Question: You are given the following model formulation for a trans-shipment problem. We have Plants, Warehouses, and Customers. Decision Variables: X15 = Units shipped from Plant
You are given the following model formulation for a trans-shipment problem. We have Plants, Warehouses, and Customers.
Decision Variables:
| X15 = | Units shipped from | Plant 1 (1) | to | Warehouse 1 (5) |
| X16 = |
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|
| Warehouse 2 (6) |
| X25 = |
| Plant 2 (2) |
| Warehouse 1 (5) |
| X26 = |
|
|
| Warehouse 2 (6) |
| X35 = |
| Plant 3 (3) |
| Warehouse 1 (5) |
| X36 = |
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|
| Warehouse 2 (6) |
| X38 = |
|
|
| Customer 2 (8) |
| X45 = |
| Plant 4 (4) |
| Warehouse 1 (5) |
| X46 = |
|
|
| Warehouse 2 (6) |
| X57 = |
| Warehouse 1 (5) |
| Customer 1 (7) |
| X58 = |
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| Customer 2 (8) |
| X59 = |
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| Customer 3 (9) |
| X67 = |
| Warehouse 2 (6) |
| Customer 1 (7) |
| X68 = |
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| Customer 2 (8) |
| X69 = |
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| Customer 3 (9) |
Objective Function:
Min: 8X15 + 10X16 + 12X25 + 13X26 + 14X35 + 15X36 + 12X38 + 12X45 + 8X46 + 12X57 + 10X58 + 8X59 + 12X67 + 13X68 + 15X69
Subject to:
C1 (Plant 1): 1X15 + 1X16 710
C2 (Plant 2): 1X25 + 1X26 820
C3 (Plant 3): 1X35 + 1X36 +1X38 920
C4 (Plant 4): 1X45 + 1X46 500
C5 (Whse 1): 1X15 + 1X25 + 1X35 + 1X45 1X57 1X58 1X59 = 0
C6 (Whse 2): 1X16 + 1X26 + 1X36 + 1X46 1X67 1X68 1X69 = 0
C7 (Node 7): 1X57 + 1X67 = 500
C8 (Node 8): 1X38 + 1X58 + 1X68 = 600
C9 (Node 9): 1X59 + 1X69 = 670
C10 (Non-neg.): X15 X69 0
Part a) What is the minimum cost shipping plan? Label your answer in your Excel spreadsheet as Total Shipping Cost.
Part b (5 Points) Use the Simplified Sensitivity Analysis handout and show your work to the right of your original spreadsheet as shown in all of the Chapter 3 Sensitivity Analysis examples. What will the objective function equal if the coefficient of X46 is now 7.80? Note: If all you do is revise your original model and re-run it, you will receive 0 points. You must perform sensitivity analysis in your spreadsheet. Answer the following questions in your spreadsheet:
How much is the Decrease?
What is the Allowable Decrease?
Is the Increase within the Allowable Decrease?
What is the new objective function value?
Part c (5 Points) Use the Simplified Sensitivity Analysis handout and show your work to the right of your original spreadsheet as shown in all of the Chapter 3 Sensitivity Analysis examples. What will the objective function equal if the coefficient of right-hand-side of Constraint 9 is now 655? Note: If all you do is revise your original model and re-run it, you will receive 0 points. You must perform sensitivity analysis in your spreadsheet. Answer the following questions in your spreadsheet:
How much is the Decrease?
What is the Allowable Decrease?
Is the Decrease within the Allowable Decrease?
What is the new objective function value?
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