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578 CHAPTER 13 DECISION ANALYSIS

a. Construct a decision tree for this problem.
b. If the decision maker knows nothing about the probabilities of the three states of nature,
what is the recommended decision using the optimistic, conservative and minimax
regret approaches?

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

State of Nature

Decision Alternative s 1 s 2 s 3 s 4
d 1 14 9 10 5
d 2 11 10 8 7
d 3 9 10 10 11
d 4 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?
3 Khobar Corporation’s decision to produce a new line of recreational products resulted in
the need to construct either a small plant or a large plant. The best selection of plant size
depends on how the marketplace reacts to the new product line. To conduct an analysis,
marketing management has decided to view the possible long-run demand as either low,
medium or high. The following payoff table shows the projected profit in millions of euros:

Long-Run Demand
Plant Size Low Medium High
Small 150 200 200
Large 50 200 500

a. What is the decision to be made, and what is the chance event for Southland’s problem?
b. Construct a decision tree.
c. Recommend a decision based on the use of the optimistic, conservative and minimax
regret approaches.
4 The following profit payoff table was presented in Problem 1. Suppose that the decision
maker obtained the probability assessments P(s 1 ) ¼ 0.65, P(s 2 ) ¼ 0.15, and P(s 3 ) ¼ 0.20.
Use the expected value approach to determine the optimal decision.

State of Nature
Decision Alternative s 1 s 2 s 3
250 100 25
d 1
100 100 75
d 2

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