# 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 */

 param a{i in I};

 /* capacity of plant i in cases */

 table plants IN "MySQL"

   'Database=glpk;UID=glpk;PWD=gnu'

   'SELECT PLANT, CAPA AS CAPACITY FROM transp_capa' :

    I <- [ PLANT ], a ~ CAPACITY;

 set J;

 /* markets */

 param b{j in J};

 /* demand at market j in cases */

 table markets IN "MySQL"

   'Database=glpk;UID=glpk;PWD=gnu'

   'transp_demand' :

   J <- [ MARKET ], b ~ DEMAND;

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

 /* distance in thousands of miles */

 table dist IN "MySQL"

   'Database=glpk;UID=glpk;PWD=gnu'

   'transp_dist' :

   [ LOC1, LOC2 ], d ~ DIST;

 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 */

 solve;

 table result{i in I, j in J: x[i,j]} OUT "MySQL"

   'Database=glpk;UID=glpk;PWD=gnu'

   'DELETE FROM transp_result;'

   'INSERT INTO transp_result VALUES (?,?,?)' :

   i ~ LOC1, j ~ LOC2, x[i,j] ~ QUANTITY;

 data;

 param f := 90;

 end;