1 | # A TRANSPORTATION PROBLEM |
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2 | # |
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3 | # This problem finds a least cost shipping schedule that meets |
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4 | # requirements at markets and supplies at factories. |
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5 | # |
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6 | # References: |
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7 | # Dantzig G B, "Linear Programming and Extensions." |
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8 | # Princeton University Press, Princeton, New Jersey, 1963, |
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9 | # Chapter 3-3. |
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10 | |
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11 | set I; |
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12 | /* canning plants */ |
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13 | |
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14 | set J; |
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15 | /* markets */ |
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16 | |
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17 | set K dimen 2; |
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18 | /* transportation lane */ |
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19 | |
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20 | set L; |
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21 | /* parameters */ |
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22 | |
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23 | param a{i in I}; |
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24 | /* capacity of plant i in cases */ |
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25 | |
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26 | param b{j in J}; |
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27 | /* demand at market j in cases */ |
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28 | |
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29 | param d{i in I, j in J}; |
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30 | /* distance in thousands of miles */ |
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31 | |
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32 | param e{l in L}; |
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33 | /* parameters */ |
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34 | |
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35 | param f; |
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36 | /* freight in dollars per case per thousand miles */ |
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37 | |
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38 | table tab_plant IN "CSV" "plants.csv" : |
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39 | I <- [plant], a ~ capacity; |
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40 | |
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41 | table tab_market IN "CSV" "markets.csv" : |
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42 | J <- [market], b ~ demand; |
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43 | |
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44 | table tab_distance IN "CSV" "distances.csv" : |
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45 | K <- [plant, market], d ~ distance; |
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46 | |
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47 | table tab_parameter IN "CSV" "parameters.csv" : |
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48 | L <- [parameter], e ~ value ; |
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49 | |
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50 | param c{i in I, j in J} := e['transport cost'] * d[i,j] / 1000; |
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51 | /* transport cost in thousands of dollars per case */ |
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52 | |
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53 | var x{(i,j) in K} >= 0; |
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54 | /* shipment quantities in cases */ |
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55 | |
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56 | minimize cost: sum{(i,j) in K} c[i,j] * x[i,j]; |
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57 | /* total transportation costs in thousands of dollars */ |
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58 | |
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59 | s.t. supply{i in I}: sum{(i,j) in K} x[i,j] <= a[i]; |
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60 | /* observe supply limit at plant i */ |
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61 | |
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62 | s.t. demand{j in J}: sum{(i,j) in K} x[i,j] >= b[j]; |
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63 | /* satisfy demand at market j */ |
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64 | |
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65 | solve; |
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66 | |
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67 | table tab_result{(i,j) in K} OUT "CSV" "result.csv" : |
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68 | i ~ plant, j ~ market, x[i,j] ~ shipment; |
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69 | |
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70 | end; |
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