You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
70 lines
1.6 KiB
70 lines
1.6 KiB
# 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;
|