Reference no: EM133173094
State of Nature decision Alternative d1 d2 d3 d4 s1 s2 14 9 11 10 9 10 8 10 s3 s4 10 5 8 7 10 11 11 13
1. Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table: 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
State of Nature decision Alternative s1 s2 d1 10 1 d2 43
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) 5 0.2 and P(s2) 5 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. Manage- ment 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 follow- ing table shows the estimated quarterly profits (in thousands of dollars):
Demand for Service Service Strong Weak Full price $960 2$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 decision Alternative d1 d2 State of Nature s1 s2 s3 250 100 25 100 100 75
the probabilities for the states of nature are P(s1) 5 0.65, P(s2) 5 0.15, and P(s3) 5 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?