alpar@1: # A TRANSPORTATION PROBLEM
alpar@1: #
alpar@1: # This problem finds a least cost shipping schedule that meets
alpar@1: # requirements at markets and supplies at factories.
alpar@1: #
alpar@1: #  References:
alpar@1: #              Dantzig G B, "Linear Programming and Extensions."
alpar@1: #              Princeton University Press, Princeton, New Jersey, 1963,
alpar@1: #              Chapter 3-3.
alpar@1: 
alpar@1: set I;
alpar@1: /* canning plants */
alpar@1: 
alpar@1: set J;
alpar@1: /* markets */
alpar@1: 
alpar@1: param a{i in I};
alpar@1: /* capacity of plant i in cases */
alpar@1: 
alpar@1: param b{j in J};
alpar@1: /* demand at market j in cases */
alpar@1: 
alpar@1: param d{i in I, j in J};
alpar@1: /* distance in thousands of miles */
alpar@1: 
alpar@1: param f;
alpar@1: /* freight in dollars per case per thousand miles */
alpar@1: 
alpar@1: param c{i in I, j in J} := f * d[i,j] / 1000;
alpar@1: /* transport cost in thousands of dollars per case */
alpar@1: 
alpar@1: var x{i in I, j in J} >= 0;
alpar@1: /* shipment quantities in cases */
alpar@1: 
alpar@1: minimize cost: sum{i in I, j in J} c[i,j] * x[i,j];
alpar@1: /* total transportation costs in thousands of dollars */
alpar@1: 
alpar@1: s.t. supply{i in I}: sum{j in J} x[i,j] <= a[i];
alpar@1: /* observe supply limit at plant i */
alpar@1: 
alpar@1: s.t. demand{j in J}: sum{i in I} x[i,j] >= b[j];
alpar@1: /* satisfy demand at market j */
alpar@1: 
alpar@1: data;
alpar@1: 
alpar@1: set I := Seattle San-Diego;
alpar@1: 
alpar@1: set J := New-York Chicago Topeka;
alpar@1: 
alpar@1: param a := Seattle     350
alpar@1:            San-Diego   600;
alpar@1: 
alpar@1: param b := New-York    325
alpar@1:            Chicago     300
alpar@1:            Topeka      275;
alpar@1: 
alpar@1: param d :              New-York   Chicago   Topeka :=
alpar@1:            Seattle     2.5        1.7       1.8
alpar@1:            San-Diego   2.5        1.8       1.4  ;
alpar@1: 
alpar@1: param f := 90;
alpar@1: 
alpar@1: end;