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: set K dimen 2;
alpar@1: /* transportation lane */
alpar@1: 
alpar@1: set L;
alpar@1: /* parameters */
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 e{l in L};
alpar@1: /* parameters */
alpar@1: 
alpar@1: param f;
alpar@1: /* freight in dollars per case per thousand miles */
alpar@1: 
alpar@1: table tab_plant IN "CSV" "plants.csv" :
alpar@1:   I <- [plant], a ~ capacity;
alpar@1: 
alpar@1: table tab_market IN "CSV" "markets.csv" :
alpar@1:   J <- [market], b ~ demand;
alpar@1: 
alpar@1: table tab_distance IN "CSV" "distances.csv" :
alpar@1:   K <- [plant, market], d ~ distance;
alpar@1: 
alpar@1: table tab_parameter IN "CSV" "parameters.csv" :
alpar@1:   L <- [parameter], e ~ value ;
alpar@1: 
alpar@1: param c{i in I, j in J} := e['transport cost'] * d[i,j] / 1000;
alpar@1: /* transport cost in thousands of dollars per case */
alpar@1: 
alpar@1: var x{(i,j) in K} >= 0;
alpar@1: /* shipment quantities in cases */
alpar@1: 
alpar@1: minimize cost: sum{(i,j) in K} 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{(i,j) in K} 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,j) in K} x[i,j] >= b[j];
alpar@1: /* satisfy demand at market j */
alpar@1: 
alpar@1: solve;
alpar@1: 
alpar@1: table tab_result{(i,j) in K} OUT "CSV" "result.csv" :
alpar@1:   i ~ plant, j ~ market, x[i,j] ~ shipment;
alpar@1: 
alpar@1: end;