NLP chenery objective value 1058 9 MIP bid optimal solution 15210109 512 MINLP procsel optimal solution 1 9231 MCP scarfmcp no objective function MPSGE scarfmge no objective function If you move the GAMS system to another directory remember to rerun gamsinst It is also good practice to rerun gamsinst when you add or change your license file if this has changed the set of licensed solvers ACCESS TO GAMS To run GAMS you must be able to execute the GAMS programs located in the GAMS system directory There are several ways to do this Remember that the GAMS system directory in the examples below may not correspond to the directory where you have installed your GAMS system Li Ds If you are using the C shell csh and its variants you can modify your cshrc file by adding the second of the two lines given below set path set path your previous path setting path usr gams 23 3 new Those of you using the Bourne sh or Korn ksh shells and their variants can modify their profile file by adding the second of the three lines below PATH your previous path setting PATH PATH usr gams 23 3 new export PATH You should log out and log in again after you have made any changes to your path You may prefer to use an alias for the names of the pro
291. n and assignment when you use the list format An element value list by itself is not interpretable by GAMS and will result in an error message 3 The GAMS compiler has an unusual feature called domain checking which verifies that each domain element in the list is in fact a member of the appropriate set For example if you were to spell Seattle correctly in the statement declaring Set i but misspell it as Seatle in a subsequent element value list the GAMS compiler would give you an error message that the element Seatle does not belong to the set i 4 Zero is the default value for all parameters Therefore you only need to include the nonzero entries in the element value list and these can be entered in any order 5 A scalar is regarded as a parameter that has no domain It can be declared and assigned with a Scalar statement containing a degenerate list of only one value as in the following statement from the transportation model Scalar f freight in dollars per case per thousand miles 90 If a parameters domain has two or more dimensions it can still have its values entered by the list format This is very useful for entering arrays that are sparse having few non zeros and super sparse having few distinct non zeros 2 4 Data 11 2 4 2 Data Entry by Tables Optimization practitioners have noticed for some time that many of the input data for a large model are derived from relatively small tables of numbers
292. n c i j values for all i j pairs without constructing do loops The GAMS standard operations and supplied functions are given later Here are some examples of valid as signments In all cases assume the left hand side parameter has already been declared and the right hand side parameters have already been assigned values in previous statements csquared sqr c 12 A GAMS Tutorial by Richard E Rosenthal e m csquared W 1 lamda eoq i sqrt 2 demand i ordcost i holdcost i t i min p i q i r i log s i euclidean i j qrt sqr xi i xi j sqr x2 i x2 3 present j future j exp interest time j The summation and product operators to be introduced later can also be used in direct assignments 2 5 Variables The decision variables or endogenous variables of a GAMS expressed model must be declared with a Variables statement Each variable is given a name a domain if appropriate and optionally text The transportation model contains the following example of a Variables statement Variables x i j shipment quantities in cases Z total transportation costs in thousands of dollars This statement results in the declaration of a shipment variable for each i j pair You will see in Chapter 8 page 71 how GAMS can handle the typical real world situation in which only a subset of the i j pairs is allowable for shipment The z variable is declared without a domain because it
293. n error 95 solvercntr GAMS call parameter 187 solverdict GAMS call parameter 187 solverdopt GAMS call parameter 187 solverinst GAMS call parameter 187 solvermatr GAMS call parameter 187 solversolu GAMS call parameter 187 solverstat GAMS call parameter 188 solvestat model attribute 79 special languages features 155 special ordered sets introduction 155 type 1 example 156 type 1 definition 155 type 2 definition 156 sqexp function 55 sqlog10 function 55 sqr function 55 sqrec function 55 sqrt function 55 stars dollar control option 213 statements 166 static set 114 166 stepsum GAMS call parameter 188 stitle dollar control option 213 stringchk GAMS call parameter 188 studentT distribution 249 subsets 52 subsys GAMS call parameter 188 suffix field width 142 file 141 model 78 numerical display control 143 page control 146 put file 136 system 139 variable 67 75 sum operator 54 superbasic 98 166 variable 98 suppress GAMS call parameter 188 symbol 166 GAMS call parameter 188 symbol reference map assigned 88 control 88 declared 88 defined 88 equ 88 impl asn 88 model 88 param 88 ref 88 set 88 var 88 sysdir GAMS call parameter 189 sysincdir GAMS call parameter 189 sysinclude dollar control option 213 sysout 97 GAMS option 219 tabin GAMS call parameter 189 table 166 a statement 45 condensing 47 conti
294. nd Encrypted Input Files gt gams transport gt gams ti We can decompress the file and compare it to the original file gt echo Decompress ti gms t3 org gt t4 gms gt gams t4 gt diff ti gms t3 org Finally we may want to encrypt the input file in a way to hide the equation definitions To do this we just insert Offlisting and Onlisting around the blocks of GAMS code we want to hide We now can encrypt the modified model file by using a privacy or target license file to lock the new encrypted file to this license key gt echo encrypt trnsport gms t1 gms gt t2 gms gt gams t2 plicense target This new version of tl gms can only be used with the target license file To simulate the target environment we can force the target license to be used instead of the installed one gt gams ti license target dumpopt 19 Note the use of dumopt 19 which is sometimes used for debugging and maintenance writes a clean copy of the input to the file t1 dmp all include files and macros are expanded In the file t1 dmp you will see that the input text between offlisting and Sonlisting is suppressed An attempt to Decompress and decrypt the file will fail as well Once a file has been encrypted it cannot be decrypted any more For example trying to decompress as in the example before will fail gt gams t4 Decompress Source C support 28Dec t1 gms Decompress Target C support 28Dec t3 org Decompress Error S
295. nderstood from the following example for s 3 4 to 0 3 by 1 4 display s The resulting listing file will contain the following lines FERN 2 PARAMETER S 3 400 FERS 2 PARAMETER S 2 000 SESS 2 PARAMETER S 0 600 Notice that the value of s was incremented by 1 4 with each pass of the loop as long as it did not exceed 0 3 The following GAMS code is illegal since one cannot define equations inside a for statement for s 1 to 5 by 1 eq sum i x i g 2 The following GAMS code is illegal since one cannot make declarations inside a for statement for s 1 to 5 by 1 scalar y y 5 Js 154 Programming Flow Control Features 17 Special Language Features 17 1 Introduction This chapter introduces special features in GAMS that do not translate across solvers or are specific to certain model types These features can be extremely useful for relevant models and are among the most widely used 17 2 Special MIP Features Some special features have been added to GAMS to help in simplifying the modeling of MIP problems Two special types of discrete variables are defined and discussed Finally creating priorities for the discrete variables is discussed The solvers use this information when solving the problem 17 2 1 Types of Discrete Variables The following types of discrete variables have been discussed so far in the book binary variables These can take on values of 0 or 1 only integer va
296. ndling is dealt with As with other GAMS statements dollar control exception handling can be used with put statements to control whether particular output items are displayed In the following example the put statement is only displayed if the dollar condition is true If it is not the put statement is ignored put flag gt 10 some output items 15 16 Source of Errors Associated with the Put Statement There are two types of errors that can occur when using the put writing facility syntax errors and put errors The following subsections discuss each of these types of errors 15 16 1 Syntax Errors Syntax errors are caused by the incorrect usage of the GAMS language These errors are the same or are similar to what one finds elsewhere with GAMS such as unmatched parentheses undefined identifiers uncontrolled sets or the incorrect use of a keyword or suffix These errors are detected during program compilation and are always fatal to program execution Errors of this kind are identified in the program listing at the location of the error with a symbol and corresponding error numbers The program listing includes a brief description of the probable cause of the error 15 16 2 Put Errors Put errors are unique to the put writing facility This type of error occurs during program execution and is caused when one or more of the file or page attributes are violated These errors are non fatal and are listed at the end of the program listi
297. ned to GAMS with full machine accuracy The single dots on the list represent zero EPS is the GAMS extended value that means very close to but different from zero It is common to see a marginal value given as EPS since GAMS uses the convention that marginal are zero for basic variables and not zero for others ts EPS is used with non basic variables whose marginal values are very close to or actually zero or in nonlinear problems with superbasic variables whose marginals are zero or very close to it A superbasic variable is one between its bounds at the final point but not in the basis There are brief explanations of technical terms used in this section in the Glossary For models that are not solved to optimality some constraints may additionally be marked with certain flags The list of these flags and their description is given below INFES The row or column is infeasible This mark is made for any entry whose level value is not between the upper and lower bounds NOPT The row or column is non optimal This mark is made for any non basic entries for which the marginal sign is incorrect or superbasic ones for which the marginal value is too large UNBND The row or column that appears to cause the problem to be unbounded 10 5 7 Report Summary The final section of the solution listing is the report summary marked with four asterisks as are all important components of the output It shows the count of rows or columns that
298. new element names and drop text WNRrRo To illustrate the use of the dumpopt option TRNSPORT has been split into two files The first file say trans1 gms contains most of the original file except for the solve statement and looks as follows sets i canning plants seattle san diego j markets new york chicago topeka parameters a i capacity of plant i in cases seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 table d i j distance in thousands of miles new york chicago topeka seattle 2 5 1 7 1 8 san diego 2 5 1 8 1 4 scalar f freight in dollars per case per thousand miles 90 parameter c i j transport cost in thousands of dollars per case c i j f d i j 1000 variables x i j shipment quantities in cases z total transportation costs in thousands of dollars positive variable x equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j cost z e sum i j c i j x i j supply i sum j x i j l a i demand j sum i x i j g b j model transport all C 3 Detailed Description of Command Line Parameters 175 All comments have been removed from TRNSPORT for brevity Running this model and saving the work files through the save parameter leads to the generation of eight work files The second file say trans2 gms generated from
299. next two sub sections provide examples illustrating the use of the linear form of the lag and lead operators in equations for reference and to modify the domain of its definition Section 13 5 3 will illustrate the use of the circular form of the lag and lead operator in equations 124 Sets as Sequences Ordered Sets 13 6 1 Linear Lag and Lead Operators Domain Control Consider the following example adapted from RAMSEY sets t time periods 1990 2000 tfirst t first period tlast t last period tfirst t yes ord t eq 1 tlast t yes ord t eq card t display tfirst tlast variables k t capital stock trillion rupees i t investment trillion rupees per year equations kk t capital balance trillion rupees tc t terminal condition provides for post term growth kk t 1 k t 1 tc tlast g k tlast k t i t i tlast e 1 The declaration of t is included as are a couple of dynamic sets that are used to handle the first and last periods terminal conditions in a clean way The interesting equation is kk the capital balance The set t contains members 1990 to 2000 and so there will be a capital stock constraint for 1991 to 2000 Spelling out the constraint for 1991 k 1991 e k 1990 i 1990 The lead operator on the domain of definition has restricted the number of constraints generated so that there are no references to non existent variables the generated problem will
300. ng SP 107150 smooth linear reciprocal SP means smoothing parameter default setting SP 107 smooth quadratic exponential funtion SP means smoothing parameter default setting SP 150 58 Data Manipulations with Parameters sqlog10 x SP NLP smooth quadratic logarithm base 10 SP means smoothing parameter default setting SP 107150 sqr x NLP returns the square of an expression or term x sqrec x SP NLP smooth quadratic reciprocal SP means smoothing parame ter default setting SP 1071 sqrt x NLP returns the squareroot of x see MathWorld tan x NLP returns the tangent of the argument x where x must be in radians see MathWorld tanh x NLP returns the hyperbolic tangent of x where x must be in radians see MathWorld trunc x DNLP truncation removes decimals from x uniform LOW HIGH none generates a random number between LOW and HIGH with uniform distribution see MathWorld vcPower x Y NLP returns zY for x gt 0 another possible command is x Y Logical functions bool_and x y DNLP boolean and returns 0 if x 0 V y 0 else returns 1 another possible command is x and y bool_eqv x y DNLP boolean equivalence returns 0 if exactly one argument is 0 else returns 1 another possible command is x eqv y bool_imp x y DNLP boolean implication returns 1 if x 0 V y 0 else returns 0 another possible command is x imp y bool_not x DNLP boolean
301. ng They typically occur when a put statement attempts to write outside of a page such as moving the cursor with the character to a location beyond the page width Other typical errors are the inability 15 17 Simple Spreadsheet Database Application 147 to open a specified file the overflow of a page or an inappropriate value being assigned to a suffix For many of these errors an additional set of asterisks will be placed at the location of the error in the output file Since put errors are non fatal and are not overemphasized in the output file their presence is sometimes overlooked Without reviewing the program listing these put errors might go undetected especially in large output files Consequently GAMS has included the following file suffix to help one detect errors errors Allows one to display the number of put errors occurring in a file To illustrate its use the following statement could be inserted at any point of a program to detect the number of errors which have occurred up to its location The choice of output file could be the same file a different file or the console as appropriate putpage error put errors out errors 0 0 In this example it is assumed that the files out put and error put have previously been defined with a file statement With this statement the number of put errors that occur in the file out put are displayed in the file error put Using putpage would allow the immediat
302. nition from some of the generated constraints Consider the following example adapted from CHENERY mb i x i g y i e i m i t i The term is added to the right hand side of the equation only for those elements of i that belong to t i Controlling indexing operations using the dollar condition can also be done as with any assignment Consider the following supply balance sb equation from GTM sb i sum j ij i j x i j l s i 11 6 2 Dollar Control over the Domain of Definition This is analogous to the dollar control on the left of assignments as discussed in Section 11 4 1 and if one thinks of on the left as meaning on the left of the then the analogy is even closer 112 Conditional Expressions Assignments and Equations ts The purpose of the dollar control over the domain of definition of equations is to restrict the number of constraints generated to less than that implied by the domain of the defining sets Consider the following example adapted from FERTS cc m i mpos m i sum p ppos p i b m p z p i 1 util k m i Cc is a capacity constraint defined for all units m and locations i Not all types of units exist at all locations however and the mapping set mpos m i is used to restrict the number of constraints actually generated The control of the summation over p with ppos p i is an additional one and is required because not all processes p are possible a
303. niversity Work space allocated aes 0 04 Mb EXIT OPTIMAL SOLUTION FOUND MAJOR ITNS LIMIT 11 200 10 5 Output Produced by a Solve Statement 97 FUNOBJ FUNCON CALLS 0 71 SUPERBASICS 4 INTERPRETER USAGE 0 02 NORM RG NORM PI 1 801E 09 The line work space allocated 0 04 MB provides the amount of memory used by the solver for the prob lem If the amount of memory the solver estimates that it needs is not available GAMS will return a message saying that not enough memory was allocated GAMS will also return the maximum amount of memory available on the machine The user can direct the solver to use less memory by entering a line containing the statement mymodel workspace xx were mymodel is the name of the model being solved as specified by the model state ment and xx is the amount of memory in Megabytes Note that the solver will attempt to solve the problem with xx MB of memory however it is not guaranteed to succeed since the problem may require more memory More information can be obtained for a successful run by entering a line containing the statement option sysout on in the program above the solve statement 10 5 6 The Solution Listing The next section of the listing file is a row by row then column by column listing of the solutions returned to GAMS by the solver program Each individual equation and variable is listed with four pieces of information This section of the listing file can be turned off by ente
304. nly the extended range arithmetic shown in the table above give non zero values for mapval For example mapval a takes a value of 6 if a is inf All regular numbers result in a mapval of 0 6 4 Summary 63 Special symbol mapval Description inf 6 Plus infinity A very large positive number inf 7 Minus infinity A very large negative number na 5 Not available Used for missing data Any Operation that uses the value NA will produce the result NA undf 4 Undefined The result of an undefined or illegal operation A user cannot directly set a value to UNDF eps 8 Very close to zero but different from zero Table 6 2 Special symbols for extended arithmetic Value Operations a b a b power a b a b 2 2 4 4 1 2 2 undf 4 1 2 2 1 4 28 undf 952 na 2 5 na na na 3 0 1 1 undf inf 2 inf inf inf 2 inf undf undf 0 Table 6 3 Exponentiation and Division The following table shows a selection of results for exponentiation and division for a variety of input parameters t One should avoid creating or using numbers with absolute values larger than 1 0E20 If a number is too large it may be treated by GAMS as undefined UNDF and all values derived from it in a model may be unusable Always use INF or INF explicitly for arbitrarily large numbers When an attempted arithmetic operation is illegal or has undefined results because of the value of arguments division by zero is the normal example an error is reported and
305. none none none none none error code of the most recently used command number of execution errors may either be read or assigned to returns the version number of the current GAMS release for example 23 8 returns the current gams version for example 238 tests if the solve of the problem identified by the calling argu ment HANDLE is done and if so loads the solution into GAMS In particular it returns e 0 if the model associated with HANDLE had not yet finished solution or could not be loaded e 1 if the solution has been loaded deletes the grid computing problem identified by the HANDLE calling argument and returns a numerical indicator of the sta tus of the deletion as follows e 0 if the the model instance has been removed e 1 if the argument HANDLE is not a legal handle e 2 if the model instance is not known to the system e 3 if the deletion of the model instance encountered errors A nonzero return indicates a failure in the deletion and causes an execution error 60 Data Manipulations with Parameters handleStatus HANDLE none tests if the solve of the problem identified by the calling ar gument HANDLE is done and if so loads the solution into a GDX file A numerical indication of the result is returned as follows e 0 if a model associated with HANDLE is not known to the system e 1 the model associaed with HANDLE exists but the solution process is incomplete e 2 the solution process has terminated
306. ns are solved the linear nonlinear and expenditure versions The model statement to define all three is 78 Model and Solve Statements model nortonl linear version cb rc dfl bc obj nortonn nolinear version cb rc dfn bc obj nortone expenditure version cb rc dfe bc obj where cb rc etc are the names of the equations We will describe below how to obtain the solution to each of the three models 9 2 2 Classification of Models Various types of problems can be solved with GAMS The type of the model must be known before it is solved The model types are briefly discussed in this section GAMS checks that the model is in fact the type the user thinks it is and issues explanatory error messages if it discovers a mismatch for instance that a supposedly linear model contains nonlinear terms This is because some problems can be solved in more than one way and the user has to choose which way to go For instance if there are binary or integer variables in the model it can be solved either as a MIP or as a RMIP The problem types and their identifiers which are needed in the a solve statement are listed below LP Linear programming There are no nonlinear terms or discrete binary or integer variables in your model QCP Quadratic constraint programming There are linear and quadratic terms but no general nonlinear term or discrete binary or integer variables in your model NLP Nonlinear programming There
