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; |
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