lemon-project-template-glpk
annotate deps/glpk/examples/transp.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 |
| rev | line source |
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| alpar@9 | 1 # A TRANSPORTATION PROBLEM |
| alpar@9 | 2 # |
| alpar@9 | 3 # This problem finds a least cost shipping schedule that meets |
| alpar@9 | 4 # requirements at markets and supplies at factories. |
| alpar@9 | 5 # |
| alpar@9 | 6 # References: |
| alpar@9 | 7 # Dantzig G B, "Linear Programming and Extensions." |
| alpar@9 | 8 # Princeton University Press, Princeton, New Jersey, 1963, |
| alpar@9 | 9 # Chapter 3-3. |
| alpar@9 | 10 |
| alpar@9 | 11 set I; |
| alpar@9 | 12 /* canning plants */ |
| alpar@9 | 13 |
| alpar@9 | 14 set J; |
| alpar@9 | 15 /* markets */ |
| alpar@9 | 16 |
| alpar@9 | 17 param a{i in I}; |
| alpar@9 | 18 /* capacity of plant i in cases */ |
| alpar@9 | 19 |
| alpar@9 | 20 param b{j in J}; |
| alpar@9 | 21 /* demand at market j in cases */ |
| alpar@9 | 22 |
| alpar@9 | 23 param d{i in I, j in J}; |
| alpar@9 | 24 /* distance in thousands of miles */ |
| alpar@9 | 25 |
| alpar@9 | 26 param f; |
| alpar@9 | 27 /* freight in dollars per case per thousand miles */ |
| alpar@9 | 28 |
| alpar@9 | 29 param c{i in I, j in J} := f * d[i,j] / 1000; |
| alpar@9 | 30 /* transport cost in thousands of dollars per case */ |
| alpar@9 | 31 |
| alpar@9 | 32 var x{i in I, j in J} >= 0; |
| alpar@9 | 33 /* shipment quantities in cases */ |
| alpar@9 | 34 |
| alpar@9 | 35 minimize cost: sum{i in I, j in J} c[i,j] * x[i,j]; |
| alpar@9 | 36 /* total transportation costs in thousands of dollars */ |
| alpar@9 | 37 |
| alpar@9 | 38 s.t. supply{i in I}: sum{j in J} x[i,j] <= a[i]; |
| alpar@9 | 39 /* observe supply limit at plant i */ |
| alpar@9 | 40 |
| alpar@9 | 41 s.t. demand{j in J}: sum{i in I} x[i,j] >= b[j]; |
| alpar@9 | 42 /* satisfy demand at market j */ |
| alpar@9 | 43 |
| alpar@9 | 44 data; |
| alpar@9 | 45 |
| alpar@9 | 46 set I := Seattle San-Diego; |
| alpar@9 | 47 |
| alpar@9 | 48 set J := New-York Chicago Topeka; |
| alpar@9 | 49 |
| alpar@9 | 50 param a := Seattle 350 |
| alpar@9 | 51 San-Diego 600; |
| alpar@9 | 52 |
| alpar@9 | 53 param b := New-York 325 |
| alpar@9 | 54 Chicago 300 |
| alpar@9 | 55 Topeka 275; |
| alpar@9 | 56 |
| alpar@9 | 57 param d : New-York Chicago Topeka := |
| alpar@9 | 58 Seattle 2.5 1.7 1.8 |
| alpar@9 | 59 San-Diego 2.5 1.8 1.4 ; |
| alpar@9 | 60 |
| alpar@9 | 61 param f := 90; |
| alpar@9 | 62 |
| alpar@9 | 63 end; |