Exercise of Operation Management
Exercise 1 page 224 a. Using Maximax, the worst payoffs for the alternatives are as follws:
Do nothing: $60 thousands
Expand: $80 thousands
Subcontract: $70 thousands
Hence, since $80 thousands is the best, choose to expand the firms using the maximax strategy
b. Using Maximin
Do nothing: $50 thousands
Expand: $20 thousands
Subcontract: $40 thousands
Hence, since $50 thousands is the best, choose to do nothing using the maximin strategy
c. Using Laplace
For the Laplace criterion, first find the row totals, and then divide each of those amounts by number of states of nature. Thus, we have Alternative | Next year’s demand | Row total | Row average | | Low | High | | | Do nothing | 50 | 60 | 110 | 55 | Expand | 20 | 80 | 100 | 50 | Subcontract | 40 | 70 | 110 | 55 |
Because the “Do nothing” facility or “Subcontract” facility has the Highest average, they would be chosen under the Laplace. d. Using Minnimax regret
Alternative | Regrets | Worst | | Low | High | | Do nothing | 0 | 20 | 20 | Expand | 30 | 0 | 30 | Subcontract | 10 | 10 | 10 |
The best of these worst regrets would be chosen using minimax regret. The lowest regret is 10, which is for a subcontract facility. Hence, that alternative would be chosen.
Exercise 2 page 224 a. Determine the expected profit of each alternative.
EP Do nothing = 0.3x50+0.7x60 =$57
EP Expand = 0.3x20+0.7x80 =$62
EP Subcontract = 0.3x40+0.7x70 =$61
b. Analyze the problem using a decision tree.
c. Compute the expected value of perfect information. ( EVPI) * Compute the expected regret
Do nothing 0.3x0 +0.7x20 = 14
Expand 0.3x30+0.7x0 = 9 (minimum)
Subcontract 0.3x10+0.7x10 = 10
The lowest expected regret is 9, which is associated with the second alternative. Hence, the EVPI is $9 thousands
The contractor could use this knowledge to know the difference between the expected pay off with perfect information and the expected payoff under the
Do nothing: $60 thousands
Expand: $80 thousands
Subcontract: $70 thousands
Hence, since $80 thousands is the best, choose to expand the firms using the maximax strategy
b. Using Maximin
Do nothing: $50 thousands
Expand: $20 thousands
Subcontract: $40 thousands
Hence, since $50 thousands is the best, choose to do nothing using the maximin strategy
c. Using Laplace
For the Laplace criterion, first find the row totals, and then divide each of those amounts by number of states of nature. Thus, we have Alternative | Next year’s demand | Row total | Row average | | Low | High | | | Do nothing | 50 | 60 | 110 | 55 | Expand | 20 | 80 | 100 | 50 | Subcontract | 40 | 70 | 110 | 55 |
Because the “Do nothing” facility or “Subcontract” facility has the Highest average, they would be chosen under the Laplace. d. Using Minnimax regret
Alternative | Regrets | Worst | | Low | High | | Do nothing | 0 | 20 | 20 | Expand | 30 | 0 | 30 | Subcontract | 10 | 10 | 10 |
The best of these worst regrets would be chosen using minimax regret. The lowest regret is 10, which is for a subcontract facility. Hence, that alternative would be chosen.
Exercise 2 page 224 a. Determine the expected profit of each alternative.
EP Do nothing = 0.3x50+0.7x60 =$57
EP Expand = 0.3x20+0.7x80 =$62
EP Subcontract = 0.3x40+0.7x70 =$61
b. Analyze the problem using a decision tree.
c. Compute the expected value of perfect information. ( EVPI) * Compute the expected regret
Do nothing 0.3x0 +0.7x20 = 14
Expand 0.3x30+0.7x0 = 9 (minimum)
Subcontract 0.3x10+0.7x10 = 10
The lowest expected regret is 9, which is associated with the second alternative. Hence, the EVPI is $9 thousands
The contractor could use this knowledge to know the difference between the expected pay off with perfect information and the expected payoff under the