Reference no: EM132323847

Problems -

1. Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table:

Decision Alternative	State of Nature
	s1	s2	s3	s4
d1	14	9	10	5
d2	11	10	8	7
d3	9	10	10	11
d4	8	10	11	13

a. If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

b. Which approach do you prefer? Explain. Is establishing the most appropriate approach before analyzing the problem important for the decision maker? Explain.

c. Assume that the payoff table provides cost rather than profit payoffs. What is the recommended decision using the optimistic, conservative, and minimax regret approaches?

2. The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives:

Decision Alternative	State of Nature
	s1	s2
d1	10	1
d2	4	3

a. Use graphical sensitivity analysis to determine the range of probabilities of state of nature s₁ for which each of the decision alternatives has the largest expected value.

b. Suppose P(s₁) = 0.2 and P(s₂) = 0.8. What is the best decision using the expected value approach?

c. Perform sensitivity analysis on the payoffs for decision alternative d₁. Assume the probabilities are as given in part (b), and find the range of payoffs under states of nature s₁ and s₂ that will keep the solution found in part (b) optimal. Is the solution more sensitive to the payoff under state of nature s₁ or s₂?

3. Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company's new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):

Service	Demand for Service
	Strong	Weak
Full price	$960	-$490
Discount	$670	$320

a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event?

b. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

c. Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal decision.

d. Suppose that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach?

e. Use graphical sensitivity analysis to determine the range of demand probabilities for which each of the decision alternatives has the largest expected value.

4. The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:

Decision Alternative	State of Nature
	s1	s2	s3
d1	250	100	25
d2	100	100	75

The probabilities for the states of nature are P(s₁) = 0.65, P(s₂) = 0.15, and P(s₃) = 0.20.

a. What is the optimal decision strategy if perfect information were available?

b. What is the expected value for the decision strategy developed in part (a)?

c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?

d. What is the expected value of perfect information?

5. The Lake Placid Town Council decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the appropriate size. Many influential citizens want a large center that would be a showcase for the area. But the mayor feels that if demand does not support such a center, the community will lose a large amount of money. To provide structure for the decision process, the council narrowed the building alternatives to three sizes: small, medium, and large. Everybody agreed that the critical factor in choosing the best size is the number of people who will want to use the new facility. A regional planning consultant provided demand estimates under three scenarios: worst case, base case, and best case. The worst-case scenario corresponds to a situation in which tourism drops substantially; the base-case scenario corresponds to a situation in which Lake Placid continues to attract visitors at current levels; and the best-case scenario corresponds to a substantial increase in tourism. The consultant has provided probability assessments of 0.10, 0.60, and 0.30 for the worst-case, base-case, and best-case scenarios, respectively.

The town council suggested using net cash flow over a 5-year planning horizon as the criterion for deciding on the best size. The following projections of net cash flow (in thousands of dollars) for a 5-year planning horizon have been developed. All costs, including the consultant's fee, have been included.

Center Size	Demand Scenario
	Worst Case	Base Case	Best Case
Small	400	500	660
Medium	-250	650	800
Large	-400	580	990

a. What decision should Lake Placid make using the expected value approach?

b. Construct risk profiles for the medium and large alternatives. Given the mayor's concern over the possibility of losing money and the result of part (a), which alternative would you recommend?

c. Compute the expected value of perfect information. Do you think it would be worth trying to obtain additional information concerning which scenario is likely to occur?

d. Suppose the probability of the worst-case scenario increases to 0.2, the probability of the base-case scenario decreases to 0.5, and the probability of the best-case scenario remains at 0.3. What effect, if any, would these changes have on the decision recommendation?

e. The consultant has suggested that an expenditure of $150,000 on a promotional campaign over the planning horizon will effectively reduce the probability of the worst-case scenario to zero. If the campaign can be expected to also increase the probability of the best-case scenario to 0.4, is it a good investment?

Textbook - Quantitative Methods for Business, 12^th edition. Authors - David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran, Michael J. Fry and Jeffrey W. Ohlmann

Chapter 4 - Decision Analysis.