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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