lemon-project-template-glpk
view deps/glpk/examples/fctp.mod @ 9:33de93886c88
Import GLPK 4.47
| author | Alpar Juttner <alpar@cs.elte.hu> |
|---|---|
| date | Sun, 06 Nov 2011 20:59:10 +0100 |
| parents | |
| children |
line source
1 /* FCTP, Fixed-Charge Transportation Problem */
3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
5 /* The Fixed-Charge Transportation Problem (FCTP) is obtained from
6 classical transportation problem by imposing a fixed cost on each
7 transportation link if there is a positive flow on that link. */
9 param m, integer, > 0;
10 /* number of sources */
12 param n, integer, > 0;
13 /* number of customers */
15 set I := 1..m;
16 /* set of sources */
18 set J := 1..n;
19 /* set of customers */
21 param supply{i in I}, >= 0;
22 /* supply at source i */
24 param demand{j in J}, >= 0;
25 /* demand at customer j */
27 param varcost{i in I, j in J}, >= 0;
28 /* variable cost (a cost per one unit shipped from i to j) */
30 param fixcost{i in I, j in J}, >= 0;
31 /* fixed cost (a cost for shipping any amount from i to j) */
33 var x{i in I, j in J}, >= 0;
34 /* amount shipped from source i to customer j */
36 s.t. f{i in I}: sum{j in J} x[i,j] = supply[i];
37 /* observe supply at source i */
39 s.t. g{j in J}: sum{i in I} x[i,j] = demand[j];
40 /* satisfy demand at customer j */
42 var y{i in I, j in J}, binary;
43 /* y[i,j] = 1 means some amount is shipped from i to j */
45 s.t. h{i in I, j in J}: x[i,j] <= min(supply[i], demand[j]) * y[i,j];
46 /* if y[i,j] is 0, force x[i,j] to be 0 (may note that supply[i] and
47 demand[j] are implicit upper bounds for x[i,j] as follows from the
48 constraints f[i] and g[j]) */
50 minimize cost: sum{i in I, j in J} varcost[i,j] * x[i,j] +
51 sum{i in I, j in J} fixcost[i,j] * y[i,j];
52 /* total transportation costs */
54 data;
56 /* These data correspond to the instance bal8x12 from [Balinski]. */
58 /* The optimal solution is 471.55 */
60 param m := 8;
62 param n := 12;
64 param supply := 1 15.00, 2 20.00, 3 45.00, 4 35.00,
65 5 25.00, 6 35.00, 7 10.00, 8 25.00;
67 param demand := 1 20.00, 2 15.00, 3 20.00, 4 15.00,
68 5 5.00, 6 20.00, 7 30.00, 8 10.00,
69 9 35.00, 10 25.00, 11 10.00, 12 5.00;
71 param varcost
72 : 1 2 3 4 5 6 7 8 9 10 11 12 :=
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
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
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
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
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
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
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
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 ;
82 param fixcost
83 : 1 2 3 4 5 6 7 8 9 10 11 12 :=
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
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
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
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
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
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
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
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 ;
93 end;