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/* FCTP, Fixed-Charge Transportation Problem */
/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
/* The Fixed-Charge Transportation Problem (FCTP) is obtained from classical transportation problem by imposing a fixed cost on each transportation link if there is a positive flow on that link. */
param m, integer, > 0;/* number of sources */
param n, integer, > 0;/* number of customers */
set I := 1..m;/* set of sources */
set J := 1..n;/* set of customers */
param supply{i in I}, >= 0;/* supply at source i */
param demand{j in J}, >= 0;/* demand at customer j */
param varcost{i in I, j in J}, >= 0;/* variable cost (a cost per one unit shipped from i to j) */
param fixcost{i in I, j in J}, >= 0;/* fixed cost (a cost for shipping any amount from i to j) */
var x{i in I, j in J}, >= 0;/* amount shipped from source i to customer j */
s.t. f{i in I}: sum{j in J} x[i,j] = supply[i];/* observe supply at source i */
s.t. g{j in J}: sum{i in I} x[i,j] = demand[j];/* satisfy demand at customer j */
var y{i in I, j in J}, binary;/* y[i,j] = 1 means some amount is shipped from i to j */
s.t. h{i in I, j in J}: x[i,j] <= min(supply[i], demand[j]) * y[i,j];/* if y[i,j] is 0, force x[i,j] to be 0 (may note that supply[i] and demand[j] are implicit upper bounds for x[i,j] as follows from the constraints f[i] and g[j]) */
minimize cost: sum{i in I, j in J} varcost[i,j] * x[i,j] + sum{i in I, j in J} fixcost[i,j] * y[i,j];/* total transportation costs */
data;
/* These data correspond to the instance bal8x12 from [Balinski]. */
/* The optimal solution is 471.55 */
param m := 8;
param n := 12;
param supply := 1 15.00, 2 20.00, 3 45.00, 4 35.00, 5 25.00, 6 35.00, 7 10.00, 8 25.00;
param demand := 1 20.00, 2 15.00, 3 20.00, 4 15.00, 5 5.00, 6 20.00, 7 30.00, 8 10.00, 9 35.00, 10 25.00, 11 10.00, 12 5.00;
param varcost : 1 2 3 4 5 6 7 8 9 10 11 12 := 1 0.69 0.64 0.71 0.79 1.70 2.83 2.02 5.64 5.94 5.94 5.94 7.68 2 1.01 0.75 0.88 0.59 1.50 2.63 2.26 5.64 5.85 5.62 5.85 4.94 3 1.05 1.06 1.08 0.64 1.22 2.37 1.66 5.64 5.91 5.62 5.91 4.94 4 1.94 1.50 1.56 1.22 1.98 1.98 1.36 6.99 6.99 6.99 6.99 3.68 5 1.61 1.40 1.61 1.33 1.68 2.83 1.54 4.26 4.26 4.26 4.26 2.99 6 5.29 5.94 6.08 5.29 5.96 6.77 5.08 0.31 0.21 0.17 0.31 1.53 7 5.29 5.94 6.08 5.29 5.96 6.77 5.08 0.55 0.35 0.40 0.19 1.53 8 5.29 6.08 6.08 5.29 5.96 6.45 5.08 2.43 2.30 2.33 1.81 2.50 ;
param fixcost : 1 2 3 4 5 6 7 8 9 10 11 12 := 1 11.0 16.0 18.0 17.0 10.0 20.0 17.0 13.0 15.0 12.0 14.0 14.0 2 14.0 17.0 17.0 13.0 15.0 13.0 16.0 11.0 20.0 11.0 15.0 10.0 3 12.0 13.0 20.0 17.0 13.0 15.0 16.0 13.0 12.0 13.0 10.0 18.0 4 16.0 19.0 16.0 11.0 15.0 12.0 18.0 12.0 18.0 13.0 13.0 14.0 5 19.0 18.0 15.0 16.0 12.0 14.0 20.0 19.0 11.0 17.0 16.0 18.0 6 13.0 20.0 20.0 17.0 15.0 12.0 14.0 11.0 12.0 19.0 15.0 16.0 7 11.0 12.0 15.0 10.0 17.0 11.0 11.0 16.0 10.0 18.0 17.0 12.0 8 17.0 10.0 20.0 12.0 17.0 20.0 16.0 15.0 10.0 12.0 16.0 18.0 ;
end;
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