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580 CHAPTER 13 DECISION ANALYSIS

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 Scot 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.
8 For the PDC problem in Section 13.3, the decision alternative to build the large complex
was found to be optimal using the expected value approach. In Section 13.4 we conducted
a sensitivity analysis for the payoffs associated with this decision alternative. We found that
the large complex remained optimal as long as the payoff for the strong demand was
greater than or equal to R17.5 million and as long as the payoff for the weak demand was
greater than or equal to R19 million.
a. Consider the medium complex decision. How much could the payoff under strong
demand increase and still keep decision alternative d 3 the optimal solution?
b. Consider the small complex decision. How much could the payoff under strong demand
increase and still keep decision alternative d 3 the optimal solution?
9 The following profit payoff table was presented in Problems 1 and 4.

State of Nature

Decision Alternative s 1 s 2 s 3
250 100 25
d 1
100 100 75
d 2

The probabilities for the states of nature are P(s 1 ) ¼ 0.65, P(s 2 ) ¼ 0.15, and
P(s 3 ) ¼ 0.20.
a. What is the optimal decision strategy if perfect information is 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?
10 Consider a variation of the PDC decision tree shown in Figure 13.7. The company must first
decide whether to undertake the market research study. If the market research study is
conducted, the outcome will either be favourable (F) or unfavourable (U). Assume there are
only two decision alternatives d 1 and d 2 and two states of nature s 1 and s 2 . The payoff table
showing profit is as follows:

State of Nature

Decision Alternative s 1 s 2

d 1 100 300
d 2 400 200

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