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544 CHAPTER 13 DECISION ANALYSIS

Table 13.2 Maximum Payoff for Each PDC Decision Alternative
Decision Alternative Maximum Payoff
8
Small complex, d 1
14
Medium complex, d 2
20 Maximum of the
Large complex, d 3
maximum payoff values

maker to choose the alternative corresponding to the largest return. For problems
involving minimization, this approach leads to choosing the alternative with the
smallest payoff.
For a maximization To illustrate the optimistic approach, we use it to develop a recommendation for
problem, the optimistic the PDC problem. First, we determine the maximum payoff for each decision
approach often is alternative; then we select the decision alternative that provides the overall max-
referred to as the
maximax approach; for a imum payoff. These steps systematically identify the decision alternative that pro-
minimization problem, vides the largest possible profit. Table 13.2 illustrates these steps.
the corresponding Because 20, corresponding to d 3 , is the largest payoff, the decision to construct
terminology is minimin.
the large complex is the recommended decision alternative using the optimistic
approach.

Conservative Approach
The conservative approach evaluates each decision alternative in terms of the worst
payoff that can occur. The decision alternative recommended is the one that pro-
vides the best of the worst possible payoffs. For a problem in which the output
measure is return, as in the PDC problem, the conservative approach would lead the
decision maker to choose the alternative that maximizes the minimum possible
return that could be obtained. For problems involving minimization, this approach
identifies the alternative that will minimize the maximum payoff.
For a maximization To illustrate the conservative approach, we use it to develop a recommendation
problem, the for the PDC problem. First, we identify the minimum payoff for each of the decision
conservative approach is
often referred to as the alternatives; then we select the decision alternative that maximizes the minimum
maximin approach; for a payoff. Table 13.3 illustrates these steps for the PDC problem.
minimization problem, Because 7, corresponding to d 1 , yields the maximum of the minimum payoffs,
the corresponding the decision alternative of a small complex is recommended. This decision
terminology is minimax.
approach is considered conservative because it identifies the worst possible payoffs
and then recommends the decision alternative that avoids the possibility of
extremely ‘bad’ payoffs. In the conservative approach, PDC is guaranteed a return
of at least R7 million. Although PDC may make more, it cannot make less than
R7 million.

Table 13.3 Minimum Payoff for each PDC Decision Alternative
Decision Alternative Minimum Payoff

7 Maximum of the
Small complex, d 1
5 minimum payoff values
Medium complex, d 2
9
Large complex, d 3

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