alpar@9: # A TRANSPORTATION PROBLEM
alpar@9: #
alpar@9: # This problem finds a least cost shipping schedule that meets
alpar@9: # requirements at markets and supplies at factories.
alpar@9: #
alpar@9: #  References:
alpar@9: #              Dantzig G B, "Linear Programming and Extensions."
alpar@9: #              Princeton University Press, Princeton, New Jersey, 1963,
alpar@9: #              Chapter 3-3.
alpar@9: 
alpar@9: set I;
alpar@9: /* canning plants */
alpar@9: 
alpar@9: param a{i in I};
alpar@9: /* capacity of plant i in cases */
alpar@9: 
alpar@9: table plants IN "MySQL"
alpar@9:   'Database=glpk;UID=glpk;PWD=gnu'
alpar@9:   'SELECT PLANT, CAPA AS CAPACITY FROM transp_capa' :
alpar@9:    I <- [ PLANT ], a ~ CAPACITY;
alpar@9: 
alpar@9: set J;
alpar@9: /* markets */
alpar@9: 
alpar@9: param b{j in J};
alpar@9: /* demand at market j in cases */
alpar@9: 
alpar@9: table markets IN "MySQL"
alpar@9:   'Database=glpk;UID=glpk;PWD=gnu'
alpar@9:   'transp_demand' :
alpar@9:   J <- [ MARKET ], b ~ DEMAND;
alpar@9: 
alpar@9: param d{i in I, j in J};
alpar@9: /* distance in thousands of miles */
alpar@9: 
alpar@9: table dist IN "MySQL"
alpar@9:   'Database=glpk;UID=glpk;PWD=gnu'
alpar@9:   'transp_dist' :
alpar@9:   [ LOC1, LOC2 ], d ~ DIST;
alpar@9: 
alpar@9: param f;
alpar@9: /* freight in dollars per case per thousand miles */
alpar@9: 
alpar@9: param c{i in I, j in J} := f * d[i,j] / 1000;
alpar@9: /* transport cost in thousands of dollars per case */
alpar@9: 
alpar@9: var x{i in I, j in J} >= 0;
alpar@9: /* shipment quantities in cases */
alpar@9: 
alpar@9: minimize cost: sum{i in I, j in J} c[i,j] * x[i,j];
alpar@9: /* total transportation costs in thousands of dollars */
alpar@9: 
alpar@9: s.t. supply{i in I}: sum{j in J} x[i,j] <= a[i];
alpar@9: /* observe supply limit at plant i */
alpar@9: 
alpar@9: s.t. demand{j in J}: sum{i in I} x[i,j] >= b[j];
alpar@9: /* satisfy demand at market j */
alpar@9: 
alpar@9: solve;
alpar@9: 
alpar@9: table result{i in I, j in J: x[i,j]} OUT "MySQL"
alpar@9:   'Database=glpk;UID=glpk;PWD=gnu'
alpar@9:   'DELETE FROM transp_result;'
alpar@9:   'INSERT INTO transp_result VALUES (?,?,?)' :
alpar@9:   i ~ LOC1, j ~ LOC2, x[i,j] ~ QUANTITY;
alpar@9: 
alpar@9: data;
alpar@9: 
alpar@9: param f := 90;
alpar@9: 
alpar@9: end;