trnsport.gms : A Transportation Problem

Description

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


References

  • Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.
  • Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide. The Scientific Press, Redwood City, California, 1988.

Small Model of Type : LP


Category : GAMS Model library


Main file : trnsport.gms

$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 ;