307. nued 46 example 46 long row labels 48 more than two dimensions 47 statement 45 46 syntax 45 tan function 55 tanh function 55 terminated by solver 95 text 166 tformat GAMS call parameter 189 The GAMS Grid Computing Facility 237 timeClose function 59 timeComp function 59 timeElapsed function 59 timeExec function 59 timeStart function 59 title dollar control option 213 INDEX 269 topmargin GAMS call parameter 189 trace GAMS call parameter 189 triangular distribution 249 trunc function 55 type 167 of discrete variables 155 unbounded 94 98 undf extended range value 63 uniform distribution 249 uniform function 55 uniformInt distribution 250 union of sets 117 unique element 167 unittype GAMS call parameter 189 UNIX Installation Notes 254 unknown error 95 use205 dollar control option 213 use225 dollar control option 214 use999 dollar control option 214 userl to user GAMS call parameter 190 using 80 variable binary 66 free 66 integer 66 negative 66 positive 66 statement 65 66 styles for declaration 66 suffix 67 syntax of declaration 65 types 66 variable attributes activity level 1 67 branching priority value prior 67 fixed value fx 67 lower bound lo 67 marginal or dual value m 67 scale value scale 67 upper bound up 67 variable bounds activity level 68 fixing 67 variable type 167 vcPower f
308. of t In this way very large models can be constructed using a small number of variables It is quite unusual for a model to have as many as 50 distinct variables It is still unclear from the declaration whether utility is not domain checked or whether it is a scalar variable i e one without associated sets Later references will be used to settle the issue It is important that variable declarations include explanatory text and that this be as descriptive as possible since the text is used to annotate the solution output Note the use of per instead of in the text above slashes are illegal in all unquoted text 7 2 2 Variable Types There are five basic types of variables that may be used in variable statements These are shown in table 7 1 Keyword Default Default Description Lower Upper Bound Bound free default inf inf No bounds on variable Both bounds can be changed from the default values by the user positive 0 inf No negative values are allowed for variable The user can change the upper bound from the default value negative inf O No positive values are allowed for variables The user can change the lower bound from the default value binary 0 1 Discrete variable that can only take values of 0 or 1 integer 0 100 Discrete variable that can only take integer values between the bounds The user can change bounds from the default value Table 7 1 Variable types and default bounds The default t
309. of the first label on that line General Algebraic Modeling System Unique Element Listing Unique Elements in Entry Order 1 1987 1988 1989 1990 1991 1983 7 1984 1985 1986 Unique Elements in Sorted Order 1 1983 1984 1985 1986 1987 1988 7 1989 1990 1991 A set can always be made ordered by moving its declaration closer to the beginning of the program With these restrictions in mind we move on the operations that are used in dealing with sets as sequences 13 3 Ord and Card In Chapter 4 it was explained that labels do not have a numerical value The examples used were that the label 1986 does not have a numerical value of 1986 and the label 01 is different from the label 1 This section introduces two operators ord and card that return integer values when applied to sets While the integer values returned do not represent the numerical value of the label they can be used for the same purpose The next two subsections describe each of these two functions in turn 13 3 1 The Ord Operator Ord returns the relative position of a member in a set amp Ord can be used only with a one dimensional static ordered set Some examples show the usage set t time periods 1985 1995 parameter val t val t ord t As a result of the statements above the value of val 1985 will be 1 va1 1986 will be 2 and so on A common use of ord is in setting up vectors that represent quantities growing in some anal
310. off the double option Consider the following example set i 1 2 scalar a 1 double set j 10 15 scalar b 2 single set k 5 10 scalar c 3 D 3 Detailed Description of Dollar Control Options 213 The resulting listing file looks as follows 1 set i 1 2 2 scalar a 1 4 set j 10 15 5 scalar b 2 7 set k 5 10 8 scalar c 3 Note that lines between the double and single options are listed double spaced while the lines after the single option revert back to being listed singly spaced stars x This option is used to redefine the marker in the GAMS listing file By default important lines like those denote errors and the solver model status are prefixed with Consider the following example stars garbage The resulting listing file looks as follows 2 garbage HHHH 140 36 299 UNEXPECTED END OF FILE 1 Error Messages 36 or or or operator expected rest of statement ignored 140 Unknown symbol 299 Unexpected end of file stitle This option sets the subtitle in the page header of the listing file to text which follows immediately the keyword stitle The next output line will appear on a new page in the listing file Consider the following example stitle data tables for input output sysinclude Equivalent to batinclude sysinclude file argl arg2 However if an incomplete path is
311. ollowed immediately by an integer value corresponding to the order of parameters on the list where 1 refers to the first argument 42 to the second argument and so on If the integer value is specified that does not correspond to a passed parameter then the parameter flag is substituted with a null string The parameter flag 0 is a special case that will substitute a fully expanded file name specification of the current batch included file The flag is the current symbol see dollar Parameters are substituted independent of context and the entire line is processed before it is passed to the compiler The exception to this is that parameter flags appearing in comments are not substituted t GAMS requires that processing the substitutions must result in a line of less than or equal to the maximum input line length currently 255 characters ts The case of the passed parameters is preserved for use in string comparisons Consider the following slice of code batinclude filel inc abcd bbbb cccc dddd In this case file1 inc is included with abcd as the first parameter bbbb as the second parameter and cccc dddd as the third parameter Consider the following slice of code parameter a b c a 1l b 0O0 c 2 batinclude inc2 inc ba display b batinclude inc2 inc b c display b batinclude inc2 inc b at5 display b where inc2 inc contains the following line 1 sqr 2 2 the listing file that results is as follow
312. olve statement can trigger additional errors called MATRIX ERRORS which report on problems encountered during transformation of the model into a format required by the solver Problems are most often caused by illegal or inconsistent bounds or an extended range value being used as a matrix coefficient The example below shows the general format of these errors variable x equation eql eqi x 1 10 x lo 10 x up 5 model wrong eq1 solve wrong using lp maximizing x oono PUNB x MATRIX ERROR LOWER BOUNDS gt UPPER BOUND X LO L UP 10 0 5 x x SOLVE from line 8 ABORTED EXECERROR 1 44 USER ERROR S ENCOUNTERED Some solve statement require the evaluation of nonlinear functions and the computation of derivatives Since these calculations are not carried out by GAMS but by other subsystems not under its direct control errors associated with these calculations are reported in the solution report Unless reset with the domlim option the subsystems will interrupt the solution process if arithmetic exceptions are encountered They are then reported on the listing as shown in the following example 1 variable x y 2 equation one 3 4 one y e sqrt 10 x 5 x l 10 6 x lo 0 7 8 model divide all 9 solve divide maximizing y using nlp SOLVE SUMMARY MODEL DIVIDE OBJECTIVE Y TYPE NLP DIRECTION MAXIMIZE SOLVER MINOS5 FROM LINE 9 SOLVER STATUS 5 EVALUATION ERROR LIMIT xxx MODEL STATUS 7 I
313. olver This is done with a solve statement which in our example is written as solve transport using lp minimizing z The format of the solve statement is as follows 1 The key word solve 2 The name of the model to be solved 3 The key word using 4 An available solution procedure The complete list is lp for linear programming qcp for quadratic constraint programming nlp for nonlinear programming dnlp for nonlinear programming with discontinuous derivatives mip for mixed integer programming rmip for relaxed mixed integer programming miqcp for mixed integer quadratic constraint programming 16 A GAMS Tutorial by Richard E Rosenthal minlp for mixed integer nonlinear programming rmigcp for relaxed mixed integer quadratic constraint programming rminlp for relaxed mixed integer nonlinear programming mcp for mixed complementarity problems mpec for mathematical programs with equilibrium constraints cns for constrained nonlinear systems 5 The keyword minimizing or maximizing 6 The name of the variable to be optimized 2 9 Display Statements The solve statement will cause several things to happen when executed The specific instance of interest of the model will be generated the appropriate data structures for inputting this problem to the solver will be created the solver will be invoked and the output from the solver will be printed to a file To get the optimal values of the primal and or dual variable
314. on log B x y log10 x NLP returns the common logarithm logarithm base 10 see Math World log2 x NLP returns the binary logarithm logarithm base 2 see MathWorld max x1 x2 x3 DNLP returns the maximum of a set of expressions or terms the number of arguments is not limited min x1 x2 x3 DNLP returns the minimum of a set of expressions or terms the num ber of arguments is not limited mod x y DNLP returns the remainder of x divided by y ncpCM x y Z NLP function that computes a Chen Mangasarian smoothing equal ing x Z In l e 7 6 3 Expressions 57 ncpF x y Z ncpVUpow r s MU ncpVUsin r s MU normal MEAN STDDEV pi poly x A0 A1 A2 A3 A4 power x Y randBinomial N P randLinear LOW SLOPE HIGH randTriangle LOW MID HIGH round x DECPL rPower x y sigmoid x sign x signPower x Y sin x sinh x slexp x SP sllog10 x SP slrec x SP sqexp x SP NLP NLP NLP none any NLP NLP none none none function that computes a Fisher smoothing equaling J a2 y2 2 Z ax y Z gt 0 default setting Z 0 NCP Veelken Ulbrich aoe min i ie ift gt y ncp pow ps E ty ty2 ss G tar se otherwise where t r s default setting MU 0 NCP Veelken Ulbrich smoothed min rt lil if ltl gt u ncpV Usin r s 2 sin 82 y i 21217 otherwise 2 where t r s default setting MU 0
315. on defx defx sum i x i 1 1 The variable x can be made binary without any change in meaning and the solution provided by the solver will be indistinguishable from the SOS1 case The use of special ordered sets may not always improve the performance of the branch and bound algorithm If there is no natural order the use of binary variables may be a better choice A good example of this is the assignment problem t Not all MIP solvers allow SOS1 variables Furthermore among the solvers that allow their use the precise definition can vary from solver to solver Any model that contains these variables may not be transferable among solvers Please verify how the solver you are interested in handles SOS1 variables by checking the relevant section of the Solver Manual 17 2 3 Special Order Sets of Type 2 SOS2 At most two variables within a SOS2 set can have non zero values The two non zero values have to be adjacent The most common use of SOS2 sets is to model piece wise linear approximations to nonlinear functions t The default bounds for SOS2 variables are 0 to 00 As with any other variable the user may set these bounds to whatever is required Special ordered sets of type 2 are defined as follows 17 2 Special MIP Features 157 sos2 Variable s2 i t2 k j w2 i j k The members of the innermost the right most index belongs to the same set For example in the sets defined above s2 represents one special ordered
316. on input file The restart does not alter work files They can be used repeatedly to continue a particular run many times possibly with many different continuation input files The most common mistake that occurs in using the save and restart feature is running GAMS on the same file twice so all the data and equation definitions get repeated which causes compilation errors during restart The following calls will cause errors F 3 Ways in which a Work File is Useful 223 gams trnsport s trans gams trnsport r trans In general definitions of data constructs should not be repeated either in the same file or across files used in the Save and Restart operation GAMS works as if the two files are actually concatenated In order to avoid any syntax problems one needs to understand the GAMS syntax regarding data entry By default GAMS requires that each data item be entered only once Once the elements that form the set have been defined the set cannot be redefined through the data statment For example the following set of statements are all invalid set i seattle san diego set i seattle san diego portland Similar rules apply to Scalar Parameter and Table declarations One can only use assignment statments to change values of scalars parameters and tables once they have been specified by the data statement For example parameter a i seattle 20 san diego 50 a seattle a san diego 10 100 One can ho
317. oop statement is provided for cases when parallel assignments are not sufficient This happens most often when there is no analytic relationship between for example the values to be assigned to a parameter It is of course also useful to have a looping statement for general programming for example the production of reports with the put statement 16 2 1 The Syntax The syntax of the loop statement is loop controlling_domain condition statement 4 statement 3 If the controlling domain consists of more than one set then parentheses are required around it The loop statement causes GAMS to execute the statements within the scope of the loop for each member of the driving set s in turn The order of evaluation is the entry order of the labels A loop is thus another more general type of indexed operation The loop set may be dollar controlled and does not need to be static or nested Loops may be controlled by more than one set t One cannot make declarations or define equations inside a loop statement t It is illegal to modify any controlling set inside the body of the loop 150 Programming Flow Control Features 16 2 2 Examples Consider a hypothetical case when a growth rate is empirical set t 1985 1990 parameter pop t 1985 3456 growth t 1985 25 3 1986 27 3 1987 26 2 1988 27 1 1989 26 6 1990 26 6 The loop statement is then used to calculate the cumulative sums loop t pop t 1 pop t
318. options send the message text to the file file Both the text and the file name can be quoted or unquoted The file name is expanded using the working directory The echo statement tries to minimize file operations by keeping the file open in anticipation of another echo to be appended to the same file The file will be closed at the end of the compilation or when a call or any kind of include statement is encountered The redirection symbols gt and gt gt have the usual meaning of starting at the beginning or appending to an existing file Consider the following example echo gt echo echo The message written goes from the first non blank gt gt echo echo to the first gt or gt gt symbol unless the text is gt gt echo echo is quoted The Listing File is gams input The gt gt echo echo file name echo will be completed with gt gt echo echo gams workdir gt gt echo echo gt gt echo The contents of the resulting file echo are as follows The message written goes from the first non blank to the first gt or gt gt symbol unless the text is is quoted The Listing File is C PROGRAM FILES GAMSIDE CC GMS The file name echo will be completed with C PROGRAM FILES GAMSIDE eject Advances the output to the next page Consider the following example eject Set i j Parameter data i j eject This will force the statements between the two eject calls to be reported on a separated page in
319. orcework fw 0 force workfile translation Most of the work files generated by GAMS using the save option are in binary format The information inside these files will change from version to version Every attempt is made to be backward compatible and ensure that all new GAMS systems are able to read save files generated by older GAMS systems However at certain versions we are forced to concede default incompatibility regarding save files not source files in order to protect efficiency The forcework option is used to force newer GAMS systems into translating and reading save files generated by older systems Values O no translation 1 try translation fsave fsave 0 force workfile to be written Values O workfile only written if save 1 workfile written if no save The option value 1 is mainly used by solvers that can be interrupted from the terminal g205 g205 0 GAMS version 2 05 backward compatability This option sets the level of the GAMS syntax This is mainly used for backward compatibility New key words have been introduced in the GAMS language since Release 2 05 Models developed earlier that use identifiers C 3 Detailed Description of Command Line Parameters 179 that have since become keywords will cause errors when run with the latest version of GAMS This option will allow one to run such models Values O latest syntax 1 syntax from Release 2 05 only 2 syntax from the first version of Release 2 25 only For exam
320. ory If no logfile is given but the value of lo is 2 then the file name will be input file name with the extension log To illustrate the use of the logfile option run TRNSPORT with the options lo 2 and 1f myfile log The resulting log file is redirected to myfile log and looks as follows Starting compilation TRNSPORT GMS 0 TRNSPORT GMS 33 TRNSPORT GMS 66 TRNSPORT GMS 66 Starting execution TRNSPORT GMS 43 Generating model TRANSPORT TRNSPORT GMS 56 TRNSPORT GMS 58 TRNSPORT GMS 60 TRNSPORT GMS 64 6 rows 7 columns and 19 non zroes Executing BDMLP GAMS BDMLP 1 1 Aug 1 1994 001 049 030 033 030 386 486 DOS W READING DATA Work space allocated 0 03 Mb Iter Sinf Objective Status Num Freq 1 2 25000000E 02 infeas 1 1 4 1 53675000E 02 nopt 0 SOLVER STATUS 1 NORMAL COMPLETION MODEL STATUS 1 OPTIMAL OBJECTIVE VALUE 153 67500 Restarting execution TRNSPORT GMS 64 Reading solution for model TRANSPORT TRNSPORT GMS 66 All done logline ll 2 amount of line tracing to log file This option is used to limit the number of line tracing sent out to the log file during the compilation phase of a GAMS run Values of 0 and 1 are special Setting 11 0 will cause the line tracing to be suppressed for all phases of the GAMS processing Values O all line tracing suppressed 1 limited line tracing n full line tracing with increm
321. ost the right most index belongs to the same set For example in the sets defined above s1 represents one special ordered set of type 1 with i elements t1 defines k sets of j elements each and wi defines i j sets with k elements each t The default bounds for SOS1 variables are 0 to 00 As with any other variable the user may set these bounds to whatever is required ts The user can in addition explicitly provide whatever convexity row that the problem may need through an equation that requires the members of the SOS set to be less than a certain value Any such convexity row would implicitly define bounds on each of the variables Consider the following example sosi Variable s1 i Equation defsoss1 defsoss1 sum i si i 1 3 5 The equation defsoss1 implicitly defines the non zero value that one of the elements of the SOS1 variable s1 can take A special case of SOS1 variables is when exactly one of the elements of the set have to be non zero In this case the defsoss1 equation will be defsoss1 sum i s1 i e 3 5 A common use of the use of this set is for the case where the non zero value is 1 In such cases the SOS1 variable behaves like a binary variable It is only treated differently by the solver at the level of the branch and bound algorithm For example consider the following example to model the case where at most one out of n options can be selected This is expressed as sosi variable x i equati
322. ot demonstrate the use of set aliases until later Just remember they are used for cases when a set has to be referred to by more than one name 4 4 Subsets and Domain Checking It is often necessary to define sets whose members must all be members of some larger set The syntax is set set_ident1 set_ident2 where set_ident1 is a subset of the larger set set_ident2 For instance we may wish to define the sectors in an economic model following the style in CHENERY 4 5 Multi dimensional Sets 39 set i all sectors light ind foodtagr heavy ind services t i traded sectors light ind foodtagr heavy ind nt non traded sectors services Some types of economic activity for example exporting and importing may be logically restricted to a subset of all sectors In order to model the trade balance for example we need to know which sectors are traded and one obvious way is to list them explicitly as in the definition of the set t above The specification t i means that each member of the set t must also be a member of the set i GAMS will enforce this relationship which is called domain checking Obviously the order of declaration is important the membership of i must be known before t is declared for checking to be done There will be much more on this topic in succeeding chapters For now it is important to note that domain checking will find any spelling errors that might be made in establishing the members of
