GAMS - Programming language

GAMS is an open source programming language created in 1963.

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The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maintainable models that can be adapted to new situations. Read more on Wikipedia...

GAMS Wikipedia page
There are at least 810 GAMS repos on GitHub
GAMS first developed in GAMS Development Corporation
file extensions for GAMS include gms
The Google BigQuery Public Dataset GitHub snapshot shows 43 users using GAMS in 49 repos on GitHub
See also: (1 related languages)Algebraic modeling language

Example from the web:

*Basic example of transport model from GAMS model library

$Title  A Transportation Problem (TRNSPORT,SEQ=1)
$Ontext

This problem finds a least cost shipping schedule that meets
requirements at markets and supplies at factories.


Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.

This formulation is described in detail in:
Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide.
The Scientific Press, Redwood City, California, 1988.

The line numbers will not match those in the book because of these
comments.

$Offtext


  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/ ;

  Solve transport using lp minimizing z ;

  Display x.l, x.m ;

$ontext
#user model library stuff
Main topic Basic GAMS
Featured item 1 Trnsport model
Featured item 2
Featured item 3
Featured item 4
Description
Basic example of transport model from GAMS model library



$offtext

Example from Wikipedia:

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/ ;
 Solve transport using lp minimizing z ;
 Display x.l, x.m ;