Question
Transshipment Model: This is an extension of the transportation model. There are now intermediate transshipment points added between the sources (plants) and destinations (retailers). Items
Transshipment Model: This is an extension of the transportation model. There are now intermediate transshipment points added between the sources (plants) and destinations (retailers). Items being shipped from a Plant (pi) must be shipped to a Warehouse (wj) before being shipped to the Retailer (rk). Each Plant will have an associated supply (si) and each Retailer will have a demand (dk). The number of plants is n, number of warehouses is q and the number of retailers is m. The edges (i,j) from plant (pi)to warehouse (wj) have costs associated denoted cp(i,j). The edges (j,k) from a warehouse (wj)to a retailer (rk) have costs associated denoted cw(j,k). The graph below shows the transshipment map for a manufacturer of refrigerators. Refrigerators are produced at four plants and then shipped to a warehouse (weekly) before going to the retailer.
Below are the costs of shipping from a plant to a warehouse and then a warehouse to a retailer. If it is impossible to ship between the two locations an X is placed in the table.
cost | W1 | W2 | W3 |
P1 | $10 | $15 | X |
P2 | $11 | $8 | X |
P3 | $13 | $8 | $9 |
P4 | X | $14 | 8 |
cost | R1 | R2 | R3 | R4 | R5 | R6 | R7 |
W1 | $5 | $6 | $7 | $10 | X | X | X |
W2 | X | X | $12 | $8 | $10 | $14 | X |
W3 | X | X | X | $14 | $12 | $12 | $6 |
P1 | P2 | P3 | P4 | |
Supply | 150 | 450 | 250 | 150 |
R1 | R2 | R3 | R4 | R5 | R6 | R7 | |
Demand | 100 | 150 | 100 | 200 | 200 | 150 | 100 |
Determine the number of refrigerators to be shipped plants to warehouses and then warehouses to retailers to minimize the cost. a) Formulate the problem as a linear program with an objective function and all constraints. b) Determine the optimal solution for the linear program using any software you want. Include a copy of the code and output. c) What are the optimal shipping routes and minimum cost.
R1 R2 P1 W1 P2 2 P3 R5 R6 R7Step by Step Solution
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