# A TRANSPORTATION PROBLEM

#

# This problem finds a least cost shipping schedule that meets

# requirements at markets and supplies at factories.

#

#  References:

#              Dantzig G B, "Linear Programming and Extensions."

#              Princeton University Press, Princeton, New Jersey, 1963,

#              Chapter 3-3.

set I;

/* canning plants */

set J;

/* markets */

param a{i in I};

/* capacity of plant i in cases */

param b{j in J};

/* demand at market j in cases */

param d{i in I, j in J};

/* distance in thousands of miles */

param f;

/* freight in dollars per case per thousand miles */

param c{i in I, j in J} := f * d[i,j] / 1000;

/* transport cost in thousands of dollars per case */

var x{i in I, j in J} >= 0;

/* shipment quantities in cases */

minimize cost: sum{i in I, j in J} c[i,j] * x[i,j];

/* total transportation costs in thousands of dollars */

s.t. supply{i in I}: sum{j in J} x[i,j] <= a[i];

/* observe supply limit at plant i */

s.t. demand{j in J}: sum{i in I} x[i,j] >= b[j];

/* satisfy demand at market j */

data;

set I := Seattle San-Diego;

set J := New-York Chicago Topeka;

param a := Seattle     350

           San-Diego   600;

param b := New-York    325

           Chicago     300

           Topeka      275;

param d :              New-York   Chicago   Topeka :=

           Seattle     2.5        1.7       1.8

           San-Diego   2.5        1.8       1.4  ;

param f := 90;

end;