323. out nj 2 out lw 10 out cc 11 loop v put v t1 21 loop c out nd suffix c nd out nz suffix c nz out nr suffix c nr out nw suffix c nw put c tl loop v put ord v 21 10 value v For readability the numeric values have purposely been made left justified using the nj suffix since the numeric field width is changed as the model goes through the suffix combinations The following is the resulting file out put which shows the value suffix combinations 144 The Put Writing Facility valuel value2 value3 comb1 123 457 0 123 1 2345670E 4 comb2 123 457 0 123 1 2345670E 4 comb3 123 457 0 123 0 000 comb4 1 23457E 2 0 12345670 0 00012346 comb5 123 456700 0 123457 0 000123 Notice that in comb1 the display of values switch to exponential notation when a value becomes smaller than the number of decimal places allowed This is triggered by the suffix nr being set to zero Of particular interest is value3 for comb2 and comb3 Value3 is greater than the zero tolerance level in nz but smaller than the number of decimals allowed by nd In comb2 since nr is set to zero the value is displayed in exponential format In comb3 nr is set to 1 so this small value is rounded to 0 In comb5 valuel is rounded to an integer because of nd being set to 0 15 13 Cursor Control Having described the display of various output items using the put statement this section describes features available to position these items in
324. ows A Quadratic Programming Model for Portfolio Analysis ALAN SEQ 124a Column Listing SOLVE PORTFOLIO USING NLP FROM LINE 48 gt fraction of portfolio invested in asset 1 X hardware LO L UP 0 0 INF 1 FSUM 8 DMEAN 0 DVAR X software LO L UP 0 0 INF 1 FSUM 9 DMEAN 0 DVAR X show biz LO L UP 0 0 INF 1 FSUM 12 DMEAN 0 DVAR REMAINING ENTRY SKIPPED VARIANCE variance of portfolio VARIANCE LO L UP INF 0 INF 1 DVAR ts The order in which the variables appear is the order in which they were declared 10 5 3 The Model Statistics The final information generated while a model is being prepared for solution is the statistics block shown below Its most obvious use is to provide details on the size and nonlinearity of the model 10 5 Output Produced by a Solve Statement 93 Model Statistics SOLVE PORTFOLIO USING NLP FROM LINE 48 MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 3 BLOCKS OF VARIABLES 2 SINGLE VARIABLES 5 NON ZERO ELEMENTS 12 NON LINEAR N Z 3 DERIVATIVE POOL 10 CONSTANT POOL 10 CODE LENGTH 87 GENERATION TIME 0 020 SECONDS 0 1 Mb WAT 50 094 The BLOCK counts refer to GAMS equations and variables the SINGLE counts to individual rows and columns in the problem generated The NON ZERO ELEMENTS entry refers to the number of non zero coefficients in the problem matrix There are four entries that provide additional information
325. page 98 Comprehensive error detection and well designed error messages are a big help in getting models implemented quickly and correctly 2 11 3 Reference Maps The next section of output which is the last if errors have been detected is a pair of reference maps that contain summaries and analyses of the input file for the purposes of debugging and documentation The first reference map is a cross reference map such as one finds in most modern compilers It is an alphabetical cross referenced list of all the entities sets parameters variables and equations of the model The list shows the type of each entity and a coded reference for each appearance of the entity in the input The cross reference map for our transportation example is as follows we do not display all tables SYMBOL TYPE REFERENCES A PARAM DECLARED 9 DEFINED 10 REF 42 B PARAM DECLARED 13 DEFINED 14 REF 44 03 PARAM DECLARED 25 ASSIGNED 27 REF 40 COST EQU DECLARED 36 DEFINED 40 IMPL ASN 48 REF 46 D PARAM DECLARED 18 DEFINED 18 REF 27 DEMAND EQU DECLARED 38 DEFINED 44 IMPL ASN 48 REF 46 F PARAM DECLARED 23 DEFINED 23 REF 27 SET DECLARED 4 DEFINED 4 REF 9 18 25 27 30 37 2 40 2 42 44 CONTROL 27 40 42 44 J SET DECLARED 5 DEFINED 5 REF 13 18 25 27 30 38 2 40 42 2 44 CONTROL 27 40 42 44 SUPPLY EQU DECLARED 37 DEFINED 42 IMPL ASN 48 REF 46 TRANSPORT MODEL DECLARED 46 DEFINED 46 IMPL ASN 48 REF 48 X VAR DECLARED 30 IMPL ASN 48 REF 33 40 42 44 2 50 22 A GAMS T
326. pe If possible choose solvers you have licensed since unlicensed solvers will only run in demonstration mode The solver defaults can be changed by a rerunning gamsinst and resetting the default values b setting a command line default e g gams trnsport l1p bdmlp c by an option statement in the GAMS model e g option 1p bdmlp If you have to support different operating systems from the same installation please use gamsinst sys all A complete log of the installation is stored in gamsinst log The system wide solver defaults are shared by the command line and the GAMS IDE so you can also choose to set these defaults using the GAMS IDE 2 Add the GAMS directory to your path To avoid having to type in an absolute path name each time you run GAMS we recommend adding the GAMS directory to your PATH when using the console mode not the GAMS IDE version of GAMS In case more than one GAMS system is installed on the machine separate paths have to be set before invoking each version Under Windows XP Vista the following procedure must be applied to add the GAMS directory to your path e Open the System Properties under the Control Panel e On the Advanced tab click on the Environment Variables button and select the existing variable Path Click Edit e In the Value Box add the GAMS directory to the path as the following example illustrates c your current path setting C gams and click OK Unix INSTALLATION To install GA
327. pecial Language Features 17 2 6 Setting Priorities for Branching The user can specify an order for picking variables to branch on during a branch and bound search for MIP models through the use of priorities Without priorities the MIP algorithm will determine which variable is the most suitable to branch on The GAMS statement to use priorities for branching during the branch and bound search is mymodel prioropt 1 where mymodel is the name of the model specified in the model statement The default value is 0 in which case priorities will not be used Using the prior suffix sets the priorities of the individual variables Note that there is one prior value for each individual component of a multidimensional variable Priorities can be set to any real value The default value is 1 As a general rule of thumb the most important variables should be given the highest priority The following example illustrates its use w nono N z prior i small z prior i medium z prior i large In the above example z i large variables are branched on before z i small variables t The lower the value given to the prior suffix the higher the priority for branching t All members of any SOS1 or SOS2 set should be given the same priority value since it is the set itself which is branched upon rather than the individual members of the set 17 3 Model Scaling The Scale Option The rules for good
328. perty execerror can be used to get and set the number of execution errors 1 5 2 Grid Model Attributes mymodel solvelink specifies the solver linking conventions 0 automatic save restart wait for completion the default start the solution via a shell and wait start the solution via spawn and wait start the solution and continue start the solution and wait same submission process as 3 or WN start the solution via shared library and wait mymodel handle specifies the current instance handle This is used to identify a specific model instance and to provide additional information needed for the process signal management mymodel number specifies the current instance number Any time a solve is attempted for mymodel the instance number is incremented by one and the handle is update accordingly The instance number can be reset by the user which then resyncs the handle 1 6 Architecture and Customization 243 1 5 3 Grid Solution Retrieval Execute loadhandle mymodel This will update the GAMS data base with the status and solution for the current instance of mymodel The underlying mechanism is a gdx file and operates otherwise like the execute_loadpoint procedure Additional arguments can be used to retrieve information from the gdx solution file 1 5 4 Grid Directory The instantiated generated models and their corresponding solution are kept in unique directories reachable from your submitting system Each GAMS job c
329. ple the word if is a key word in GAMS introduced with the first version of Release 2 25 Setting the g205 1 option allows if to be used as an identifier since it was not a keyword in Release 2 05 As another example the word for is a key word in GAMS introduced with the later versions of Release 2 25 Setting the g205 2 option allows for to be used as an identifier since it was not a keyword in the first version of Release 2 25 t Using values of 1 or 2 for g205 will not permit the use of enhancements to the language introduced in the later versions ide ide 0 Integrated Development Environment flag Values n tells GAMS about the environment 1 runs under GAMS IDE input i input file name Completing the input file name with the current directory composes the final name If such a file does not exist and the extension was not specified the standard input extension is attached and a second attempt is made to open an input file inputdir idir input search path In general GAMS searches for input and include files in the current working directory only This option allows the user to specify additional directories for GAMS to search for the input files A maximum of 18 separate directories can be included with the directories separated by Operating System specific symbols On a PC the separator is a semicolon character and under Unix it is the colon character Note that libinclude and sysinclude files are handled differently and th
330. ply limit at plant i 38 demand j satisfy demand at market j 39 40 cost z e sum i j c i j x i j 41 42 supply i sum j x i j 1 a i 43 44 demand j sum i x i j g b j 45 46 Model transport all 47 48 Solve transport using lp minimizing z 49 50 Display x l x m 51 The reason this echo print starts with line number 3 rather than line number 1 is because the input file contains two dollar print control statements This type of instruction controls the output printing but since it has nothing to do with defining the optimization model it is omitted from the echo The dollar print controls must start in column 1 title a transportation model offuppper The title statement causes the subsequent text to be printed at the top of each page of output The offupper statement is needed for the echo to contain mixed upper and lowercase Other available instructions are given in Appendix D page 193 2 11 2 Error Messages When the GAMS compiler encounters an error in the input file it inserts a coded error message inside the echo print on the line immediately following the scene of the offense These messages always start with and contain a directly below the point at which the compiler thinks the error occurred The is followed by a numerical error code which is explained after the echo print Several examples follow Example 1 Entering the statement set q quarterly ti
331. polation This library has been repackaged to work with the GAMS Function Library Facility As it can be seen in the GAMS Test Library model fit1ib01 the function data needs to be stored in a GDX file fit gdx containing a three dimensional parameter fitdata The first argument of that parameter contains the function index the second argument is the index of the supporting point and the last one needs to be one of w weight x x value y y value or z z value Function Endogenous Description Classifica tion fitFunc FUNIND x y DNLP Evalute Spline fitParam FUNIND PARAM VALUE none Read or set parameters Table J 1 Fitpack functions Paul Dierckx Curve and Surface Fitting with Splines Oxford University Press 1993 http www netlib org dierckx 248 Extrinsic Functions The function FitParam can be used to change certain parameters used for the evaluation e 1 Smoothing factor S e 2 Degree of spline in direction x Kx Degree of spline in direction y Ky Lower bound of function in direction x LOx Lower bound of function in direction y LOy Upper bound of function in direction x UPx UPy Upper bound of function in direction y UPy e I Dn BR Y This library is made available by the following directive FuncLibIn lt InternalLibName gt fitfclib J 3 Piecewise Polynomial Library This library can be used to evaluate piecewise polynomial functions The functions which should be eva
332. port writing providing output to a file for use by another computer program or simply the display of intermediate calculations But the surface of the put writing facility has just barely been scratched In the sections that follow the many features and structure of the put writing facility are described in more detail along with examples 15 4 Output Files As noted earlier the put statement allows the user to write to external files This section describes the various features related to the use of external files 15 4 1 Defining Files The complete syntax for defining files is file fname text external file name where file is the keyword used to define files Fname is the internal file name and is used inside the GAMS model to refer to an external file External files are the actual files that output is written to During file declaration the external file name and explanatory text are optional When the external file name is omitted GAMS will provide a system specific default external file name often fname put Note that multiple files can be defined using a single file statement Consider the following example file classi class2 this defines a specific external file report txt con this defines access to the console screen for PC systems The first output file is recognized in the model by the name class1 and corresponds to the default file class1 put for a PC system The second output file is recognized in the model by th
333. ppended to and not rewritten Values O reset listing file 1 append to listing file botmargin bm 0 bottom margin This option controls the width of the bottom margin of the text in the listing file If bm is greater than 0 blank lines added at the end of a page This option is used only with pagecontr 0 padding C 3 Detailed Description of Command Line Parameters 173 case case 0 output case option Values O write listing file in mixed case 1 write listing file in upper case only cerr cerr 0 compile time error limit The compilation will be aborted after n errors have occurred By default there is no error limit and GAMS compiles the entire input file and collects all the compilation errors that occur If the file is too long and the compilation process is time consuming cerr could be used to set to a low value while debugging the input file Values O no error limit n stop after n errors charset charset 0 extended character set Values O use limited GAMS characters set 1 accept any charcater in comments and text items foreign langage characters cns cns text default CNS solver codex cx 0 overrides default size of execution code length codex Values O use system defaults 1 use size 1 2 use size 2 3 use size 3 4 use largest size possible ctrlm ctrlm 0 control M indicator The Control M character appears as the end of line character when files have been incorrectly transferred from PC to Unix plat
334. ptions 197 id1 id2 are the identifiers whose data is being reset Note that this is carried out during compile time and not when the GAMS program executes Not all data types can be cleared only set parameter equation and variable types can be reset Consider the following example set i 1 20 scalar a 2 clear ia display i a The clear option resets i and a to their default values The result of the display statement in the listing file shows that i is now an empty set and a takes a value of 0 3 SET I EMPTY 3 PARAMETER A 0 000 t The two pass processing of a GAMS file can lead to seemingly unexpected results Both the dollar control options and the data initialization is done in the first pass and assignments in the second irrespective of their relative locations This is an issue particularly with clear since data can be both initialized and assigned Consider the following example scalar a 12 a 5 clear a display a The scalar data initialization statement is processed during compilation and the assignment statement a 5 during execution In the order that it is processed the example above is read by GAMS as compilation step scalar a 12 clear a execution step a 5 display a The example results in a taking a value of 5 The display statement in the resulting listing file is as follows 4 PARAMETER A 5 000 comment This option changes the start of lin
335. quence number and target is the target file name If the target file name is not provided the default is modelname gms For example the TRNSPORT model could be copied in any of the following ways 170 The GAMS Model Library gt gamslib trnsport target file trnsport gms gt gamslib 1 trnsport gms gt gamslib trnsport myname myname gt gamslib 1 myname myname The full and annotated list of the models of the GAMS Model Library is available at http www gams com modlib modlib htm C The GAMS Call The entire GAMS system appears to the user as a single call that reads the input file and produces an output file Several options are available at this level to define the overall layout of the output page and when to save and restore the entire environment Although details will vary with the type of computer and operating system used the general operating principles are the same on all machines C 1 The Generic no frills GAMS Call The simplest way to start GAMS is to enter the command gt gams myfile from the system prompt and GAMS will compile and execute the GAMS statements in the file myfile If a file with this name cannot be found GAMS will look for a file with the extended name myfile gms The output will be written by default on the file myfile 1st on PC and Unix systems and myfile lis on OpenVMS systems For example the following statement compiles and executes the example problem TRNSPORT from the GAMS model l
336. r to use it again Simply make the file current and use put statements as would be done normally Of course the existing file will either be overwritten or appended to depending on the value of the append file suffix t One application where this is useful is to write the solver option file from within the GAMS model Option file statements can be written using put and the file closed with a putclose prior to the solve statement This makes the option file available for use by the solver The following example shows the creation and closing of an option file for the MINOS solver file opt Minos option file minos opt put opt put Iteration limit 500 Feasibility tolerance 1 0E 7 gt putclose opt This program segment would be placed inside the GAMS model prior to the solve statement 15 4 4 Appending to a File The put writing facility has the ability to append to or overwrite an existing file The file suffix ap determines which operation occurs The default suffix value 0 overwrites the existing file while the value 1 causes appending to the file Let s consider our report txt file to be an existing file Using the following statement appends output items to it class2 ap 1 Any items put into report txt will from that point on be added to the end of the existing file contents If the file had not existed the file would be created 15 5 Page Format The pages within files can also be structured using file suffi
337. ral name for the information produced by a computer program output file A disk file containing output A GAMS task produces one such file that can be inspected parameter A constant or group of constants that may be a scalar a vector or a matrix of two or more dimensions Of the six data types in GAMS problem type A model class that is dependent on functional form and specification Examples are linear nonlinear and mixed integer programs program A GAMS input file that provides a representation of the model or models relational operator This term may be used in two ways First in an equation definition it describes the type of relationships the equation specifies for example equality as specified with the e symbol Second in a logical expression the symbols eq ne 1t and so on are also called relational operators and are used to specify a required relationship between two values right hand side The value of constant term in a constraint scalar One of the forms of parameter inputs Used for single elements set A collection of elements labels The set statement is used to declare and define a set simplex method The standard algorithm used to solve linear programming problems slack The amount by which an inequality constraint is not binding slack variable An artificial column introduced by a solver into a linear programming problem Makes the implementation of simplex method much easier smooth A classification of a func
338. rates pc suffix value 5 The program segment could be placed at the end of the original MEXSS model file out put out out pc 5 put capacity metric tons loop i put i tl loop m put m te m loop i put k m i The first line of this program segment creates the file out put as the delimited file Notice that in the remainder of this program field widths justifications and horizontal cursor relocations are completely avoided All text items are quoted The following is the resulting output file 148 The Put Writing Facility CAPACITY tons AHMSA FUNDIDORA SICARTSA HYLSA HYLSAP BLAST FURNACES 3 25 1 40 1 10 0 00 0 00 OPEN HEARTH FURNACES 1 50 0 85 0 00 0 00 0 00 BASIC OXYGEN CONVERTERS 2 07 1 50 1 30 0 00 0 00 DIRECT REDUCTION UNITS 0 00 0 00 0 00 0 98 1 00 ELECTRIC ARC FURNACES 0 00 0 00 0 00 1 13 0 56 Notice that each item is delimited with a comma and that textual output is quoted 16 Programming Flow Control Features 16 1 Introduction The previous chapters have focused on the ability of GAMS to describe models This chapter will describe the various programming features available in GAMS to help the advanced user The various programming flow control features discussed in this chapter are Loop Statement If Else Statement For Statement While Statement Each of these statements will be discussed in detail in the following sections 16 2 The Loop Statement The l
