A company has three warehouses that supply four stores with a given product. Each warehouse has 30 units of the product. Stores 1, 2, 3, and 4 require 20, 25, 30, and 35 units of the product, respectively. The per unit shipping costs from each warehouse to each store are given in the following table. (Let Xij represent the number of units that flow from warehouse i to store j for i = 1, 2, 3 and j = 1, 2, 3, 4.) Store Warehouse 1 2 3 4 1 7 6 7 6 2 4 7 6 5 3 6 4 4 4 Solve the problem using Solver. Caution: You should note that the amount of supply at the warehouses is less than the amount of demand at the stores. You will need to address this when structuring the flow balance constraints. (Hint: You want to ship everything from the warehouses even though there will be a demand shortage at the stores). (X11, X12, X13, X14, X21, X22, X23, X24, X31, X32, X33, X34) = ( ??? ) What is the optimal solution to the modified problem? (X11, X12, X13, X14, X21, X22, X23, X24, X31, X32, X33, X34) = ( ??? )
A company has three warehouses that supply four stores with a given product. Each warehouse has 30 units of the product. Stores 1, 2, 3, and 4 require 20, 25, 30, and 35 units of the product, respectively. The per unit shipping costs from each warehouse to each store are given in the following table. (Let Xij represent the number of units that flow from warehouse i to store j for i = 1, 2, 3 and j = 1, 2, 3, 4.) Store Warehouse 1 2 3 4 1 7 6 7 6 2 4 7 6 5 3 6 4 4 4 Solve the problem using Solver. Caution: You should note that the amount of supply at the warehouses is less than the amount of demand at the stores. You will need to address this when structuring the flow balance constraints. (Hint: You want to ship everything from the warehouses even though there will be a demand shortage at the stores). (X11, X12, X13, X14, X21, X22, X23, X24, X31, X32, X33, X34) = ( ??? ) What is the optimal solution to the modified problem? (X11, X12, X13, X14, X21, X22, X23, X24, X31, X32, X33, X34) = ( ??? )
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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A company has three warehouses that supply four stores with a given product. Each warehouse has 30 units of the product. Stores 1, 2, 3, and 4 require 20, 25, 30, and 35 units of the product, respectively. The per unit shipping costs from each warehouse to each store are given in the following table. (Let Xij represent the number of units that flow from warehouse i to store j for i = 1, 2, 3 and j = 1, 2, 3, 4.)
| Store | ||||
|---|---|---|---|---|
| Warehouse | 1 | 2 | 3 | 4 |
| 1 | 7 | 6 | 7 | 6 |
| 2 | 4 | 7 | 6 | 5 |
| 3 | 6 | 4 | 4 | 4 |
Solve the problem using Solver. Caution: You should note that the amount of supply at the warehouses is less than the amount of demand at the stores. You will need to address this when structuring the flow balance constraints. (Hint: You want to ship everything from the warehouses even though there will be a demand shortage at the stores).
(X11, X12, X13, X14, X21, X22, X23, X24, X31, X32, X33, X34) = ( ??? )
What is the optimal solution to the modified problem?
What is the optimal solution to the modified problem?
(X11, X12, X13, X14, X21, X22, X23, X24, X31, X32, X33, X34) = ( ??? )
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Suppose that shipments are not allowed between warehouse 1 and store 2 or between warehouse 2 and store 3. What is the easiest way to modify the spreadsheet so that you can solve this modified problem?
a) Assign arbitrarily small costs such as $0.01 to the arcs representing these flows.
b) Assign arbitrarily large costs such as $999 to the arcs representing these flows.
(I picked option b, which is correct)
What is the optimal solution to the modified problem?
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How would you write the optimal solution for these?
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