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# 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;
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