339. rd value pairs can be present on the same line This parameter is an immediate switch that forces only one keyword value pair to be read on a line If there are more than one such pairs on a line then this option will force only the first pair to be read while all the other pairs are ignored Values O any number of keys or values 1 only one key value pair on a line error error text Force a parameter error with message text Forces a parameter error with given message string This option is useful if one needs to incorporate GAMS within another batch file and need to have control over the conditions when GAMS is called To illustrate the use of the error option the default GAMS log file from running a model with the option error hullo ERROR hullo Status Terminated due to parameter errors Erasing scratch files Exit code 6 errmsg errmsg 0 error message option This option controls the location in the listing file of the messages explaining the compilation errors Values O error messages at the end of compiler listing 1 error messages immediately following error line 2 no error messages To illustrate the option consider the following slice of GAMS code set i 1 10 set j i 10 11 parameter a jj 12 25 0 EE The listing file that results from running this model contains the following section 1 set i 1 10 set j i 10 11 CK 170 2 parameter a jj 12 25 0 CK 120 3 120 Unknown identifier
340. re ready to send the restart file to the target user or system The target user can now run the model with new data add new GAMS statements and make new save restart files The only restrictions are that some of the symbols are hidden and that this model can only be executed using the target license file For example the target user may want to half the demand and compare the original solution with the new one We will call this program t3 gms and it will be executed on the target system gt type t3 gms parameter rep summary report rep i j base x 1 i j b j b j 0 5 solve transport minimizing z using lp rep i j half x 1 i j display rep gt gams t3 r t2 2When using the GAMS IDE interface the GAMS parameters are entered and mainened in the text window just right to the Run GAMS F9 button G 3 Secure Work Files 229 GAMS Rev 124 Copyright C 1987 2001 GAMS Development Licensee Target User Name Target User Company Restarting from a Secure Restart File created by xk Source User Name eK Source Company Name Starting continued compilation T3 GMS 5 1 Mb Note that the originator owner of the secure work file is mentioned by name on the log file A similar message is contained in the listing file gt type t3 1st EXECUTION TIME 0 000 SECONDS 1 1 Mb WIN201 124 k Secure Save Restart File Source Source User Name Source Company Name xkxk Secure Save Restart File Target
341. re tractable One of the most common examples of such a method is the Generalized Bender s Decomposition method An example of a problem that is solved in this way is an input output system with endogenous prices described in Henaff 1980 The model consists of two groups of equations The first group uses a given final demand vector to determine the output level in each sector The second group uses some exogenous process and input output data to compute sectoral price levels Then the resulting prices are used to compute a new vector of final demands and the two block of equations are solved again This iterative procedure is repeated until satisfactory convergence is obtained Henaff has used GAMS statements to perform this kind of calculation The statements that solve the system for the first time and the next iteration are shown below model usaio mb output model dualmodel dual totp solve usaio using lp maximizing total solve dualmodel using lp maximizing totprice pbar ta sum ipd 1 i ta 4 d i t db i g t pd 1 i t pbar t solve usaio using lp maximizing total solve dualmodel using lp maximizing totprice lHenaff Patrick 1980 An Input Output Model of the French Economy Master s Thesis Department of Economics University of Maryland 9 5 Making New Solvers Available with GAMS 83 Mb is a set of material balance input output equations and output is a total output equation Dual is
342. reference rf text symbol reference file If specified all symbol references will be written to this file If not specified symbol references are written to the listing file To illustrate the use of the rf option a part of the trnsport ref file generated by running TRNSPORT using the option rf trnsport ref is shown below 1 471 SETS DECLARED 26 26 9 0 1 E WORK TRNSPORT GMS 2 471 SETS DEFINED 26 26 29 0 1 E WORKXTRNSPORT GMS 3 48 J SETS DECLARED 27 27 9 0 1 E WORK TRNSPORT GMS 4 48 J SETS DEFINED 27 27 29 0 1 E WORK TRNSPORT GMS relpath relpath 0 relative or absolute path names By default the maximum length of a file name under Windows is 255 and the maximum length of a command line is 255 characters The internal call to GAMS requires five file names to be passed as arguments If these files are nested deep in the directory structure the 255 character limit may be crossed and system errors may result This option allows for relative paths to be used instead of absolute paths as is the default in the file names Note that this may not always reduce the length of the file name Values O pathnames are completed to be absolute gt 9 1 pathnames beginning with a will be used as is restart r tewt restart file name This option provides the name of the save files to restart from The final name is composed by completing the file name with the current directory and the standard workfile extension Th
343. riables These can take on integer values between the defined bounds The default lower and upper bounds are 0 and 100 respectively In addition to these two two new types of discrete variables that are introduced in this section Both these variables exploit special structures in MIP models during the solution phase These are the following Special Ordered Sets SOS The precise definition of special ordered sets differ from one solver to another and the development of these features has been driven more by internal algorithmic consideration than by broader modeling concepts GAMS offers sos1 and sos2 variables as two types of compromise features that model special ordered sets Sections 17 2 2 and 17 2 3 discuss these two types of variables in greater detail Semi continuous variables GAMS offers semicont and semiint variables to model this class of variables These are explained in Sections 17 2 3 and 17 2 4 The presence of any of the above types of discrete variables requires a mixed integer model and all the discreteness is handled by the branch and bound algorithm in the same way as binary and general integer variables are handled 17 2 2 Special Order Sets of Type 1 SOS1 At most one variable within a SOS1 set can have a non zero value This variable can take any positive value Special ordered sets of type 1 are defined as follows 156 Special Language Features sosi Variable si i t1 k j wi i j k The members of the innerm
344. ring a line containing the statement option solprint off in the program above the solve statement The solution listing section from our example is shown below LOWER LEVEL UPPER MARGINAL EQU FSUM 1 000 1 000 1 000 13 529 EQU DMEAN 10 000 10 000 10 000 1 933 EQU DVAR gt a 1 000 FSUM fractions must add to 1 0 DMEAN definition of mean return on portfolio DVAR definition of variance VAR X fraction of portfolio invested in asset i LOWER LEVEL UPPER MARGINAL hardware f 0 303 INF software 0 087 INF EPS show biz 0 505 INF 7 t bills 0 106 INF EPS LOWER LEVEL UPPER MARGINAL VAR VARIANCE INF 2 899 INF VARIANCE variance of portfolio The order of the equations and variables are the same as in the symbol listing described before and will be described later The four columns associated with each entry have the following meaning LOWER lower bound 10 LEVEL level value 1 UPPER upper bound up MARGINAL marginal m 98 GAMS Output For variables the values in the LOWER and UPPER columns refer to the lower and upper bounds For equations they are obtained from the constant right hand side value and from the relational type of the equation These relationships were described in Chapter 8 t The LEVEL and MARGINAL values have been determined by the solver and the values shown are used to update the GAMS values In the list they are shown with fixed precision but the values are retur
345. ro In this case EPS indicates degeneracy The slack variable for the Seattle supply constraint is in the basis at zero level The marginal is marked with EPS rather than zero to facilitate restarting the optimizer from the old basis If the solvers results contain either infeasibilities or marginal costs of the wrong sign then the offending entries are marked with INFES or NOPT respectively If the problem terminates unbounded then the rows and columns corresponding to extreme rays are marked UNBND At the end of the solvers solution report is a very important report summary which gives a tally of the total number of non optimal infeasible and unbounded rows and columns For our example the report summary shows all zero tallies as desired xxx REPORT SUMMARY 0 NONOPT O INFEASIBLE O UNBOUNDED After the solver s report is written control is returned from the solver back to GAMS All the levels and marginals obtained by the solver are entered into the GAMS database in the 1 and m fields These values can then be transformed and displayed in any desired report As noted earlier the user merely lists the quantities to be displayed and GAMS automatically formats and labels an appropriate array For example the input statement 2 12 Summary 25 display x l x m results in the following output Lan 50 VARIABLE X L shipment quantities in cases new york chicago topeka seattle 50 000 300 000 san diego 275 000 275 000 ER
346. rocessed independently of its context They are now checked only for consistency GAMS now assumes that sets i and j as well as the identifiers a b and c are defined and if necessary initialized elsewhere The only error that is reported is the inconsistency of indices in the second statement nilcon nlcon 0 nonlinear instructions search length Values O use system default n max number of unique constants A pool of n unique nonlinear constants is kept Lookup for first n constants only nocheck nocheck 0 ignore parameter errors This options controls the report of parameter errors The effect of this option is immediate and affects all options that follow it on the command line Values O report parameter errors 1 ignore parameter errors Consider the following call gams myfile a q Since there is no action called q GAMS will complain and provide the following message x Incorrect action q Status Terminated due to parameter errors Erasing scratch files nocr nocr 0 ignore copyright messages everywhere Values O report copyright 1 suppress copyright opt opt 0 optimization level for GAMS execution Values O standard optimization 1 First Level optdir optdir tezt option file directory Solver option files are assumed to be located in optdir Path name completed with workdir 184 The GAMS Call optfile optfile 0 option file indicator This option initializes the modelname optfile parameter
347. rod Product over controlling index smin Minimum value over controlling index smax Maximum value over controlling index These four operations are performed over one or more controlling indices The syntax in GAMS for these operations is indexed_op controlling_indices expression If there is only one controlling index the parentheses around it can be removed The most common of these is sum which is used to calculate totals over the domain of a set Consider the following simple example adapted from ANDEAN for illustration sets i plants cartagena callao moron m product nitr acid sulf acid amm sulf parameter capacity i m capacity in tons per day totcap m total capacity by process totcap m sum i capacity i m 6 3 Expressions 55 This would be written using normal mathematical representation as totC gt Cim The index over which the summation is done i is separated from the reserved word sum by a left parenthesis and from the data term capacity i m by a comma i is again called the controlling index for this operation The scope of the control is the pair of parentheses that starts immediately after the sum It is not likely to be useful to have two independent index operations controlled by the same index It is also possible to sum simultaneously over the domain of two or more sets in which case more parentheses are needed Also of course an arithmetic expression may be used instead of
348. rred as if it were a sequence The notion of static sets was introduced already the set must be initialized with a list of labels enclosed in slashes at the time the set is declared and never changed afterwards ts Ordered sets must be static sets In other words no order is possible for dynamic sets t GAMS maintains one list of unique elements the labels that are used as elements in one or more sets The order of the elements in any one set is the same as the order of those elements in that unique element list This means that the order of a set may not be what it appears to be if some of the labels were used in an earlier definition t The map of your labels in the GAMS order can be seen by putting the compiler directive onuellist somewhere before the first set declaration t A good rule of thumb is that if the labels in a set one wants to be ordered have not been used already then they will be ordered The map is shown with the other compiler maps after the listing of your program In the example below we show ordered and unordered sets and the map showing the order The input is 120 Sets as Sequences Ordered Sets onuellist set ti 1987 1988 1989 1990 1991 t2 1983 1984 1985 1986 1987 t3 1987 1989 1991 1983 1985 The map below shows the entry order the important one and the sorted order obtained by sorting the labels into dictionary order The single digits on the left are the sequence numbers
349. rrent directory unittype ut tezt unit insert file operations override All units from previous runs and current inserts are set to the codes below Values X simulate without writing files U unix type pipe style 1 C spawn process with coded files B spawn process with binary files 190 The GAMS Call userl to user5 ul tezt u5 text strings passed on to the subsystems workdir wdir curdir This option sets the working directory This option is useful when GAMS is called from an external system like Visual Basic If not specified it will be set to the curdir directory xsave xs texwt extended save file name Uses and ASCII formated workfile otherwise like save C 3 Detailed Description of Command Line Parameters 191 Parameters controlling the specific GAMS run action dumpopt error expand fsave nocheck processing options workfile dump option parameter error message expands file name force workfile to be written ignores parameter errors Parameters controlling system settings charset codex dnlp errorlog ide inputdiri license mcp mpec nocr putdir relpath rmip scriptexit scriptnext solvercntr solverdopt solvermatr solverstat symbol sysincdir unittype workdir extended character set size of execution code length default DNLP solver error messages to log file Integrated Development Environment sets individual input search path sets license file name default MCP solver
350. ry item subitem item 25 116 Dynamic Sets 12 3 2 Indexed Operations Another important use of dollar controls with dynamic sets is to control the domain while performing indexed operations like sum and prod Consider the following adaptation of the second example from Section 12 3 1 parameter totinv total inventory totinv sum item subitem1 item inventory item This example has been shown only for illustration Note that the second statement above can also be rewritten tersely as totinv sum subitem1 inventory subitem1 This is not always possible Consider the following artificially created example sets item items sold pencil pen sup suppliers bic parker waterman dep department stationery household supply item sup supply pencil bic yes supply pen sup yes parameter totsales dep totsales dep sum item supply item bic sales dep item The assignment above is used to find the total sales of all departments that sell items supplied by bic Note that the dynamic set is used to limit the domain of summation to those for which supply item bic is true 12 3 3 Equations Dynamic sets can be used inside dollar conditions in equations both as part of the equation algebra or while defining the domain of the equation The first case is similar to the case of assignments discussed in Section 12 3 1 The latter case is used to restrict the equation over
351. s 1 parameter a b c 2 a 1 b 0 3Cc 2 BATINCLUDE D GAMS INC2 INC 4 b sqr a a 196 Dollar Control Options 5 display b BATINCLUDE D GAMS INC2 INC 7 b sqr c c 8 display b BATINCLUDE D GAMS INC2 INC 10 b sqr at5 a 5 11 display b Note that the three calls to batinclude with the various arguments lead to GAMS interpreting the contents of batch include file in turn as b sqr a a b sqr c c b sqr at5 atd Note that third call is not interpreted as sqr a 5 a 5 but instead as sqr a 5 a 5 The results of the display statement are shown at the end of the listing file 5 PARAMETER B 0 000 8 PARAMETER B 2 000 11 PARAMETER B 40 000 The third call leads to b sqr 6 1 5 which results in b taking a value of 40 If the statement in the batch include file was modified to read as follows 1 sqr 2 42 the results of the display statement in the listing file would read 5 PARAMETER B 0 000 8 PARAMETER B 2 000 11 PARAMETER B 30 000 The third call leads to b sqr 6 6 which results in b taking a value of 30 w A batinclude call without any arguments is equivalent to a include call call Passes a followed string command to the current operating system command processor and interrupts compilation until the command has been completed If the command string is empty or omitted a new interactive command processor will be loaded Consider the following sli
352. s are used on the top and the left to map out a rectangular grid that contains the data values The order of labels is unimportant but if domain checking has been specified each label must match one in the associated set Labels must not be repeated but can be left out if the corresponding numbers are all zero or not needed At least one blank must separate all labels and data entries Blank entries imply that the default value zero will be associated with that label combination ts Notice also that in contrast to the set scalar and parameter statements only one identifier can be declared and initialized in a table statement 5 4 2 An Illustrative Example The example below adapted from KORPET is preceded by the appropriate set definitions sets i plants inchon ulsan yosu m productive units atmos dist atmospheric distillation unit steam cr steam cracker aromatics aromatics unit hydrodeal hydrodealkylator table ka m i initial cap of productive units 100 tons per yr inchon ulsan yosu atmos dist 3702 12910 9875 steam cr 517 1207 aromatics 181 148 hydrodeal 180 In the example above the row labels are drawn from the set m and those on the column from the set i Note that the data for each row is aligned under the corresponding column headings If there is any uncertainty about which data column a number goes with GAMS will protest with an error message and mark the ambiguous entry 5 4 3 Cont
353. s follows dj d 2 75 da d This assignment is known technically as an indexed assignment and set d will be referred to as the controlling index or controlling set ts The index sets on the left hand side of the assignment are together called the controlling domain of the assignment The extension to two or more controlling indices should be obvious There will be an assignment made for each label combination that can be constructed using the indices inside the parenthesis Consider the following example of an assignment to all 100 data elements of a Set row r 1x r 10 col c 1x c 10 sro row xr 7 r 10 parameters a row col a row col 13 2 r row c col The calculation in the last statement is carried out for each of the 100 unique two label combinations that can be formed from the elements of row and col The first of these is explicitly a r 1 c 1 13 2 r r 1 x c c 1 6 2 3 Using Labels Explicitly in Assignments It is often necessary to use labels explicitly in assignments This can be done as discussed earlier with parameters by using quotes around the label Consider the following assignment a r 7 c 4 2 36 This statement assigns a constant value to one element of a All other elements of a remain unchanged Either single or double quotes can be used around the labels 6 2 4 Assignments Over Subsets In general wherever a set name can occur in an indexed assignment a
354. s j markets Parameters a i capacity of plant i in cases 224 The Save and Restart Feature b j demand at market j in cases c i j transport cost in 1000 case d i j distance in 1000 miles Scalar f freight in case per 1000 miles Variables x i j shipment quantities in cases z total transportation costs in 1000 Positive Variable x Equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j cost z e sum i j c i j x i j supply i sum j x i j l a i demand j sum i x i j g b j Model transport all Note that this representation does not contain any data and is a purely algebraic representation of the trans portation problem Running this model and saving the resulting work file will allow the model to be used with the data stored in a separate file file2 gms Sets i seattle san diego j new york chicago topeka Parameters a i seattle 350 san diego 600 b j new york 325 chicago 300 topeka 275 Table d i j new york chicago topeka seattle 2 5 TT 1 8 san diego 2 5 1 8 1 4 Scalar f 90 c i j f d i j 1000 Solve transport using lp minimizing z Display x 1 x m This file contains the data for the model and the solve statement F 3 2 Incremental Program Development GAMS programs are often developed in stages A typically style is to put the
355. s we can look at the solver output or if we wish we can request a display of these results from GAMS Our example contains the following statement display x 1 x m that calls for a printout of the final levels x 1 and marginal or reduced costs x m of the shipment variables x i j GAMS will automatically format this printout in to dimensional tables with appropriate headings 2 10 The lo l up m Database GAMS was designed with a small database system in which records are maintained for the variables and equations The most important fields in each record are lo lower bound 1 level or primal value up upper bound m marginal or dual value The format for referencing these quantities is the variable or equation s name followed by the field s name followed if necessary by the domain or an element of the domain GAMS allows the user complete read and write access to the database This may not seem remarkable to you now but it can become a greatly appreciated feature in advanced use Some examples of use of the database follow 2 10 1 Assignment of Variable Bounds and or Initial Values The lower and upper bounds of a variable are set automatically according to the variable s type free positive negative binary or integer but these bounds can be overwritten by the GAMS user Some examples follow capacity i j 10 0 new york 1 2 capacity seattle new york x up i j
