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: param a{i in I};
alpar@1: /* capacity of plant i in cases */
alpar@1: 
alpar@1: table plants IN "MySQL"
alpar@1:   'Database=glpk;UID=glpk;PWD=gnu'
alpar@1:   'SELECT PLANT, CAPA AS CAPACITY FROM transp_capa' :
alpar@1:    I <- [ PLANT ], a ~ CAPACITY;
alpar@1: 
alpar@1: set J;
alpar@1: /* markets */
alpar@1: 
alpar@1: param b{j in J};
alpar@1: /* demand at market j in cases */
alpar@1: 
alpar@1: table markets IN "MySQL"
alpar@1:   'Database=glpk;UID=glpk;PWD=gnu'
alpar@1:   'transp_demand' :
alpar@1:   J <- [ MARKET ], b ~ DEMAND;
alpar@1: 
alpar@1: param d{i in I, j in J};
alpar@1: /* distance in thousands of miles */
alpar@1: 
alpar@1: table dist IN "MySQL"
alpar@1:   'Database=glpk;UID=glpk;PWD=gnu'
alpar@1:   'transp_dist' :
alpar@1:   [ LOC1, LOC2 ], d ~ DIST;
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: solve;
alpar@1: 
alpar@1: table result{i in I, j in J: x[i,j]} OUT "MySQL"
alpar@1:   'Database=glpk;UID=glpk;PWD=gnu'
alpar@1:   'DELETE FROM transp_result;'
alpar@1:   'INSERT INTO transp_result VALUES (?,?,?)' :
alpar@1:   i ~ LOC1, j ~ LOC2, x[i,j] ~ QUANTITY;
alpar@1: 
alpar@1: data;
alpar@1: 
alpar@1: param f := 90;
alpar@1: 
alpar@1: end;