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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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