How to get started with GAMS

1. How to get started with GAMS MS&E 348 – Lecture 1/20/04

2. GAMS Basics • The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical programming problems • It consists of a language compiler and a stable of integrated high-performance solvers • GAMS is tailored for complex, large scale modeling applications, and allows you to build large maintainable models that can be adapted quickly to new situations

3. Some GAMS References • www.gams.com • A User’s Guide by Brooke et al. • GAMS Tutorial by Rosenthal (ch. 2 of above) Transportation Problem Canning plants / Capacity a(i) Markets / Demand b(j) Transport cost c(i,j) Seattle New York Chicago San Diego Topeka

4. Structure of a GAMS model Output Input file_name.lst file_name.gms Sets Echo Print Data Reference Maps Variables Equation Listings Equations Status Reports Model specification Results Solve statement

5. Program Listing 1/3 * Instance of the transportation problem * From R. Rosenthal's GAMS Tutorial 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 /;

6. Program Listing 2/3 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 1000 miles / 90 /; parameter c(i,j) transport cost in 1000s 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 1000s of dollars; positive variable x;

7. Program Listing 3/3 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/; solve transport using lp minimizing z; display x.l, x.m;

8. Implementation • From Leland account • Type input file in standard text editor (emacs, etc.) • Run with following command:/usr/sweet/apps/gams-2.50/gams file_name.gms • Programming styles • Data -> Model -> Solution • Model -> Data -> Solution • General remarks • Distinguish between ‘declaration’ and ‘assignment’ or ‘definition’ • An entity of the model cannot be referenced before it is declared to exist • Useful feature not discussed in the tutorial: the ‘dollar’ operator • This powerful feature of GAMS operates with a logical condition $(condition), which can be read as ‘such that condition is valid’ • Example: • If (b > 1.5) then a = 2 becomes • a$(b > 1.5) = 2; • This operator is very useful to handle exceptions

9. Other Remarks • Documentation is crucial. It is returned in the output file • Compiler options can be used Example of line: $include file_name • Advantage of GAMS over Fortran or C: values can be assigned without ‘do loops’ • Key idea is that the definition of the constraints is exactly the same regardless of the size of the problem: the user just enters equations algebraically and GAMS creates the specific equations appropriate for the model at hand • Don’t get confused by error messages! • Read the output file! • Equation listings are useful for checking the model • Don’t wait to get started!