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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 */
set J;/* markets */
set K dimen 2;/* transportation lane */
set L;/* parameters */
param a{i in I};/* capacity of plant i in cases */
param b{j in J};/* demand at market j in cases */
param d{i in I, j in J};/* distance in thousands of miles */
param e{l in L};/* parameters */
param f;/* freight in dollars per case per thousand miles */
table tab_plant IN "CSV" "plants.csv" : I <- [plant], a ~ capacity;
table tab_market IN "CSV" "markets.csv" : J <- [market], b ~ demand;
table tab_distance IN "CSV" "distances.csv" : K <- [plant, market], d ~ distance;
table tab_parameter IN "CSV" "parameters.csv" : L <- [parameter], e ~ value ;
param c{i in I, j in J} := e['transport cost'] * d[i,j] / 1000;/* transport cost in thousands of dollars per case */
var x{(i,j) in K} >= 0;/* shipment quantities in cases */
minimize cost: sum{(i,j) in K} c[i,j] * x[i,j];/* total transportation costs in thousands of dollars */
s.t. supply{i in I}: sum{(i,j) in K} x[i,j] <= a[i];/* observe supply limit at plant i */
s.t. demand{j in J}: sum{(i,j) in K} x[i,j] >= b[j];/* satisfy demand at market j */
solve;
table tab_result{(i,j) in K} OUT "CSV" "result.csv" : i ~ plant, j ~ market, x[i,j] ~ shipment;
end;
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