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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 param a{i in I};
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15 /* capacity of plant i in cases */
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16
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17 table plants IN "iODBC"
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18 'DSN=glpk;UID=glpk;PWD=gnu'
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19 'SELECT PLANT, CAPA AS CAPACITY'
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20 'FROM transp_capa' :
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21 I <- [ PLANT ], a ~ CAPACITY;
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22
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23 set J;
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24 /* markets */
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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 table markets IN "iODBC"
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30 'DSN=glpk;UID=glpk;PWD=gnu'
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31 'transp_demand' :
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32 J <- [ MARKET ], b ~ DEMAND;
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33
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34 param d{i in I, j in J};
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35 /* distance in thousands of miles */
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36
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37 table dist IN "iODBC"
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38 'DSN=glpk;UID=glpk;PWD=gnu'
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39 'transp_dist' :
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40 [ LOC1, LOC2 ], d ~ DIST;
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41
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42 param f;
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43 /* freight in dollars per case per thousand miles */
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44
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45 param c{i in I, j in J} := f * d[i,j] / 1000;
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46 /* transport cost in thousands of dollars per case */
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47
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48 var x{i in I, j in J} >= 0;
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49 /* shipment quantities in cases */
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50
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51 minimize cost: sum{i in I, j in J} c[i,j] * x[i,j];
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52 /* total transportation costs in thousands of dollars */
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53
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54 s.t. supply{i in I}: sum{j in J} x[i,j] <= a[i];
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55 /* observe supply limit at plant i */
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56
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57 s.t. demand{j in J}: sum{i in I} x[i,j] >= b[j];
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58 /* satisfy demand at market j */
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59
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60 solve;
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61
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62 table result{i in I, j in J: x[i,j]} OUT "iODBC"
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63 'DSN=glpk;UID=glpk;PWD=gnu'
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64 'DELETE FROM transp_result;'
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65 'INSERT INTO transp_result VALUES (?,?,?)' :
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66 i ~ LOC1, j ~ LOC2, x[i,j] ~ QUANTITY;
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67
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68 data;
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69
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70 param f := 90;
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71
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72 end;
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