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