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1 /* FCTP, Fixed-Charge Transportation Problem */ |
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2 |
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3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */ |
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4 |
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5 /* The Fixed-Charge Transportation Problem (FCTP) is obtained from |
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6 classical transportation problem by imposing a fixed cost on each |
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7 transportation link if there is a positive flow on that link. */ |
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8 |
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9 param m, integer, > 0; |
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10 /* number of sources */ |
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11 |
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12 param n, integer, > 0; |
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13 /* number of customers */ |
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14 |
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15 set I := 1..m; |
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16 /* set of sources */ |
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17 |
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18 set J := 1..n; |
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19 /* set of customers */ |
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20 |
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21 param supply{i in I}, >= 0; |
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22 /* supply at source i */ |
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23 |
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24 param demand{j in J}, >= 0; |
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25 /* demand at customer j */ |
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26 |
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27 param varcost{i in I, j in J}, >= 0; |
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28 /* variable cost (a cost per one unit shipped from i to j) */ |
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29 |
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30 param fixcost{i in I, j in J}, >= 0; |
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31 /* fixed cost (a cost for shipping any amount from i to j) */ |
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32 |
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33 var x{i in I, j in J}, >= 0; |
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34 /* amount shipped from source i to customer j */ |
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35 |
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36 s.t. f{i in I}: sum{j in J} x[i,j] = supply[i]; |
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37 /* observe supply at source i */ |
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38 |
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39 s.t. g{j in J}: sum{i in I} x[i,j] = demand[j]; |
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40 /* satisfy demand at customer j */ |
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41 |
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42 var y{i in I, j in J}, binary; |
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43 /* y[i,j] = 1 means some amount is shipped from i to j */ |
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44 |
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45 s.t. h{i in I, j in J}: x[i,j] <= min(supply[i], demand[j]) * y[i,j]; |
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46 /* if y[i,j] is 0, force x[i,j] to be 0 (may note that supply[i] and |
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47 demand[j] are implicit upper bounds for x[i,j] as follows from the |
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48 constraints f[i] and g[j]) */ |
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49 |
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50 minimize cost: sum{i in I, j in J} varcost[i,j] * x[i,j] + |
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51 sum{i in I, j in J} fixcost[i,j] * y[i,j]; |
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52 /* total transportation costs */ |
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53 |
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54 data; |
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55 |
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56 /* These data correspond to the instance bal8x12 from [Balinski]. */ |
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57 |
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58 /* The optimal solution is 471.55 */ |
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59 |
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60 param m := 8; |
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61 |
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62 param n := 12; |
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63 |
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64 param supply := 1 15.00, 2 20.00, 3 45.00, 4 35.00, |
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65 5 25.00, 6 35.00, 7 10.00, 8 25.00; |
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66 |
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67 param demand := 1 20.00, 2 15.00, 3 20.00, 4 15.00, |
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68 5 5.00, 6 20.00, 7 30.00, 8 10.00, |
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69 9 35.00, 10 25.00, 11 10.00, 12 5.00; |
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70 |
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71 param varcost |
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72 : 1 2 3 4 5 6 7 8 9 10 11 12 := |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 ; |
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81 |
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82 param fixcost |
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83 : 1 2 3 4 5 6 7 8 9 10 11 12 := |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 ; |
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92 |
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93 end; |