356. s can be carried over as many lines of input as needed Blanks can be inserted to improve readability and expressions can be arbitrarily complicated t An equation once defined can not be altered or re defined If one needs to change the logic a new equation with a new name will have to be defined It is possible however to change the meaning of an equation by changing the data it uses or by using exception handling mechanisms dollar operations built into the definition 8 3 2 An Illustrative Example Consider the following example adapted from MEXSS The associated declarations are also included Variables phi phipsi philam phipi phieps equations obj obj phi e phipsi philam phipi phieps Obj is the name of the equation being defined The e symbol means that this is an equality Any of the following forms of the equation are mathematically equivalent 8 3 Equation Definitions 73 obj phipsi philam phipi phieps e phi obj phieps phipsi e philam phi phipi obj phi phieps phipsi philam phipi e 0 obj 0 e phi phieps phipsi philam phipi ts The arrangement of the terms in the equation is a matter of choice but often a particular one is chosen because it makes the model easier to understand 8 3 3 Scalar Equations A scalar equation will produce at most one equation in the associated optimization problem The equation defined in the last Section is an example
357. s itself echoed on the listing file while the offdollar line is not onjofflempty offempty This option allows empty data statements for list or table formats By default data statements cannot be empty Consider running the following slice of code D 3 Detailed Description of Dollar Control Options 205 set i 1 2 3 set j i parameter x i empty parameter table y i i headers only 1 2 3 onempty set k i parameter xx i empty parameter table yy i i 1 2 3 The listing file that results looks like 1 set i 1 2 3 2 set j i kkk 460 3 parameter x i empty parameter AK 460 4 table y i i headers only 5 1 2 3 6 AK 462 8 set k i 9 parameter xx i empty parameter 10 table yy i i 11 1 2 3 12 Error Messages 460 Empty data statements not allowed You may want to use 0N OFFEMPTY 462 The row section in the previous table is missing Note that empty data statements are not allowed for sets parameters or tables These are most likely to occur when data is being entered into the GAMS model by an external program Using the onempty dollar control option allows one to overcome this problem t The empty data statement can only be used with symbols which have a known dimension If the dimension is also derived from the data the phantom dollar control option should be used to generate phantom set elements onjofflend offend Offers alternative synt
358. s set to a specific value to use as an alignment tab Symbols which hold common alignment values such as margins or tabs are often useful for large structured documents The first put statement uses the current column cursor control character to relocate the cursor In this example the cursor is moved to column 8where out cc and its value is displayed 15 13 Cursor Control 145 The second put statement illustrates the updating of the cursor control suffixes by writing the letters x y and z On three different lines Each is preceded by the cursor being moved to the out cc value Initially the value for the cursor control suffice is 20 Since a single put statement is used for these three items the out cc value remains constant and consequently the letters end up in the same column Following this put statement the out cc value is updated to 23 which is the location of the cursor at the end of the second put statement note the additional blank spaces displayed with the letter z 15 13 2 Current Cursor Row These suffixes have numeric values corresponding to coordinates in the window of the page Because of this they can be used in conjunction with cursor control characters to manipulate the position of the cursor in the output file cr current cursor row in window hdcr header current row tler title current row The convention for updating the values stored for the cr suffix is that it are updated at the conclusion of a put statement
359. s that first 1 isa reference to last and last 2 is the same as first 1 and so on All references and assignments are defined This is useful for modeling time periods that repeat such as months of the year or hours in the day It is quite natural to think of January as the month following December Agricultural farm budget models and workforce scheduling models are examples of applications where circular leads occur naturally The operators are and The next two sections will describe the use of these lag and lead operators in assignment statements and in equations respectively 13 5 Lags and Leads in Assignments One use of the lag and lead operator is in assignment statements The use of a lag and lead operator on the right hand side of an assignment is called a reference while its use in the left hand side is called an assignment and 122 Sets as Sequences Ordered Sets involves the definition of a domain of the assignment The concepts behind reference and assignment are equally valid for the linear and circular forms of the lag and lead operator However the importance of the distinction between reference and assignment is not pronounced for circular lag and lead operators because non existent elements are not used in this case t A reference to a non existent element causes the default value zero in this case to be used whereas an attempt to assign to a non existent element results in no assignment being m
360. se controls are a compromise to provide some flexibility The display statement will not provide a publication quality reporting function but is instead aimed for functionality that is easy to use and provides graceful defaults The execution of the display statement allows the data to be written into the listing file only 14 2 The Syntax In general the syntax in GAMS for the display statement is display ident ref quoted text 1 ident ref quoted text Ident ref means the name without domain lists or driving indices of a set or parameter or a sub field of an equation or variable The identifier references and the text can be mixed and matched in any order and the whole statement can be continued over several lines The output produced by a display consists of labels and data For sets the character string yes indicating existence is used instead of values t Only the non default values are displayed for all data types The default value is generally zero except for the lo and up subtypes of variables and equations The default values for these are shown in table 14 1 143 An Example An example of a display statement is given below set s si s4 t t5 t7 parameter p s si 0 33 s3 0 67 parameter q t t5 0 33 t7 0 67 variable v s t v 1 5 t p s q t display first a set s then a parameter p then the activity level of a variable v 1 The resulting listing file will conta
361. set of type 2 with i elements t2 defines k sets of j elements each and w2 defines i j sets with k elements each PRODSCHX shows SOS type formulations with binary SOS1 and S0S2 sets The default bounds for SOS variables are 0 to 00 As with any other variable the user may set these bounds to whatever is required t Not all MIP solvers allow SOS2 variables Furthermore among the solvers that allow their use the precise definition can vary from solver to solver Any model that contains these variables may not be transferable among solvers Please verify how the solver you are interested in handles SOS2 variables by checking the relevant section of the Solver Manual 17 2 4 Semi Continuous Variables Semi continuous variables are those whose values if non zero must be above a given minimum level This can be expressed algebraically as Either x O or L lt x lt U By default this lower bound L is 1 and the upper bound U is 00 The lower and upper bounds are set through lo and up In GAMS a semi continuous variable is declared using the reserved phrase semicont variable The following example illustrates its use semicont variable x x lo 1 5 x up 23 1 The above slice of code declares the variable x to be semi continuous variable that can either be 0 or can behave as a continuous variable between 1 5 and 23 1 ts Not all MIP solvers allow semi continuous variables Please verify that the solver you are interested in
362. sets as well 12 2 4 Assignments over the Domain of Dynamic Sets One can make an assignment over the domain of a dynamic set because dynamic sets are known to be proper subsets of static sets This is not the same as doing domain checking using a dynamic set The following example adapted from the Section 12 2 2 illustrates the use of dynamic sets as domains subitemi item no subiteml subitem2 yes The first assignment ensures that subitem1 is empty Note that this can also be done with parameters For example parameter inventory item inventory subitem1 25 12 3 Using Dollar Controls with Dynamic Sets 115 12 2 5 Equations Defined over the Domain of Dynamic Sets It is sometimes necessary to define an equation over a dynamic set ts The trick is to declare the equation over the entire domain but define it over the dynamic set The following example illustrates its use set allr all regions n s w e n e s w r alr region subset for particular solution scalar price 10 equations prodbal allr production balance variables activity allr first activity revenue allr revenue A prodbal r activity r price e revenue r To repeat the important point the equation is declared over allr but referenced over r Then arbitrary assign ments can be made to r within the membership of allr 12 3 Using Dollar Controls with Dynamic Sets The rest of this chapter requires an understanding of the dol
363. sets first followed by tables and data manipulations then equations and finally the assignments used to generate reports As each piece of the model is built it should be run and checked for errors by inserting diagnostic display and abort statements As confidence mounts in the correctness of what has been done it is useful to save the completed parts in a work file Then by restarting it is possible to work only on the piece under active development thereby minimizing computer costs and the amount of output produced in each of the developmental runs This approach is especially useful when entering the statements needed for reporting The solution is much more expensive than the report but the report is likely to involve many details of content and layout that have to be tried several times before they are satisfactory The model can be solved and the result saved in a work file One can then restart from the work file when developing the report It is a great relief not to have to solve the model every time F 3 Ways in which a Work File is Useful 225 F 3 3 Tacking Sequences of Difficult Solves In many cases where solves are known to be difficult and expensive it may be too risky to ask GAMS to process a job containing many solve statements The risk is that if one solve does not proceed to normal completion then the following one will be started from a bad initial point and much time and effort will be wasted An alternative is to reque
364. signments 6 2 3 Using Labels Explicitly in Assignments TABLE OF CONTENTS 6 2 4 Assignments Over Subsets lt lt csoc rrr trcat aaru tarat ee ee 6 2 5 Issues with Controlling Indices co oo ooo porro 6 2 6 Extended Range Identifiers in Assignments o e eee 6 2 7 Acronyms ln Assignments o sa a 63 ENPIESIOUS se g eos gened ao eee be DEAD we eee ea a ee eR es 6 3 1 Standard Arithmetic Operations 0200 cee ee 632 Indexed Operations e e woe mareos d e dhe aa Ba a eee ee Oe eee ets Dao PLANOS or aa e a G a a A A A ee es ea 6 3 4 Extended Range Arithmetic and Error Handling 04 GA o cc en Pe ew AA 7 Variables Sel TOABEROR ee s to ee ee Se ee eee Wh eae Ee eee ore EA Rs YE Variable Declarations ocaso 6 085466 0444 44 SG G44 be toed eee bee G Toal GA oh fk Ao Sind he ee ee ee eH de we A ee ek a A toe Variable Types cc aac Saree A ee Re A eS 72 3 Styles for Variable Declaration e des Vatlabile Attributes sa aa e a a a RS val Boumds on Variables lt se ea 044 a a e a a a a e a TaS PREM vaas carr e A E d a ee ee oa Be ee AA lk 7 3 3 Activity Levels of Variables ee 7 4 Variables in Display and Assignment Statements e 7 4 1 Assigning Values to Variable Attributes e e eee eee eee 7 42 Variable Attributes in Assignments ee ee tan Displaying Variable Attributes oa s umoa
365. sion solvermatr smatr text solver matrix file name default name override Name completed with scratch directory and scratch extension solversolu ssolu text solver solution file name default name override Name completed with scratch directory and scratch extension 188 The GAMS Call solverstat sstat texwt solver status file name default name override Name completed with scratch directory and scratch extension stepsum stepsum 0 step summary option This option controls the generation of a step summary of the processing times taken by GAMS during a given run Values O no step summary 1 step summary printed To illustrate the use of the stepsum option the default GAMS log file from running TRNSPORT with the option stepsum 1 contains the following step summaries STEP SUMMARY 0 090 0 090 STARTUP 0 070 0 070 COMPILATION 0 090 0 090 EXECUTION 0 060 0 030 CLOSEDOWN 0 310 0 280 TOTAL SECONDS 0 000 ELAPSED SECONDS STEP SUMMARY 0 070 0 160 STARTUP 0 000 0 070 COMPILATION 0 030 0 120 EXECUTION 0 000 0 030 CLOSEDOWN 0 100 0 380 TOTAL SECONDS 1 000 ELAPSED SECONDS The first step summary occurs before the model is sent to the solver and the second occurs after the solver completes its task and returns control back to GAMS The first column reports time for the individual section of the run while the second column reports accumulated times including previous sections stringchk stringchk 0 string substitution
366. solution we will set the handle parameter to zero In addition we want to remove the instance from the system by calling the function handledelete which returns zero if successful see definition No harm is done if it fails but we want to be notified via the conditional display statement Before running the collection loop again we may want to wait a while to give the system time to complete more solution steps This is done with the sleep command that sleeps some time The final wrinkle is to terminate after 100 seconds elapsed time even if we did not get all solutions This is important because if one of the solution steps fails our program would never terminate The last statement sets the results of the missed solves to NA to signal the failed solve The parameter h will now contain the handles of the failed solvers for later analysis Alternatively we could have used the function handlestatus and collect the solution which is stored in a GDX file For example we could write loop pp handlestatus h pp 2 minvar handle h pp execute_loadhandle minvar xres i pp x 1 i report pp i inc xi 1 i report pp i dec xd 1 i The function handlestatus interrogates the solution process and returns 2 if the solution process has been completed and the results can be retrieved The solution is stored in a GDX file which can be loaded in a way similar to other gdx solution points First we need to tell GAMS
367. sponding term that the logical dollar condition is operating on evaluates to 0 Consider the following example which is a slight modification to the one described in Section 11 3 1 x 2 y gt 1 5 Expressed in words this is equivalent to if y gt 1 5 then x 2 else x 0 Therefore an if then else type of construct is implied but the else operation is predefined and never made explicit Notice that the statement in the illustrative example above can be re written with an explicit if then else and equivalent meaning as x 2 y gt 1 5 O y le 1 5 This use of this feature is more apparent for instances when an else condition needs to be made explicit Consider the next example adapted from FERTD The set i is the set of plants and are calculating mur i the cost of transporting imported raw materials In some cases a barge trip must be followed by a road trip because the plant is not alongside the river and we must combine the separate costs The assignment is mur i 1 0 0030 ied i barge ied i barge 0 5 0144 ied i road ied i road This means that if the entry in the distance table is not zero then the cost of shipping using that link which has a fixed and a variable components is added to the total cost If there is no distance entry there is no contribution to the cost presumably because that mode is not used 11 4 3 Filtering Controlling Indices in Indexed Operat
368. st all of the statements in the GAMS input file we are about to present would remain unchanged if a much larger transportation problem were considered In the familiar transportation problem we are given the supplies at several plants and the demands at several markets for a single commodity and we are given the unit costs of shipping the commodity from plants to markets The economic question is how much shipment should there be between each plant and each market so as to minimize total transport cost The algebraic representation of this problem is usually presented in a format similar to the following Indices i plants j markets Given Data a supply of commodity of plant i in cases bj demand for commodity at market j Cij cost per unit shipment between plant i and market j case Decision Variables zij amount of commodity to ship from plant to market j cases where xij gt 0 for all i 7 Constraints Observe supply limit at plant i X j Big S aj for alli cases Satisfy demand at market j X tij 2 bj for all j cases Objective Function Minimize 2 CijUij K Note that this simple example reveals some modeling practices that we regard as good habits in general and that are consistent with the design of GAMS First all the entities of the model are identified and grouped by type Second the ordering of entities is chosen so that no symbol is referred to before it is defined Third the lDantzig
369. st of the listing is self explanatory The name text and type of constraints are shown The four dashes are useful for mechanical searching t All the terms that depend on variables are collected on the left and all the constant terms are combined into one number on the right any necessary sign changes being made Four places of decimals are shown if necessary but trailing zeroes following the decimal point are suppressed E format is used to prevent small numbers being displayed as zero t The nonlinear equations are treated differently If the coefficient of a variable in the equation listing is enclosed in parentheses then the corresponding constraint is nonlinear and the value of the coefficient depends on the activity levels of one or more of the variables The listing is not algebraic but shows the partial derivative of each variable evaluated at their current level values Note that in the equation listing from our example the equation dvar is nonlinear A simpler example will help to clarify the point Consider the following equation and associated level values eqi 2 sqr x power y 3 5 x 1 5 y e 2 x l 2 y l 3 then the equation listing will appear as EQ1 221 X 216 1667 Y E 2 LHS 225 5 92 GAMS Output The coefficient of x is determined by first differentiating the equation above with respect to x This results in 2 2 x 1 power y 1 3 5 which evaluates to 221 Similarly the coefficien
370. st one solve at a time and save the work file Then the output is carefully inspected before proceeding If everything is normal the job is restarted with the next solve requested If not the previous solve can be repeated probably with a different initial point or continued if the cause of the trouble was an iteration limit for example This approach is common when doing repeated solves of a model that successively represent several consecutive time periods It uses a work file in a sequential rather than a tree structure way It also produces many files which can be difficult to manage if the solves are especially difficult it is possible to lose track of exactly what was done Great care is needed to avoid losing control of this process F 3 4 Multiple Scenarios The majority of modeling exercises involves a base case and the point of the study is to see how the system changes when circumstances change either naturally or by design This is often done by making many different changes to the base case and separately considering the effects it is sometimes called what if analysis The point is that the base can be saved using a work file and as many different scenarios as may be interesting can then be run separately by restarting Each scenario probably involves only making a change in data or in bounds solving the changed model the base solution is automatically used as a starting point and reporting This procedure is an example
371. stem General Algebraic Modeling System GAMS Data Exchange High Performance Computing 246 The GAMS Grid Computing Facility J Extrinsic Functions J 1 Introduction Functions play an important part in the GAMS language especially for non linear models Similar to other programming languages GAMS provides a number of built in intrinsic functions However GAMS is used in an extremely diverse set of application areas and this creates frequent requests for the addition of new and often sophisticated and specialized functions There is a trade off between satisfying these requests and avoiding com plexity not needed by most users The GAMS Function Library Facility 6 3 3 provides the means for managing that trade off In this Appendix the extrisic function libraries which are included in the GAMS distribution are described In the tables that follow the Model Function Type first column specifies in which models the function can legally appear with endogenous non constant arguments In order of least to most restrictive the choices are any NLP DNLP or none The following conventions are used for the function arguments Lower case indicates that an endogenous variable is allowed Upper case indicates that a constant argument is required The arguments in square brackets can be omitted and default values will be used J 2 Fitpack Library FITPACK by Paul Dierckx is a FORTRAN based library for one and two dimensional spline inter
