1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/examples/transp.mod	Mon Dec 06 13:09:21 2010 +0100
     1.3 @@ -0,0 +1,63 @@
     1.4 +# A TRANSPORTATION PROBLEM
     1.5 +#
     1.6 +# This problem finds a least cost shipping schedule that meets
     1.7 +# requirements at markets and supplies at factories.
     1.8 +#
     1.9 +#  References:
    1.10 +#              Dantzig G B, "Linear Programming and Extensions."
    1.11 +#              Princeton University Press, Princeton, New Jersey, 1963,
    1.12 +#              Chapter 3-3.
    1.13 +
    1.14 +set I;
    1.15 +/* canning plants */
    1.16 +
    1.17 +set J;
    1.18 +/* markets */
    1.19 +
    1.20 +param a{i in I};
    1.21 +/* capacity of plant i in cases */
    1.22 +
    1.23 +param b{j in J};
    1.24 +/* demand at market j in cases */
    1.25 +
    1.26 +param d{i in I, j in J};
    1.27 +/* distance in thousands of miles */
    1.28 +
    1.29 +param f;
    1.30 +/* freight in dollars per case per thousand miles */
    1.31 +
    1.32 +param c{i in I, j in J} := f * d[i,j] / 1000;
    1.33 +/* transport cost in thousands of dollars per case */
    1.34 +
    1.35 +var x{i in I, j in J} >= 0;
    1.36 +/* shipment quantities in cases */
    1.37 +
    1.38 +minimize cost: sum{i in I, j in J} c[i,j] * x[i,j];
    1.39 +/* total transportation costs in thousands of dollars */
    1.40 +
    1.41 +s.t. supply{i in I}: sum{j in J} x[i,j] <= a[i];
    1.42 +/* observe supply limit at plant i */
    1.43 +
    1.44 +s.t. demand{j in J}: sum{i in I} x[i,j] >= b[j];
    1.45 +/* satisfy demand at market j */
    1.46 +
    1.47 +data;
    1.48 +
    1.49 +set I := Seattle San-Diego;
    1.50 +
    1.51 +set J := New-York Chicago Topeka;
    1.52 +
    1.53 +param a := Seattle     350
    1.54 +           San-Diego   600;
    1.55 +
    1.56 +param b := New-York    325
    1.57 +           Chicago     300
    1.58 +           Topeka      275;
    1.59 +
    1.60 +param d :              New-York   Chicago   Topeka :=
    1.61 +           Seattle     2.5        1.7       1.8
    1.62 +           San-Diego   2.5        1.8       1.4  ;
    1.63 +
    1.64 +param f := 90;
    1.65 +
    1.66 +end;