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63 lines
1.4 KiB
63 lines
1.4 KiB
# A TRANSPORTATION PROBLEM
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#
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# This problem finds a least cost shipping schedule that meets
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# requirements at markets and supplies at factories.
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#
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# References:
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# Dantzig G B, "Linear Programming and Extensions."
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# Princeton University Press, Princeton, New Jersey, 1963,
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# Chapter 3-3.
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set I;
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/* canning plants */
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set J;
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/* markets */
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param a{i in I};
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/* capacity of plant i in cases */
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param b{j in J};
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/* demand at market j in cases */
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param d{i in I, j in J};
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/* distance in thousands of miles */
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param f;
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/* freight in dollars per case per thousand miles */
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param c{i in I, j in J} := f * d[i,j] / 1000;
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/* transport cost in thousands of dollars per case */
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var x{i in I, j in J} >= 0;
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/* shipment quantities in cases */
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minimize cost: sum{i in I, j in J} c[i,j] * x[i,j];
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/* total transportation costs in thousands of dollars */
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s.t. supply{i in I}: sum{j in J} x[i,j] <= a[i];
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/* observe supply limit at plant i */
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s.t. demand{j in J}: sum{i in I} x[i,j] >= b[j];
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/* satisfy demand at market j */
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data;
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set I := Seattle San-Diego;
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set J := New-York Chicago Topeka;
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param a := Seattle 350
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San-Diego 600;
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param b := New-York 325
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Chicago 300
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Topeka 275;
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param d : New-York Chicago Topeka :=
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Seattle 2.5 1.7 1.8
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San-Diego 2.5 1.8 1.4 ;
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param f := 90;
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end;
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