372. straints are to be hidden from other users and only the demand figures can be changed Data that is not needed any more will be purged as well This will be demonstrated below using the command line interface to GAMS First we will copy the model from the GAMS model library run the model and save a normal work file gt gamslib trnsport gt gams trnsport s t1 We continue to enter access control commands in a file called t2 gms and create a secure work file with the name t2 g00 gt type t2 gms eolcom protect all make all symbol read only purge df remove items d and f hide cost supply a make objective invisible expose transport b allow changes to b gt gams t2 r t1 s t2 plicense target GAMS Rev 124 Copyright C 1987 2001 GAMS Development Licensee Source User Name Source Company Name Creating a Secure Restart File for RK Target User Name eK Target Company Name Starting continued compilation T2 GMS 6 1 Mb Starting execution Status Normal completion The access control commands are activated by the use of the privacy GAMS license option PLICENSE This option specifies the name of the target user license file The save restart file t2 g00 can only be read with the target license file The three lines starting with are a recap of the content of the target license file From now on the source and the target licensees are burned into this file and all its descendants We a
373. subsections can be used to generate more complex logical conditions The default precedence order in a logical condition used by GAMS in the absence of parenthesis is shown in table 11 2 in decreasing order Operation Operator Exponentiation Numerical Operators Multiplication Division Unary operators Plus Minus ty Binary operators addition subtraction Numerical Relationship operators lt lt lt gt gt gt Logical Operators not not and and or XOr or xor Table 11 2 Operator precedence Note that in the case of operators with the same precedence the order in which the operator appears in the expression is used as the precedence criterion with the order reducing from left to right ts It is always advisable to use parentheses rather than relying on the precedence order of operators It prevents errors and makes the intention clear Consider the following example for illustration 106 Conditional Expressions Assignments and Equations x 5 y and z 5 is treated equivalent to x 5 y and z 5 However note that the use of parenthesis does make the expression clearer to understand 11 2 8 Mixed Logical Conditions Examples Some simple examples of logical conditions containing the building blocks described in the previous sub sections are shown in table 11 3 to illustrate the generation and use of more complex logical conditions Logical Condition
374. subset or even a label can be used instead if you need to make the assignment over a subset instead of the whole domain Consider the following example a sro col 10 2 44 33 r sro where sro has already been established to be a proper subset of row 6 2 5 Issues with Controlling Indices t The number of controlling indices on the left of the sign should be at least as many as the number of indices on the right There should be no index on the right hand side of the assignment that is not present on the left unless it is operated on by an indexed operator Consider the following statement a row col 2 22 c col 1 6 3 Expressions 53 GAMS will flag this statement as an error since col is an index on the right hand side of the equation but not on the left t Each set is counted only once to determine the number of controlling indices If the same set appears more than once within the controlling domain the second and higher occurrences of the set should be aliases of the original set in order for the number of controlling indices to be equal to the number of indices Consider the following statement as an illustration b row row 7 7 r row This statement has only one controlling index row If one steps through the elements of row one at a time assignments will be made only to the diagonal entries in b This will assign exactly 10 values None of the off diagonal elements of b will be filled
375. t ts For an assignment statement with a dollar condition on the left hand side no assignment is made unless the logical condition is satisfied This means that the previous contents of the parameter on the left will remain unchanged for labels that do not satisfy the condition ts If the parameter on the left hand side of the assignment has not previously been initialized or assigned any values zeroes will be used for any label for which the assignment was suppressed Consider the following example adapted from CHENERY rho i sig i ne 0 1 sig i 1 The parameter sig i has been previously defined in the model and the statement above is used to calculate rho i The dollar condition on the statement protects against dividing by zero If any of the values associated with sig i turn out to be zero no assignment is made and the previous values of rho i remain As it happens rho i was previously not initialized and therefore all the labels for which sig i is 0 will result in a value of 0 Now recall the convention explained in Section 11 2 1 that non zero implies True and zero implies False The assignment above could therefore be written as rho i sig i 1 sig i 1 108 Conditional Expressions Assignments and Equations 11 4 2 Dollar on the Right t For an assignment statement with a dollar condition on the right hand side an assignment is always made If the logical condition is not satisfied the corre
376. t Iems oe cind deoii A a a ee eed 1592 Nuimerie ems pacans sonat aa a ew a e 159 3 Set Value Items cocos A Global Item Formatting o 15 10 1 Field Justification 15 10 2 Field Width 202 56 eae Be A Geb eee Dad Local Item Formatting s ieo acr matindi ea ee daa Additional Numeric Display Control 15 12 1 Musttative Example lt a o sa poan i as Cursor COBOL sos mor iaoe a a ea gp a g p a ne a 15 13 1 Current Cursor Column 2 6 0 06680 66 bea 15 13 23 Current Cursor Raw ocu Pee es 15 13 39 Last Line Control 2 624 5446 24 0 aaa Paging Gontrol 4 56364 h i e ee eke aed Exception Handling lt Source of Errors Associated with the Put Statement 18 16 1 Syntax Errors e o e a cosas sa ba es Lolo Pit Briere so ai 2 ke ee de aa da Ea e Simple Spreadsheet Database Application RT An ERAS a he A A a Eee a 16 Programming Flow Control Features 16 1 16 2 16 3 16 4 16 5 IETT CUENO N sucedido ad ee a a The Loop Statement o raddai 16 21 The Syntax ocre mod 1622 Examples cos ek ae a ee a ee aie BG Sos The If Elseif Else Statement 0 163 1 Th Syntax ey ke sea a a Boke ee a 1632 Examples oa swa aioe AR A e ee a The While Statement oaaae a IBAI Tie DBA lt lt sensie a nya ee OE ee da Examples e ke ek aa aa A The For Statement 02 6 4 62 bk debe eee e aa 1631 The BE ca A ee a eS 16 5 2
377. t a classification of a function A plot of the function values will be a line without breaks in it Second a classification of variables A continuous variable may assume any value within its bounds controlling sets See driving sets data types Each symbol or identifier has to be declared to be one of the seven data types which are set parameter variable equation model file and acronym The keywords scalar and table do not introduce separate data types but rather comprise a shorthand way to declare a symbol to be a parameter that will use a particular format for specifying initial values declaration The entry of a symbol and the specification of its data type A declaration may include the specification of initial values and then it is more properly called a definition default The value used or the action taken if the user provides no information 164 Glossary definition The definitions of the algebraic relationships in an equation are the assignment of initial values to parameters or of elements to sets as part of the initial declaration of the identifier definition statements Units that describe symbols assign initial values to them and describe symbolic relationships Some examples of the set parameter table and model statements and the equation definition statement direction Either maximization or minimization depending on whether the user is interested in the largest or the smallest possible value for the object
378. t all locations i 11 6 3 Filtering the Domain of Definition The same rules that apply to filtering assignments and controlling indices in indexed operations applies to equation domains as well Consider the following equation using the same set definitions as described before parameter bigM i j variable shipped i j binary variable bin i j equation logical i j logical i j ij i j shipped i j 1 bigM i j bin i j The equation logical relates the continuous variable shipped i j to the binary variable bin i j This can be simplified as follows logical ij shipped ij l bigM ij bin ij Note that if the right hand side of the equation contained any term that was indexed over i or j separately then the equation logical i j ij i j would have to be simplified as logical ij i j 12 Dynamic Sets 12 1 Introduction All the sets that have been discussed so far had their membership declared as the set itself was declared and the membership was never changed In this chapter we will discuss changing the membership of sets A set whose membership can change is called a dynamic set to contrast it with a static set whose membership will never change The distinction is important and will be discussed in detail in this chapter This is a topic that has been avoided until now because of a potential confusion for new users Advanced Users will however find it useful 12 2 Assigning Membership to Dynamic
379. t have the numerical value 1986 and the label 101 is different from the label 1 Each element in a set must be separated from other elements by a comma or by an end of line In contrast each element is separated from any associated text by a blank Consider the following example from the Egyptian fertilizer model FERTS where the set of fertilizer nutrients could be written as set cq nutrients N P205 or as set cq nutrients N P205 The order in which the set members are listed is normally not important However if the members represent for example time periods then it may be useful to refer to next or previous member There are special operations to do this and they will be discussed in Chapter 13 For now it is enough to remember that the order in which set elements are specified is not relevant unless and until some operation implying order is used At that time the rules change and the set becomes what we will later call an ordered set 4 2 4 Associated Text It is also possible to associate text with each set member or element Explanatory text must not exceed 254 char acters and must all be contained on the same line as the identifier or label it describes For example label text for the set of final products in SHALE contains details of the units of measurement 4 2 Simple Sets 37 Set f final products yncrude refined crude million barrels lpg liquified petroleum gas million
380. t of y is obtained by differenti ating the equation above with respect to y which results in 2 sqr x 1 3 sqr y 1 1 5 sqr y 1 giving 216 1667 Notice that the coefficient of y could not have been determined if its level had been left at zero The attempted division by zero would have produced an error and premature termination The result of evaluating the left hand side of the equation at the initial point is shown at the end of each individual equation listing In the example above it is 225 5 and the three asterisks are a warning that the constraint is infeasible at the starting point t The order in which the equations are listed depends on how the model was defined If it was defined with a list of equation names then the listing will be in the order in that list If it was defined as al11 then the list will be in the order of declaration of the equations The order of the entries for the individual constraints is determined by the label entry order 10 5 2 The Column Listing The next section of the listing file is the Column Listing This is a list of the individual coefficients sorted by column rather than by row Once again the default is to show the first three entries for each variable along with their bound and level values The format for the coefficients is exactly as in the equation listing with the nonlinear ones enclosed in parentheses and the trailing zeroes dropped The column listing section from our example foll
381. t respects hidden from the user The solution values reported back from a solution algorithm are always reported in the user s notation The algorithm s versions of the equations and variables are 17 3 Model Scaling The Scale Option 159 only reflected in the derivatives in the equation and column listings in the GAMS output if the options limrow and limcol are positive and the debugging output from the solution algorithm generated with sysout option set to on 17 3 2 Variable Scaling The scale factor on a variable Vs is used to relate the variable as seen by the user V to the variable as seen by the algorithm Va as follows Va Vi Vs For example consider the following equation positive variables x1 x2 equation eq eq 200 x1 0 5 x2 1 5 x1 up 0 01 x2 up 10 x1 scale 0 01 x2 scale 10 By setting x1 scale to 0 01 and x2 scale to 10 the model seen by the solver is positive variables xprime1 xprime2 equation eq eq 2 xprimel 5 xprime2 1 5 xprimel up 1 xprime2 up 1 Note that the solver does not see the variables x1 or x2 but rather the scaled and better behaved variables xprimel and xprime2 t Upper and lower bounds on variables are automatically scaled in the same way as the variable itself ts Integer and binary variables cannot be scaled 17 3 3 Equation Scaling Similarly the scale factor on an equation Gs is used to relate the equation as seen by the user
382. tements in GAMS Set t time periods 1991 2000 Set m machines machi mach24 Here the effect is to assign t 1991 1992 1993 2000 m mach machg macho Note that set elements are stored as character strings so the elements of t are not numbers Another convenient feature is the alias statement which is used to give another name to a previously declared set In the following example Alias t tp the name tp is like a in mathematical notation It is useful in models that are concerned with the interactions of elements within the same set The sets i j t and m in the statements above are examples of static sets i e they are assigned their members directly by the user and do not change GAMS has several capabilities for creating dynamic sets which acquire their members through the execution of set theoretic and logical operations Dynamic sets are discussed in Chap ter 12 pagel13 Another valuable advanced feature is multidimensional sets which are discussed in Section 4 5 page 39 2 4 Data The GAMS model of the transportation problem demonstrates all of the three fundamentally different formats that are allowable for entering data The three formats are e Lists e Tables e Direct assignments The next three sub sections will discuss each of these formats in turn 10 A GAMS Tutorial by Richard E Rosenthal 2 4 1 Data Entry by Lists The first format is illustrated by the first
383. ten 138 The Put Writing Facility Title Block Header Block Window In the illustrative example described in Section 15 3 all the data was written to the window A title block might have been included if more elaboration were needed to provide the model name along with the page number In addition a header block might have been used to display a disclaimer or an instruction which we wanted consistently repeated on every page Once this information is placed in the title or header blocks it is displayed on each page thereafter unless modified This could be especially useful for a long document covering many pages 15 6 1 Accessing Various Page Sections Each of these areas of a page are accessed by using different variations of the keyword put These variations are puttl write to title block puthd write to header block put write to window The size of any area within a given page is based entirely on the number of lines put into it Note that the total number of lines for all areas must fit within the specified page size If the total number of lines written to the title and header block equals or exceeds the page size an overflow error will be displayed in the program listing When this occurs this means there is no room remaining on the page to write to the window As mentioned above the syntax for writing an output item to any of the three possible writing areas of the page is basically the same the only dif
384. ternative way of writing table techi tech2 strategy 1 small medium 05 strategy 2 strategy 3 small medium 2 trategy 4 medium 25 display attrib attribx Here we encounter the display statement again It causes the data associated with upgrade and upgradex to be listed on the output file 5 4 6 Handling Long Row Labels It is possible to continue the row labels in a table on a second or even third line in order to accommodate a reasonable number of columns The break must come after a dot and the rest of each line containing an incomplete row label tuple must be blank The following example adapted from INDUS is used to illustrate As written this table actually has nine columns and many rows we have just reproduced a small part to show continued row label tuples table yield c t s w z crop yield metric tons per acre nwfp pmw wheat bullock semi mech la plant heavy january 385 338 wheat bullock semi mech la plant light 506 446 wheat bullock semi mech la plant standard 592 524 wheat bullock semi mech qk harv standard heavy january 439 387 5 5 Acronyms An acronym is a special data type that allows the use of strings as values 5 5 1 The Syntax The declaration for an acronymis similar to a set or parameter declaration in that several of them can be declared in one statement Acronym s acronym_name acronym_name Acronym_name is an identifier and follows the same nam
385. than the list based approach since each label appears only once at least in small tables 5 4 1 The Syntax In general the syntax in GAMS for a table declaration is table table_name text EOL element element element signed_num signed_num EOL element signed_num signed_num EOL 46 Data Entry Parameters Scalars amp Tables Table_name is the internal name of the table also called an identifier in GAMS The accompanying text is used to describe the parameter immediately preceding it Signed_num is a signed number and is declared to be the value of the entry associated with the corresponding element t The table statement is the only statement in the GAMS language that is not free format The following rules apply gt The relative positions of all entries in a table are significant This is the only statement where end of line EOL has meaning The character positions of the numeric table entries must overlap the character positions of the column headings gt The column section has to fit on one line gt The sequence of signed numbers forming a row must be on the same line gt The element definition of a row can span more than one line gt A specific column can appear only once in the entire table The rules for forming simple tables are straightforward The components of the header line are the by now familiar keyword identifier domain_list text sequence the domain list and text being optional Label
386. the domain of a dynamic set The equation defined in the example from Section 12 2 5 can be rewritten with equivalent effect as follows prodbal allr r allr activity allr price e revenue allr The domain of definition of equation prodbal is restricted to those elements that belong to the dynamic set r 12 3 4 Filtering through Dynamic Sets The filtering process explained in previous sections is valid when the conditional set is a dynamic one Consider the following two examples as described before inventory item subitemi item 25 prodbal allr r allr activity allr price e revenue allr These statements can be rewritten as inventory subitem1 25 prodbal r activity r price e revenue r 12 4 Set Operations This section describes how various symbolic set operations can be performed in GAMS using dynamic sets The Union Intersection Complement and Difference set operations are described individually in the following subsections Once again the example from Section 12 2 2 is used to illustrate each operation 12 5 Summary 117 12 4 1 Set Union The symbol performs the set union operation Consider the following example subitem3 item subitemi item subitem2 item The membership of subitem3 is set equal to all the elements of subitem1 and all the elements of subitem2 The operation above is equivalent to the following longer way of representation subitem3 item no subitem3 subitem2
387. the second piece The content of the output that results is the same though slightly rearranged as the case when the large file was run Splitting the files allows one to interrupt a GAMS task and restart it later without loss of information Furthermore changes could be made or errors corrected to the later parts F 2 The Save and Restart Feature Using the save and restart command line parameters provides a mechanism to break up the compilation of a large input file into many components and stages Some of the reasons for using these features and running a model in pieces are explained in Section F 3 The next two sub sections explain the save and restart mechanisms in GAMS The save and restart command line parameters described in Appendix C are used for this purpose TRNSPORT is used for the purposes of illustration Consider the following file containing code extracted from this model called file1 gms Sets i canning plants seattle san diego j markets new york chicago topeka Parameters a i capacity of plant i in cases seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 Table d i j distance in 1000 miles new york chicago topeka seattle 2 5 1 7 1 8 222 The Save and Restart Feature san diego 2 5 1 8 1 4 Scalar f freight in dollars case per 1000 miles 90 Parameter c i j transport cost in 1000 case c i j f d i j 100
