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Stateline Transportation Case Assignment

684 words - 3 pages

1) The model for the transportation problem consists of 18 decision variables, representing the number of barrels of wastes transported from each of the 6 plants to each of the 3 waste disposal sites:
[pic]= Number of Barrels transported per week from plant ‘i’ to the j-th waste disposal site, where i = 1, 2, 3, 4, 5, 6 and j = A, B, C.
The objective function of the manager is to minimize the total transportation cost for all shipments. Thus the objective function is the sum of the individual shipping costs from each plant to each waste disposal site:
Minimize Z = 12X1A+ 15X1B+ 17X1C+ 14X2A+ 9X2B+ 10X2C+ 13X3A+ 20X3B +11X3C
+17X4A +16X4B +19X4C +7X5A +14X5B +12X5C +22X6A +16X6B +18X6C
The ...view middle of the document...

The linear programming model for the transportation problem is summarized as follows:
Minimize Z = 12X1A+ 15X1B+ 17X1C+ 14X2A+ 9X2B+ 10X2C+ 13X3A+ 20X3B +11X3C
+17X4A +16X4B +19X4C +7X5A +14X5B +12X5C +22X6A +16X6B +18X6C
Subject to
X1A+ X1B+ X1C = 35
X2A+ X2B+ X2C = 26
X3A+ X3B +X3C = 42
X4A + X4B +X4C = 53
X5A + X5B +X5C = 29
X6A + X6B +X6C = 38
X1A+ X2A+ X3A+X4A+ X5A+X6A ≤ 65
X1B+ X2B+ X3B+X4B+X5B +X6B ≤ 80
X1C+ X2C+X3C+ X4C+X5C +X6C ≤ 105
Xij > 0
Minimize Z = 2282

2.)
  | Northwest Corner Method Stateline Shipping |   |   |
  | | | | Plants | | | |   |
Disposals | Kingsport | Danville | Macon | Selma | Columbus | Allentown | Dummy | Demand |
A | 35 | 14 | 13 | 3 | 0 | 0 | 0 | 65 |
B | 0 | 12 | 29 | 13 | 14 | 12 | 0 | 80 |
C | 0 | 0 | 0 | 37 | 15 | 26 | 27 | 105 |
Capacity | 35 | 26 | 42 | 53 | 29 | 38 | 27 | 250 |

5.) If each of the plants and waste disposal sites is considered as intermediate shipping points, the total transportation cost for the revised transshipment model is obtained as $2630. The optimal routes and the...

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