# 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 */

 set K dimen 2;

 /* transportation lane */

 set L;

 /* parameters */

 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 e{l in L};

 /* parameters */

 param f;

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

 table tab_plant IN "CSV" "plants.csv" :

   I <- [plant], a ~ capacity;

 table tab_market IN "CSV" "markets.csv" :

   J <- [market], b ~ demand;

 table tab_distance IN "CSV" "distances.csv" :

   K <- [plant, market], d ~ distance;

 table tab_parameter IN "CSV" "parameters.csv" :

   L <- [parameter], e ~ value ;

 param c{i in I, j in J} := e['transport cost'] * d[i,j] / 1000;

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

 var x{(i,j) in K} >= 0;

 /* shipment quantities in cases */

 minimize cost: sum{(i,j) in K} c[i,j] * x[i,j];

 /* total transportation costs in thousands of dollars */

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

 /* observe supply limit at plant i */

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

 /* satisfy demand at market j */

 solve;

 table tab_result{(i,j) in K} OUT "CSV" "result.csv" :

   i ~ plant, j ~ market, x[i,j] ~ shipment;

 end;