388. the set t These would cause errors in the model if they went undetected It is legal but unwise to define a subset without reference to the larger set as is done above for the set nt If services were misspelled no error would be marked but the model would give incorrect results So we urge you to use domain checking whenever possible It catches errors and allows you to write models that are conceptually cleaner because logical relationships are made explicit This completes the discussion of sets in which the elements are simple This is sufficient for most GAMS appli cations however there are a variety of problems for which it is useful to have sets that are defined in terms of two or more other sets 4 5 Multi dimensional Sets It is often necessary to provide mappings between elements of different sets For this purpose GAMS allows the use of multi dimensional sets t GAMS allows sets with up to 20 dimensions The next two sub sections explain how to express one to one and many to many mappings between sets 4 5 1 One to one Mapping Consider a set whose elements are pairs A b d a c c e In this set there are three elements and each element consists of a pair of letters This kind of set is useful in many types of modeling As an illustrative example consider the world aluminum model ALUM where it is necessary to associate with each bauxite supplying country a port that is near to the bauxite mines The set of
389. the solver status file as part of the listing file The contents of the solver status file are useful if you are interested in the behavior of the solver If the solver crashes or encounters any difficulty the contents of the solver status file will be automatically sent to the listing file on Prints the system output file of the solver off No subsystem output appears on output file unless a subsystem error has occurred 220 The Option Statement F The Save and Restart Feature F 1 Introduction GAMS saves the information provided in the input files in intermediate mostly binary files These files are referred to as work files or scratch files Some of these files are used to exchange information between GAMS and the various solvers Just before a GAMS run is complete these files are usually deleted Input files can be processed in parts through the use of these intermediate files This is an extremely powerful feature that can reduce the time needed when several runs of the same model are being made with different data It may be clearer if the process is described in a different way Imagine taking a large GAMS program and running it producing one output file Then think of splitting the program into two pieces The first piece is run and the resulting work file is saved along with the resulting listing file Then the second piece is run after reading in the data from the work file saved previously A new listing file is generated for
390. tion that has continuous first derivatives solver A computer code used to solve a given problem type An example is GAMS MINOS which is used to solve either linear or nonlinear programming problems statements Sometimes called units The fundamental building block of GAMS programs Statements or sentences that define data structures initial values data modifications and symbolic relationships Examples are table parameter variable model assignment and display statements static set See constant set superbasic In nonlinear programming a variable that it is not in the basis but whose value is between the bounds Nonlinear algorithms often search in the space defined by the superbasic variables symbol An identifier table One of the ways of initializing parameters Used for two and higher dimensional data structures text A description associated with an identifier or label 167 type See data type problem type or variable type unique element A label used to define set membership variable type The classification of variables The default bounds are implicit in the type and also whether continuous or discrete The types are free positive binary integer semicont semiint and negative vector A one dimensional array corresponding to a symbol having one index position zero default Parameter values are initially set to zero Other values can be initialized using parameter or table statements Assignment statements have
391. tives but has continuous function values A plot of the function values will be a line with kinks in it nonzero element The coefficient of a particular column in a particular row if it is not zero Most mathematical programming problems are sparse meaning that only a small proportion of the entries in the full tableau of dimensions number of rows by number of columns is different from zero objective row or function Solver system require the specification of a row on for nonlinear systems a function whose value will be maximized or minimized GAMS users in contrast must specify a scalar variable 166 Glossary objective value The current value of the objective row or of the objective variable objective variable The variable specified in the solve statement optimal A feasible solution in which the objective value is the best possible option The statement that allows users to change the default actions or values in many different parts of the system ordered set A set is ordered if its content has been initialized with a set definition statement and the entry order of the individual elements of the set has the same partial order as the chronological order of the labels A set name alone on the left hand side of an assignment statement destroys the ordered property Lag and Ord operations rely on the relative position of the individual elements and therefore require ordered sets Ordered sets are by definition constant output A gene
392. to be used thereafter to change parameter values 168 Glossary B The GAMS Model Library Professor Paul Samuelson is fond of saying that he hopes each generation economists will be able to stand on the shoulders of the previous generation The library of models included with the GAMS system is a reflection of this desire We believe that the quality of modeling will be greatly improved and the productivity of modelers enhanced if each generation can stand on the shoulders of the previous generation by beginning with the previous models and enhancing and improving them Thus the GAMS systems includes a large library collectively called GAMSLIB The models included have been selected not only because they collectively provide strong shoulders for new users to stand on but also because they represent interesting and sometimes classic problems For example the trade off between consumption and investment is richly illustrated in the Ramsey problem which can be solved using nonlinear programming methods Examples of other problems included in the library are production and shipment by firms investment planning in time and space cropping patterns in agriculture operation of oil refineries and petrochemical plants macroeconomics stabilization applied general equilibrium international trade in aluminum and in copper water distribution networks and relational databases Another criterion for including models in the library is that they
393. to the value set This parameter has to be set to a value between 1 and 999 in order for GAMS to inform the solver to read the solver option file Modelname is the name of the model specified in the model statement For example the file myfile contains the slice of GAMS code model m all solve m using nlp maximizing dollars Consider the following call gams myfile optfile 1 The option file that is being used after this assignment is solvername opt where solvername is the name of the solver that is specified For CONOPT the option file is called conopt opt for MINOS it is minos opt The names that you can use are listed in the Solver Manual ts Setting modelname optfile in the GAMS input file overrides the value of the optfile parameter passed through the command line To allow different option file names for the same solver the optfile parameter can take other values as well Formally the rule is optfile n will use solvename opt if n 1 and solvername opX solvername oXX or solvername XXX where X s are the characters representing the value of n for n gt 1 and will use no option file at all for n 0 This scheme implies an upper bound on n of 999 For example the following optfile values profile the option file names for the CONOPT solver O no option file used 1 conopt opt 2 conopt op2 26 conopt o26 345 conopt 345 output o tezt output file name If no name is given the input file name is combined with the current
394. trast to previous approaches only one document need be moved the GAMS statement of the model It contains all the data and logical specifications needed to solve the model 1 2 4 User Interface Portability concerns also have implications for the user interface The basic GAMS system is file oriented and no special editor or graphical input and output routines exist Rather than burden the user with having to learn yet another set of editing commands GAMS offers an open architecture in which each user can use his word processor or editor of choice This basic user interface facilitates the integration of GAMS with a variety of existing and future user environments 1 2 5 Model Library When architects begin to design a new building they develop the new structure by using ideas and techniques that have been tested in previous structures The same is true in other fields design elements from previous projects serve as sources of ideas for new developments From the early stages of the development of GAMS we have collected models to be used in a library of examples Many of these are standard textbook examples and can be used in classes on problem formulation or to illustrate points about GAMS Others are models that have been used in policy or sector analysis and are interesting for both the methods and the data they use All the substantive models in the library are described in the open literature A collection of models is now included with
395. ttribute 79 jdate function 58 jnow function 58 jobHandle function 59 jobKill function 59 jobStatus function 59 jobTerminate function 59 jstart function 58 jtime function 58 keep GAMS call parameter 180 kill dollar control option 202 KORPET example from GAMSLIB 46 label 29 31 40 dollar control option 202 order 131 order on displays 128 quoted 31 36 row and column 47 unquoted 31 using in equations 73 laplace distribution 249 le relational operator 30 103 leftmargin GAMS call parameter 180 legal characters 30 level 68 libincdir GAMS call parameter 180 libinclude dollar control option 202 license GAMS call parameter 180 licenseLevel function 59 licenseStatus function 59 limcol GAMS call parameter 180 GAMS option 217 model attribute 79 limrow GAMS call parameter 181 GAMS option 217 model attribute 79 lines dollar control option 203 list 165 of labels using Asterisks 37 list format 165 locally infeasible 94 optimal 94 log dollar control option 203 function 74 log function 55 log10 function 55 log2 function 55 logarithmic distribution 250 logBeta function 55 logfile GAMS call parameter 181 logistic distribution 249 logline GAMS call parameter 181 logNormal distribution 249 logoption GAMS call parameter 182 loop example 150 statement 149 syntax 149 lower bound 67 lo 67 lower case 30 Ip GAMS call parameter
396. ttributes for example 1 and m attributes are used as arguments The expression is evaluated once when the model is being set up and all functions except the random distribution functions uniform and normal are allowed Endogenous arguments The arguments are variables and therefore unknown The function will be evaluated many times at intermediate points while the model is being solved t The occurrence of any function with endogenous arguments implies that the model is not linear ts It is forbidden to use the uniform and normal functions in an equation definition Functions with endogenous arguments can be further classified into types listed in table 8 1 Type Function Derivative Examples Smooth Continuous Continuous exp sin log Non Smooth Continuous Discontinuous max min abs Discontinuous Discontinuous Discontinuous ceil sign Table 8 1 Classification of functions with endogenous arguments Smooth functions can be used routinely in nonlinear models but non smooth ones may cause numerical problems and should be used only if unavoidable and only in a special model type called dnlp However the use of the dnlp model type is strongly discouraged and the use of binary variables is recommended to model non smooth functions Discontinuous functions are not allowed at all with variable arguments A fuller discussion is given in Chapter 9 page 77 For convenience all the available functions are classified in table 6 1
397. two labels If the only characters that differ are digits and if the number say L formed by these digits in the left one is less than that from the right one R then a label is constructed for every integer in the sequence L to R Any non numeric differences or other inconsistencies cause errors The following example illustrates the most general form of the asterisked definition set g albc a20bc Note that this is not the same as set g a0ibc a20bc although the sets which have 20 members each have 11 members in common As a last example the following are all illegal because they are not consistent with the rule given above for making lists set illegali a20bc al0bc illegal2 alx1 a9x9 illegal3 al b9 y Note one last time that set elements often referred to as labels can contain the sign characters and as well as letters and numbers 4 2 6 Declarations for Multiple Sets The keyword set if you prefer say sets instead the two are equivalent does not need to be used for each set rather only at the beginning of a group of sets It is often convenient to put a group of set declarations together 38 Set Definitions at the beginning of the program When this is done the set keyword need only be used once If you prefer to intermingle set declarations with other statements you will have to use a new set statement for each additional group of sets The following examp
398. uccinctly stated and easily read In this chapter we will discuss how sets are declared and initialized There are some more advanced set concepts such as assignments to sets as well as lag and lead operations but these are not introduced until much later in the book However the topics covered in this chapter will be enough to provide a good start on most models 4 2 Simple Sets A set S that contains the elements a b and c is written using normal mathematical notation as S a b c In GAMS notation because of character set limitations the same set must be written as set S a b c The set statement begins with the keyword set or sets S is the name of the set and its members are a b and c They are labels but are often referred to as elements or members 4 2 1 The Syntax In general the syntax in GAMS for simple sets is as follows set set_name text element text element text set_name text element text element text set_name is the internal name of the set also called an identifier in GAMS The accompanying text is used to describe the set or element immediately preceding it 4 2 2 Set Names The name of the set is an identifier An identifier has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long This is enough to construct meaningful names and explanatory text can be used to provide more
399. ucture INDEX 1 first i ii one b 5 636 two a 2 939 0 029 two b 10 346 three b 6 316 INDEX 1 second i ii one a INF 1 004 one b 17 299 two a INF two b 19 835 Notice that there are two sub tables one for each label in the first index position Note that the zero in the list for x first one a ii has vanished since zero values are suppressed in each sub table separately The order of the labels is not the same as in the input data list 14 5 Display Controls GAMS allows the user to modify the number of row and column labels in the display listing as well as the accuracy of the data being displayed The global display controls allows the user to affect more than one display statement If specific data need to be listed in a particular format the local display controls can be used to over ride the global controls The next two sub sections will deal with each of these display controls in turn 130 The Display Statement 14 5 1 Global Display Controls The simplest of these options is the one controlling the number of digits shown after the decimal point It affects numbers appearing in all display output following the option statement unless changed for a specific identifier as shown below The general form of the statement is option decimals value where value is an integer between 0 and 8 If you use 0 the decimal point is suppressed as well The width of the number field does not change j
400. uld be easy for anyone with a positive pulse rate GAMS is designed with the understanding that even the most experienced users will make errors GAMS attempts to catch the errors as soon as possible and to minimize their consequences 2 11 1 Echo Prints Whether or not errors prevent your optimization problem from being solved the first section of output from a GAMS run is an echo or copy of your input file For the sake of future reference GAMS puts line numbers on the left hand side of the echo For our transportation example which luckily contained no errors the echo print is as follows 3 Sets 4 i canning plants seattle san diego 5 j markets new york chicago topeka 6 7 Parameters 8 9 a i capacity of plant i in cases 10 seattle 350 11 san diego 600 12 13 b j demand at market j in cases 14 new york 325 15 chicago 300 16 topeka 275 17 18 Table d i j distance in thousands of miles 19 new york chicago topeka 20 seattle 2 5 La 1 8 2 11 GAMS Output 19 21 san diego 2 5 1 8 1 4 22 23 Scalar f freight in dollars per case per thousand miles 90 24 25 Parameter c i j transport cost in thousands of dollars per case 26 27 c i j f d i j 1000 28 29 Variables 30 x i j shipment quantities in cases 31 Zz total transportation costs in thousands of dollars 32 33 Positive Variable x 34 35 Equations 36 cost define objective function 37 supply i observe sup
401. unction 55 vector 167 weibull distribution 249 while example 152 statement 152 syntax 152 Windows 253 workdir GAMS call parameter 190 workspace model attribute 79 xor relational operator 115 xsave GAMS call parameter 190 zero default 167 ZLOOF example from GAMSLIB 113
402. use and add a table of the included functions to the listing file Before using individual functions you must declare them Function lt InternalFuncName gt lt InternalLibName gt lt FuncName gt Note that the syntax is similar to that used for declaring Sets Parameters Variables and so forth and that the control over potential naming conflicts extends to the names of the individual functions The lt InternalFuncName gt is the one that you will use in the rest of your model code The lt InternalLibName gt is the one that you created with the FuncLibIn directive and lt FuncName gt is the name given the function when the library was created Once functions have been declared with the Function statement they may be used exactly like intrinsic functions in the remainder of your model code 62 Data Manipulations with Parameters Example Here is an example that adds some concrete detail eolcom FuncLibIn trilib tridclib Make the library available trilib is the internal name being created now tridclib is the external name With no path GAMS will look for tridclib in the standard GAMS installation Declare each of the functions that will be used myCos mySin and MyPi are names being declared now for use in this model Cosine Sine and Pi are the function names from the library Note the use of the internal library name Y Ke Function myCos trilib Cosine mySin trilib Sine myPi trilib
403. use the GridDir option in order to be able to access previously created model instances I 6 Architecture and Customization The current Grid Facility relies on very basic operating system features and does not attempt to offer real and direct job or process control The file system is used to signal the completion of a submitted task and GAMS has currently no other way to interact with the submitted process directly like forcing termination or change the priority of a submitted task This approach has its obvious advantages and disadvantages There are a number of attempts to use grid computing to provide value added commercial remote computing services notably is SUN s recent commercial entry Commercial services require transparent and reliable charge approaches and related accounting and billing features which are still missing or inadequate When GAMS executes a solve under solvelink 3 it will perform the following steps 1 Create a subdirectory in the GridDir with the name gridnnn Where nnn stands for the numeric value of the handle The handle value is the internal symbol ID number x le6 the model instance number For example in the QMEANVAR example the first grid subdirectory was grid137000002 2 Remove the completion signal in case the file already exists Currently the signal is a file called finished For example grid137000002 finished 3 Create or replace a gdx file called gmsgrid gdx which will contain a dummy solution with
404. ust the number of decimals but this may cause numbers which would normally be displayed in fixed to appear in E format i e with the exponent represented explicitly Consider the following extension to the example discussed in the previous section option decimals 1 display x GAMS has rounded or converted numbers to E format where necessary and the output is as follows SENA 12 PARAMETER X a four dimensional structure INDEX 1 first i ii one b 5 6 two a 2 9 2 873000E 2 two b 10 3 three b 6 3 INDEX 1 second i ii one a INF 1 0 one b 17 3 two a INF two b 19 8 14 5 2 Local Display Control It is often more useful to control the number of decimals for specific identifiers separately Using a statement whose general form can do this option ident d value Ident represent the name of a parameter variable or equation and d value must be as before in the range 0 and 8 Exactly d value places of decimals will be shown on all displays of ident that follow This form can be extended to control layout of the data The general form is option ident d value r value c value Here r value means the number of index positions that are combined to form the row label and c value means the number on the column headers The example discussed in the previous section is further extended in order to illustrate the local display control option x 5 3 1 display x and the output 12 PARAMETER X a four dimensional
