1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/examples/fctp.mod Mon Dec 06 13:09:21 2010 +0100
1.3 @@ -0,0 +1,93 @@
1.4 +/* FCTP, Fixed-Charge Transportation Problem */
1.5 +
1.6 +/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
1.7 +
1.8 +/* The Fixed-Charge Transportation Problem (FCTP) is obtained from
1.9 + classical transportation problem by imposing a fixed cost on each
1.10 + transportation link if there is a positive flow on that link. */
1.11 +
1.12 +param m, integer, > 0;
1.13 +/* number of sources */
1.14 +
1.15 +param n, integer, > 0;
1.16 +/* number of customers */
1.17 +
1.18 +set I := 1..m;
1.19 +/* set of sources */
1.20 +
1.21 +set J := 1..n;
1.22 +/* set of customers */
1.23 +
1.24 +param supply{i in I}, >= 0;
1.25 +/* supply at source i */
1.26 +
1.27 +param demand{j in J}, >= 0;
1.28 +/* demand at customer j */
1.29 +
1.30 +param varcost{i in I, j in J}, >= 0;
1.31 +/* variable cost (a cost per one unit shipped from i to j) */
1.32 +
1.33 +param fixcost{i in I, j in J}, >= 0;
1.34 +/* fixed cost (a cost for shipping any amount from i to j) */
1.35 +
1.36 +var x{i in I, j in J}, >= 0;
1.37 +/* amount shipped from source i to customer j */
1.38 +
1.39 +s.t. f{i in I}: sum{j in J} x[i,j] = supply[i];
1.40 +/* observe supply at source i */
1.41 +
1.42 +s.t. g{j in J}: sum{i in I} x[i,j] = demand[j];
1.43 +/* satisfy demand at customer j */
1.44 +
1.45 +var y{i in I, j in J}, binary;
1.46 +/* y[i,j] = 1 means some amount is shipped from i to j */
1.47 +
1.48 +s.t. h{i in I, j in J}: x[i,j] <= min(supply[i], demand[j]) * y[i,j];
1.49 +/* if y[i,j] is 0, force x[i,j] to be 0 (may note that supply[i] and
1.50 + demand[j] are implicit upper bounds for x[i,j] as follows from the
1.51 + constraints f[i] and g[j]) */
1.52 +
1.53 +minimize cost: sum{i in I, j in J} varcost[i,j] * x[i,j] +
1.54 + sum{i in I, j in J} fixcost[i,j] * y[i,j];
1.55 +/* total transportation costs */
1.56 +
1.57 +data;
1.58 +
1.59 +/* These data correspond to the instance bal8x12 from [Balinski]. */
1.60 +
1.61 +/* The optimal solution is 471.55 */
1.62 +
1.63 +param m := 8;
1.64 +
1.65 +param n := 12;
1.66 +
1.67 +param supply := 1 15.00, 2 20.00, 3 45.00, 4 35.00,
1.68 + 5 25.00, 6 35.00, 7 10.00, 8 25.00;
1.69 +
1.70 +param demand := 1 20.00, 2 15.00, 3 20.00, 4 15.00,
1.71 + 5 5.00, 6 20.00, 7 30.00, 8 10.00,
1.72 + 9 35.00, 10 25.00, 11 10.00, 12 5.00;
1.73 +
1.74 +param varcost
1.75 + : 1 2 3 4 5 6 7 8 9 10 11 12 :=
1.76 + 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
1.77 + 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
1.78 + 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
1.79 + 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
1.80 + 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
1.81 + 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
1.82 + 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
1.83 + 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 ;
1.84 +
1.85 +param fixcost
1.86 + : 1 2 3 4 5 6 7 8 9 10 11 12 :=
1.87 + 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
1.88 + 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
1.89 + 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
1.90 + 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
1.91 + 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
1.92 + 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
1.93 + 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
1.94 + 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 ;
1.95 +
1.96 +end;