Decision Theory (6 problems)

A study of accounts receivables at the A&W Department Store indicates that bills are either current, one month overdue, two months overdue, written off as bad debts, or paid in full. Of those that are current, 80% are paid that month, and the rest become one month overdue. Of the one month overdue bills, 90% are paid, and the rest become two months overdue. Those that are two months overdue will either be paid (85%) or be listed as bad debts. If the sales each month average $150,000, determine how much the company expects to receive of this amount. How much will become bad debt?

A CEO is 90% sure that the Financial VP of the company transmits secrets to competitors. She does not know what is better: to fire or not the VP

If the CEO fires the VP and he is an informer, the company will be better off with $500,000. However, if the VP is fired but is not an informer, the company looses $2,500,000 (loosing his expertise) and still remains with an informer. If the CEO decides not to fire the VP, she estimates that the company will loose $1,500,000, either the VP is an informer or not.

Before making a decision, the CEO is thinking about a lie detector test for all the employees. The test costs $150,000, and its accuracy is 95% for liars and only 85% for non-liars.

a) What strategy should the CEO choose in order to minimize the expected total cost?

b) Should the CEO order a lie detector test for all employees?

c) Determine the maximum amount of money that the CEO will be willing to pay for the lie detector test.

The following is a payoff table giving profits for various situations.

The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a person selected Alternative 1, what would the expected profit be?

Nick has plans to open some pizza restaurants, but he is not sure how many to open. He has prepared a payoff table to help analyze the situation.

Nick believes that there is a 40 percent chance that the market will be good, a 30 percent chance that it will be fair, and a 30 percent chance that it will be poor. A market research firm will analyze the market conditions and will provide a perfect forecast of the future (they provide a money back guarantee). What is the most that should be paid for this forecast?

Bakery Products is considering the introduction of a new line of products. In order to produce the new line, the bakery is considering either a major or minor renovation of the current plant. The following conditional values table has been developed by the bakery.

Under the assumption that the probability of a favorable market is equal to the probability of an unfavorable market, determine:

(a) the EMV of a major renovation.

(b) the EMV of a minor renovation.

(c) the EMV of the do nothing option.

(d) the best alternative using EMV.

The following is an opportunity loss table.

What decision should be made based on the minimax regret criterion? (Minimax regret criterion is based on opportunity loss)