405. utorial by Richard E Rosenthal Z VAR DECLARED 31 IMPL ASN 48 REF 40 48 For example the cross reference list tells us that the symbol A is a parameter that was declared in line 10 defined assigned value in line 11 and referenced in line 43 The symbol I has a more complicated entry in the cross reference list It is shown to be a set that was declared and defined in line 5 It is referenced once in lines 10 19 26 28 31 38 45 and referenced twice in lines 41 and 43 Set I is also used as a controlling index in a summation equation definition or direct parameter assignment in lines 28 41 43 and 45 For the GAMS novice the detailed analysis of the cross reference list may not be important Perhaps the most likely benefit he or she will get from the reference maps will be the discovery of an unwanted entity that mistakenly entered the model owing to a punctuation or syntax error The second part of the reference map is a list of model entities grouped by type and listed with their associated documentary text For example this list is as follows sets i canning plants j markets parameters a capacity of plant i in cases b demand at market j in cases c transport cost in 1000s of dollars per case d distance in thousands of miles f freight in dollars per case per thousand miles variables x shipment quantities in cases z total transportation costs in 1000s of dollars equations cost define objective function demand sat
406. value of 255 will be used parmfile pf text secondary parameter file profile profile 0 global execution profiling option This option initializes the profile option see Appendix E to the value set and allows the profile of a GAMS run to be printed in the listing file The profile contains the individual and cumulative time required for the various sections of the GAMS model tw Setting the profile option through the option statement in the GAMS input file overrides the value of the profile parameter passed through the command line Values O no profiling 1 minimum profiling 2 detailed profiling A value of 0 does not cause an execution profile to be generated A value of 1 reports execution times for each statement and the number of set elements over which the particular statement is executed A value of 2 reports specific times for statements inside control structures like loops Running TRNSPORT with profile 1 provides the following additional information in the listing file aaa 1 EXEC INIT 0 010 0 010 SECONDS 43 ASSIGNMENT C 0 000 0 010 SECONDS 6 al 63 ASSIGNMENT TRANSPORT 0 000 0 010 SECONDS 65 SOLVE INIT TRANSPORT 0 000 0 020 SECONDS aS 56 EQUATION COST 0 000 0 020 SECONDS 1 asa 58 EQUATION SUPPLY 0 030 0 050 SECONDS 2 60 EQUATION DEMAND 0 000 0 050 SECONDS 3 ae 65 SOLVE FINI TRANSPORT 0 040 0 090 SECONDS Ssss 65 GAMS FINI 0 030 0 120 SECONDS A 1 EXEC INIT 0 000 0 000 SECONDS a 65 SOLVE READ TRANSPORT 0 020 0 0
407. wever separate the definition of the data type from the actual data entry For example the following succession of statements is valid Set i Set i seattle san diego This is true with the other data types as well This last feature is very useful in completely separating the model definition from the data and leads to the development of a good runtime GAMS model ts It is the responsibility of the modeler to ensure that the contents of the input file matches that of the work file although the compiler will issue errors if it detects any inconsistencies such as references to symbols not previously declared t A Work file can be used only by GAMS tasks requesting a restarted run t A Work file can be saved following a restarted run thus producing another work file that reflects the state of the job following completion of the statements in the continuation file F 3 Ways in which a Work File is Useful The basic function of a work file is to preserve information that has been expensive to produce Several reasons for wanting to do this are described in this section F 3 1 Separation of Model and Data The separation of model and data is one of the core principles of the GAMS modeling paradigm The use of save and restart features helps to exploit this separation Let us re arrange the contents of file1 gms and file2 gms to separate the model from the data The modified version of file1 gms is shown below Sets i canning plant
408. will be one constraint generated for each label combination that can constructed using the indices inside the parenthesis Here are two examples from AIRCRAFT a scheduling model bd j h b j h yd j m y j h dd j h y j h sum i p i j x i j e 1 The domain of definition of both equations is the Cartesian product of j and h constraints will be generated for every label pair that can be constructed from the membership of the two sets 8 3 5 Using Labels Explicitly in Equations It is often necessary to use labels explicitly in equations This can be done as with parameters by using quotes around the label Consider the following example dz tz e y jan yC feb y mar y apr 74 Equations 8 4 Expressions in Equation Definitions The arithmetic operators and functions that were described in Section 6 3 page 53 can be used inside equations as well 8 4 1 Arithmetic Operators in Equation Definitions t All the mechanisms that may be used to evaluate expressions in assignments are also available in equations Consider the following example adapted from CHENERY showing parentheses and exponentiation dem i y i e ynot i pd p i thet i 8 4 2 Functions in Equation Definitions Function references in equation definitions can be classified into two types based on the type of the arguments Exogenous arguments The arguments s are known Parameters and variable a
409. will be stopped at the next convenient opportunity A model will never be solved after an error has been detected The only remedy is to fix the error and repeat the run Errors are grouped into the three phases of GAMS modeling compilation execution and model generation which includes the solution that follows The following three sub sections discuss these types of errors 10 6 1 Compilation Errors Compilation errors were discussed in some detail in Chapter 2 There is some overlap between the material in those sections and this one Several hundred different types of errors can be detected during compilation and can often be traced back to just one specific symbol in the GAMS input Most of the errors will be caused by simple mistakes forgetting to declare an identifier putting indices in the wrong order leaving out a necessary semicolon or misspelling a label For errors that are not caused by mistakes the explanatory error message text will help you diagnose the problem and correct it ts When a compilation error is discovered a symbol and error number are printed below the offending symbol usually to the right on a separate line that begins with the four asterisks If more than one error is encountered on a line possibly because the first error caused a series of other spurious errors the signs may be suppressed and error number squeezed GAMS will not list more than 10 errors on any one line t At the end of the echo print
410. x 1o i j x up seattle 2 10 The lo l up m Database 17 It is assumed in the first and third examples that capacity i j is a parameter that was previously declared and assigned values These statements must appear after the variable declaration and before the Solve statement All the mathematical expressions available for direct assignments are usable on the right hand side In nonlinear programming it is very important for the modeler to help the solver by specifying as narrow a range as possible between lower and upper bound It is also very helpful to specify an initial solution from which the solver can start searching for the optimum For example in a constrained inventory model the variables are quantity i and it is known that the optimal solution to the unconstrained version of the problem is a parameter called eoq i As a guess for the optimum of the constrained problem we enter quantity 1 i 0 5 eoq i The default initial level is zero unless zero is not within the bounded range in which case it is the bound closest to zero It is important to understand that the 1o and up fields are entirely under the control of the GAMS user The l and m fields in contrast can be initialized by the user but are then controlled by the solver 2 10 2 Transformation and Display of Optimal Values This section can be skipped on first reading if desired After the optimizer is called via the solve statement the v
411. xcept the last statement where a semicolon is optional 3 2 1 Format of GAMS Input GAMS input is free format A statement can be placed anywhere on a line multiple statements can appear on a line or a statement can be continued over any number of lines as follows statement statement statement statement statement the words that you are now reading is an example of a very long statement which is stretched over two lines Blanks and end of lines can generally be used freely between individual symbols or words GAMS is not case sensitive meaning that lower and upper case letters can be mixed freely but are treated identically Up to 255 characters can be placed on a line and completely blank lines can be inserted for easier reading Not all lines are a part of the GAMS language Two special symbols the asterisk and the dollar symbol can be used in the first position on a line to indicate a non language input line An asterisk in column one means 28 GAMS Programs that the line will not be processed but treated as a comment A dollar symbol in the same position indicates that compiler options are contained in the rest of the line Multiple files can be used as input through the use of the include facility described in Appendix D In short the statement include filel inserts the contents of the specified file filel in this case at the location of the call A more complex versions of this is the batinc
412. xes to specify many attributes such as the printing format page size page width margins and the case which text is displayed in The following file suffixes can be used for formatting print control pc Used to specify the format of the external file The options 4 5 6 and 8 create delimited files which are especially useful when preparing output for the direct importation into other computer programs such as spreadsheets 0 Standard paging based on the current page size Partial pages are padded with blank lines Note that the bm file suffix is only functional when used with this print control option 1 FORTRAN page format This option places the numeral one in the first column of the first row of each page in the standard FORTRAN convention 2 Continuous page default This option is similar to pc option zero with the exception that partial pages in the file are not padded with blank lines to fill out the page 3 ASCII page control characters inserted 15 6 Page Sections 137 4 Formatted output Non numeric output is quoted and each item is delimited with a blank space 5 Formatted output Non numeric output is quoted and each item is delimited with commas 6 Formatted output Non numeric output is quoted and each item is delimited with tabs 7 Fixed width Fills up line with trailing blanks 8 Formatted output Each item is delimited with a blank space page size ps Used to specify the number of rows lines which can be plac
413. xplained In Chapter 9 all the actions that are triggered by a solve were listed All output produced as a result of a solve is labeled with a subtitle identifying the model its type and the line number of the solve statement 10 5 1 The Equation Listing The first output is the Equation Listing which is marked with that subtitle on the output file By default the first three equations in every block are listed If there are three or fewer single equations in any equation block then all the single equations are listed The equation listing section from the example is listed below This model has three equation blocks each producing one single equation A Quadratic Programming Model for Portfolio Analysis ALAN SEQ 124a Equation Listing SOLVE PORTFOLIO USING NLP FROM LINE 48 FSUM E fractions must add to 1 0 FSUM X hardware X software X show biz X t bills E 1 LHS 0 INFES 1 DMEAN E definition of mean return on portfolio DMEAN 8 X hardware 9 X software 12 X show biz 7 X t bills i t i p o LHS 0 INFES 10 xxx DVAR E definition of variance DVAR 0 X hardware 0 X software 0 X show biz VARIANCE E O LHS 0 ts The equation listing is an extremely useful debugging aid It shows the variables that appear in each constraint and what the individual coefficients and right hand side value evaluate to after the data manipulations have been done Mo
414. y for the reader and meet all the requirements of proper English GAMS acts like a personal assistant with knowledge of mathematical modeling and of the syntactic and semantic details of the language Errors are detected at various stages in the modeling process Most of them are caught at the compilation stage which behaves like the proofreading stage of the modeling process Once a problem has passed through the rigorous test of this stage the error rate drops almost to zero Most of the execution runs which are much more expensive than compilation proceed without difficulties because GAMS knows about modeling and has anticipated problems Many of the typical errors made with conventional programming languages are associated with concepts that do not exist in GAMS Those error sources such as address calculations storage assignment subroutine linkages input output and flow control create problems at execution time are difficult to locate often lead to long and frustrating searches and leave the computer user intimidated GAMS takes a radically different approach Errors are spotted as early as possible are reported in a way understandable to the user including clear suggestions for how to correct the problem and a presentation of the source of the error in terms of the user s problem t All errors are marked with four asterisks at the beginning of a line in the output listing As soon as an error is detected processing
415. y people and by computers This means that the GAMS program itself is the documentation of the model and that the separate description required in the past which was a burden to maintain and which was seldom up to date is no longer needed Moreover the design of GAMS incorporates the following features that specifically address the user s documentation needs gt A GAMS model representation is concise and makes full use of the elegance of the mathematical representation gt All data transformations are specified concisely and algebraically This means that all data can be entered in their most elemental form and that all transformations made in constructing the model and in reporting are available for inspection gt Explanatory text can be made part of the definition of all symbols and is reproduced whenever associated values are displayed gt All information needed to understand the model is in one document Of course some discipline is needed to take full advantage of these design features but the aim is to make models more accessible more understandable more verifiable and hence more credible 1 2 3 Portability The GAMS system is designed so that models can be solved on different types of computers with no change A model developed on a small personal computer can later be solved on a large mainframe One person can develop a model that is later used by others who may be physically distant from the original developer In con
416. y sensitivity analysis can be done but also how the associated multi case reporting can be handled The parameter qs is used to set the upper bound on the sulfur content in the fuel oil and the value is retrieved for the report The output from the display is shown below Notice that there is no production at all if the permissible sulfur content is lowered The case attributes have been listed in the row SULFUR LIMIT The wild card domain is useful when generating reports otherwise it would be necessary to provide special sets containing the labels used in the report Any mistakes made in spelling labels used only in the report should be immediately apparent and their effects should be limited to the report Section 14 5 1 page 130 contains more detail on how to arrange reports in a variety of ways Sao 205 PARAMETER REPORT PROCESS LEVEL REPORT BASE ONE TWO MID C A DIST 89 718 35 139 MID C N REFORM 20 000 6 772 MID C CC DIST 7 805 3 057 W TEX CC GAS OIL 5 902 W TEX A DIST 64 861 W TEX N REFORM 12 713 W TEX CC DIST 4 735 W TEX HYDRO 28 733 SULFUR LIMIT 3 500 3 400 5 000 9 4 3 Iterative Implementation of Non Standard Algorithms Another use of multiple solve statements is to permit iterative solution of different blocks of equations solution values from the first are used as data in the next These decomposition methods are useful for certain classes of problems because the sub problems being solved are smaller and therefore mo
417. yes subitem3 subitem1 yes 12 4 2 Set Intersection The symbol performs the set intersection operation Consider the following example subitem3 item subitemi item subitem2 item The membership of subitem3 is set equal to only those present in both subitem1 and subitem2 The operation above is equivalent to the following longer way of representation subitem3 item yes subitem1 item and subitem2 item 12 4 3 Set Complement The operator not performs the set complement operation Consider the following example subitem3 item not subitemi item The membership of subitem3 is set equal to all those in item but not in subitem1 The operation above is equivalent to the following longer way of representation subitem3 item yes subitem3 subitem1 no 12 4 4 Set Difference The operator performs the set difference operation Consider the following example subitem3 item subitemi item subitem2 item The membership of subitem3 is set equal to all elements that are members of subitem1 but subitem2 The operation above is equivalent to the following longer way of representation subitem3 item yes subitem1 item subitem3 subitem2 no 12 5 Summary The purpose of set assignments is to make calculations based on given data the static sets for use in exception handling It is one more example of the principle of entering a small amount of data and building a model up from the most elemental information
418. ype lp sets solver for 1p model type nlp sets solver for nlp model type mcp sets solver for mcp model type rminlp sets solver for rminlp model type minlp sets solver for minlp model type rmip sets solver for rmip model type Options affecting input program control seed resets seed for pseudo random number generator solveopt controls return of solution values to GAMS Table E 1 GAMS options E 3 Detailed Description of Options This section describes each of the options in detail The options are listed in alphabetical order for easy reference In each of the following options the default value if available is bracketed E 3 Detailed Description of Options 217 lt identifier gt Display specifier identifier d identifier d r c Defines print formats for identifier when used in a display statement d is the number of decimal places r is the number of index positions printed as row labels c is the number of index positions printed as column labels the remaining index positions if any will be used to index the planes index order plane row column if r is zero list format will be used The default setting is described in Section 14 4 bratio 0 25 Certain solution procedures can restart from an advanced basis that is constructed automatically This option is used to specify whether or not basis information probably from an earlier solve is used The use of this basis is rejected if the number of basic variables is smaller th
419. ype is free which means that if the type of the variable is not specified it will not be bounded at all The most frequently used types are free and positive for descriptions of variables for which negative values are meaningless such as capacities quantities or prices Four additional although more exotic variable types sos1 sos2 semicont and semiint are available in GAMS These are explained in Section 17 2 1 7 2 3 Styles for Variable Declaration Two styles are commonly used to declare variable types The first is to list all variables with domain specifications and explanatory text as a group and later to group them separately as to type The example shown below is adapted from MEXSS The default type is free so phi phipsi etc will be free variables in the example below Note the use of variable names derived from the original mathematical representation variables u c i purchase of domestic materials mill units per yr v c j imports mill tpy e c i exports mill tpy phi total cost mill us phipsi raw material cost mill us positive variables u v e The commas in the list of positive variables are required separators ts It is possible to declare an identifier more than once but that the second and any subsequent declarations should only add new information that does not contradict what has already been entered The second popular way of declaring variables is to list them in groups by type W
420. ytically specified way For example suppose a country has 56 million people in the base period and population is growing at the rate of 1 5 percent per year Then the population in succeeding years can be calculated by using population t 56 1 015 ord t 1 It is often useful to simulate general matrix operations in GAMS The first index on a two dimensional parameter can conveniently represent the rows and the second the columns and order is necessary The example below shows how to set the upper triangle of a matrix equal to the row index plus the column index and the diagonal and lower triangle to zero set i row and column labels x1 x10 alias i j parameter a i j a general square matrix a i j ord i 1t ord j ord i ord j 13 4 Lag and Lead Operators 121 13 3 2 The Card Operator Card returns the number of elements in a set Card can be used with any set even dynamic or unordered ones The following example illustrates its use set t time periods 1985 1995 parameter s s card t As a result of the statement above s will be assigned the value 11 A common use of card is to specify some condition only for the final period for example to fix a variable An artificial example is c fx t ord t card t demand t which fixes the variable for the last member only no assignment is made for other members of t The advantage of this way of fixing c is that the membership of t can be

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GAMS — A User's Guide