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Saint Com315 chapter 8 problems

1. ABC Inc. must make a decision on its current capacity for next year. Estimated profits (in $000’s) based on next year’s demand are shown in the table below.

Next Year’s

Demand

Alternative Low High
Expand $100 $200
Subcontract $50 $120
Do Nothing $40 $50

a. Which alternative should be chosen based on the maximax criterion?

b. Which alternative should be chosen based on the maximin criterion?

c. Which alternative should be chosen based on the Lapalce criterion?

d. Which alternative should be chosen based on criterion of realism with alpha = 0.7?

e. Which alternative should be chosen based on the minimax regret criterion?

2. Refer to problem 1. Assume that ABC Inc. has hired a marketing research firm that provided additional information regarding next year’s demand. Suppose that the probabilities of low and high demand are assessed as follows: P(Low) = 0.4 and P(High) = 0.6.

a. Which alternative should be chosen using the expected monetary value (EMV) criterion?

b. What is the expected value under certainty?

c. What is the expected value under perfect information (EVPI)?

3. Refer to problem 2.

a. Develop a decision tree for this problem.

b. b. Analyze the decision tree and determine which alternative should be chosen.

c. c. Using the expected opportunity loss (EOL) criterion, which alternative should be chosen?

4. A plant manager is considering buying additional stamping machines to accommodate increasing demand. The alternatives are to buy 1 machine, 2 machines, or 3 machines. The profits realized under each alternative are a function of whether their bid for a recent defense contract is accepted or not. The payoff table below illustrates the profits realized (in $000’s) based on the different scenarios faced by the manager.

Alternative Bid Accepted Bid Rejected
Buy 1 machine $10 $5
Buy 2 machines $30 $4
Buy 3 machines $40 $2

a. Which alternative should be chosen based on the maximax criterion?

b. Which alternative should be chosen based on the maximin criterion?

c. Which alternative should be chosen based on the Lapalce criterion?

d. Which alternative should be chosen based on criterion of realism with alpha = 0.8?

e. Which alternative should be chosen based on the minimax regret criterion?

5. Refer to problem 4. Assume that based on historical bids with the defense contractor, the plant manager believes that there is a 65% chance that the bid will be accepted and a 35% chance that the bid will be rejected.

a. Which alternative should be chosen using the expected monetary value (EMV) criterion?

b. What is the expected value under certainty?

c. What is the expected value under perfect information (EVPI)?

6. Refer to problem 5.

a. Develop a decision tree for this problem.

b. Analyze the decision tree and determine which alternative should be chosen.

c. Using the expected opportunity loss (EOL) criterion, which alternative should be chosen?

7. A bakery must decide how many pies to prepare for the upcoming weekend. The bakery has the option to make 50, 100, or 150 pies. Assume that demand for the pies can be 50, 100, or 150. Each pie costs $5 to make and sells for $7. Unsold pies are donated to a nearby charity center. Assume that there is no opportunity cost for lost sales.

a. Which alternative should be chosen based on the maximax criterion?

b. Which alternative should be chosen based on the maximin criterion?

c. Which alternative should be chosen based on the Lapalce criterion?

d. Which alternative should be chosen based on criterion of realism with alpha = 0.8?

e. Which alternative should be chosen based on the minimax regret criterion?

8. Assume that the bakery (see problem 7) has obtained the following probability information regarding demand for the pies: P(50) = 0.3, P(100) = 0.5, and P(150) = 0.2.

a. Which alternative should be chosen using the expected monetary value (EMV) criterion?

b. What is the expected value under certainty?

c. What is the expected value under perfect information (EVPI)?

9. Refer to problem 8.

a. Develop a decision tree for this problem.

b. Analyze the decision tree and determine which alternative should be chosen.

c. Using the expected opportunity loss (EOL) criterion, which alternative should be chosen?

10.AAA auto supply store sells snow tires which are ordered every Friday to meet next week’s demand. The sales price for the most popular size is $50 per tire and its cost for AAA is $35. If too many tires are ordered AAA incurs an inventory carrying cost of $2 per tire. If AAA is out of stock, it forgoes the profits from missed sales. AAA has the option to order 100, 150, or 200 tires to meet next week’s demand which can be either 100, 150, or 200 tires.

a. Which alternative should be chosen based on the maximax criterion?

b. Which alternative should be chosen based on the maximin criterion?

c. Which alternative should be chosen based on the Lapalce criterion?

d. Which alternative should be chosen based on criterion of realism with alpha = 0.7?

e. Which alternative should be chosen based on the minimax regret criterion?

]

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