lemon-project-template-glpk

annotate deps/glpk/examples/fctp.mod @ 9:33de93886c88

find changesets by author, revision, files, or words in the commit message
Import GLPK 4.47
author Alpar Juttner <alpar@cs.elte.hu>
date Sun, 06 Nov 2011 20:59:10 +0100
parents
children
rev   line source
alpar@9 1 /* FCTP, Fixed-Charge Transportation Problem */
alpar@9 2
alpar@9 3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
alpar@9 4
alpar@9 5 /* The Fixed-Charge Transportation Problem (FCTP) is obtained from
alpar@9 6 classical transportation problem by imposing a fixed cost on each
alpar@9 7 transportation link if there is a positive flow on that link. */
alpar@9 8
alpar@9 9 param m, integer, > 0;
alpar@9 10 /* number of sources */
alpar@9 11
alpar@9 12 param n, integer, > 0;
alpar@9 13 /* number of customers */
alpar@9 14
alpar@9 15 set I := 1..m;
alpar@9 16 /* set of sources */
alpar@9 17
alpar@9 18 set J := 1..n;
alpar@9 19 /* set of customers */
alpar@9 20
alpar@9 21 param supply{i in I}, >= 0;
alpar@9 22 /* supply at source i */
alpar@9 23
alpar@9 24 param demand{j in J}, >= 0;
alpar@9 25 /* demand at customer j */
alpar@9 26
alpar@9 27 param varcost{i in I, j in J}, >= 0;
alpar@9 28 /* variable cost (a cost per one unit shipped from i to j) */
alpar@9 29
alpar@9 30 param fixcost{i in I, j in J}, >= 0;
alpar@9 31 /* fixed cost (a cost for shipping any amount from i to j) */
alpar@9 32
alpar@9 33 var x{i in I, j in J}, >= 0;
alpar@9 34 /* amount shipped from source i to customer j */
alpar@9 35
alpar@9 36 s.t. f{i in I}: sum{j in J} x[i,j] = supply[i];
alpar@9 37 /* observe supply at source i */
alpar@9 38
alpar@9 39 s.t. g{j in J}: sum{i in I} x[i,j] = demand[j];
alpar@9 40 /* satisfy demand at customer j */
alpar@9 41
alpar@9 42 var y{i in I, j in J}, binary;
alpar@9 43 /* y[i,j] = 1 means some amount is shipped from i to j */
alpar@9 44
alpar@9 45 s.t. h{i in I, j in J}: x[i,j] <= min(supply[i], demand[j]) * y[i,j];
alpar@9 46 /* if y[i,j] is 0, force x[i,j] to be 0 (may note that supply[i] and
alpar@9 47 demand[j] are implicit upper bounds for x[i,j] as follows from the
alpar@9 48 constraints f[i] and g[j]) */
alpar@9 49
alpar@9 50 minimize cost: sum{i in I, j in J} varcost[i,j] * x[i,j] +
alpar@9 51 sum{i in I, j in J} fixcost[i,j] * y[i,j];
alpar@9 52 /* total transportation costs */
alpar@9 53
alpar@9 54 data;
alpar@9 55
alpar@9 56 /* These data correspond to the instance bal8x12 from [Balinski]. */
alpar@9 57
alpar@9 58 /* The optimal solution is 471.55 */
alpar@9 59
alpar@9 60 param m := 8;
alpar@9 61
alpar@9 62 param n := 12;
alpar@9 63
alpar@9 64 param supply := 1 15.00, 2 20.00, 3 45.00, 4 35.00,
alpar@9 65 5 25.00, 6 35.00, 7 10.00, 8 25.00;
alpar@9 66
alpar@9 67 param demand := 1 20.00, 2 15.00, 3 20.00, 4 15.00,
alpar@9 68 5 5.00, 6 20.00, 7 30.00, 8 10.00,
alpar@9 69 9 35.00, 10 25.00, 11 10.00, 12 5.00;
alpar@9 70
alpar@9 71 param varcost
alpar@9 72 : 1 2 3 4 5 6 7 8 9 10 11 12 :=
alpar@9 73 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
alpar@9 74 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
alpar@9 75 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
alpar@9 76 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
alpar@9 77 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
alpar@9 78 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
alpar@9 79 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
alpar@9 80 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 ;
alpar@9 81
alpar@9 82 param fixcost
alpar@9 83 : 1 2 3 4 5 6 7 8 9 10 11 12 :=
alpar@9 84 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
alpar@9 85 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
alpar@9 86 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
alpar@9 87 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
alpar@9 88 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
alpar@9 89 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
alpar@9 90 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
alpar@9 91 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 ;
alpar@9 92
alpar@9 93 end;