General Algebraic Modeling System

The General Algebraic Modeling System is an algebraic modeling language for mathematical optimization problems whose origins lie in a research project of the World Bank. From 1987 the system will be further developed by the GAMS Development Corp.. , USA and distributed in Europe by the GAMS Software GmbH.

In addition to large linear and integer optimization problems can be personalized with algebraic modeling languages ​​such as GAMS or AMPL other Modellierungssprobleme, basically formulate and efficiently solve such as quadratic, nonlinear, gemischtganzzahlig not linear, quadratic, stochastic or global optimization problems independently of the algorithms used. The fundamental separation of levels

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

And extensive model libraries provide further elements of algebraic modeling languages ​​dar.

The main applications of the GAMS system lie in the classic operations research areas. Besides, the system is also frequently used for macroeconomic issues as under equilibrium models.

Model example

Transport model by George Dantzig. This model is part of the GAMS model library. In this problem, the transportation plan is searched with the lowest total cost that satisfies both the market conditions of the customer so well the the producers.

Sets        i canning plants / seattle, san diego - /        j markets / new-york, chicago, topeka /;   parameter        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; References

General equilibrium theory
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