GAMS的使用

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The General Algebraic Modeling System (GAMS)是一款数学规划和优化的高级建模系统。本文简单通过一个例子简单介绍GAMS的用法。

GAMS官方网站：http://www.gams.com/

例子：运输问题基本模型

代码：

复制代码

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 thousand 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 thousand of dollars per case;
              c(i,j) = f*d(i,j)/1000;
      variables
          x(i,j)
          z;
      positive variable x;
      equations
          cost
          supply(i)
          demand(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;

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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 thousand 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 thousand of dollars per case;
              c(i,j) = f*d(i,j)/1000;
      variables
          x(i,j)
          z;
      positive variable x;
      equations
          cost
          supply(i)
          demand(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;