General Algebraic Modeling System

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GAMS
Basic data

developer GAMS Development Corporation
Current  version 31.1.1
( May 16, 2020 )
operating system Platform independent
category Algebraic modeling language
License Proprietary
www.gams.com

The G eneral A lgebraic M odeling S ystem is an algebraic modeling language for mathematical optimization problems whose origins in a research project of the World Bank are. From 1987 the system is further developed by GAMS Development Corp., USA, and distributed in Europe by GAMS Software GmbH.

In addition to large linear or integer optimization problems , algebraic modeling languages ​​such as GAMS or AMPL can also be used to efficiently formulate and solve other modeling problems such as non-linear, mixed- integer non-linear, quadratic, stochastic or global optimization problems, regardless of the algorithms used. The basic separation of the levels

  • Problem representation and solution,
  • Modeling level and user interface,
  • Model formulation and data,
  • Model formulation and operating system ,

as well as extensive model libraries represent further elements of algebraic modeling languages.

The main areas of application of the GAMS system are in the classic operations research areas. In addition, the system is also often used for macroeconomic issues, for example in the context of equilibrium models.

Model example

Transport model by George Dantzig . This model is part of the GAMS model library. In this problem, the transport plan with the lowest total cost is sought that meets both the market conditions of the buyers and those of the producers. 

  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 ;

See also

literature

  • Anthony Brooke, David Kendrick, Alexander Meeraus: Gams: A User's Guide. Tutorial by Rick Rosenthal . GAMS Development Corporation, Washington, DC, USA 2010 ( gams.com [PDF]).

Web links

Individual evidence

  1. ↑ George B. Dantzig: Linear Programming and Extensions . Princeton University Press, Princeton 2016, ISBN 978-1-4008-8417-9 , 3.3. A Transportation Problem , p. 35 ( books.google.de - first edition: 1963, excerpt).