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542 CHAPTER 13 DECISION ANALYSIS

Table 13.1 Payoff Table for the PDC Project (Payoffs in Million Rials)
State of Nature
Decision Alternative Strong Demand s 1 Weak Demand s 2

8 7
Small complex, d 1
14 5
Medium complex, d 2
20 9
Large complex, d 3
Payoff Tables

Given the three decision alternatives and the two states of nature, which complex
size should PDC choose? To answer this question, PDC will need to know the
consequence associated with each decision alternative and each state of nature. In
decision analysis, we refer to the consequence resulting from a specific combination
of a decision alternative and a state of nature as a payoff. A table showing payoffs for
all combinations of decision alternatives and states of nature is a payoff table.
Because PDC wants to select the complex size that provides the largest return,
Payoffs can be expressed return is used as the consequence. The payoff table with return expressed in millions
in terms of profit, cost,
time, distance or any of Rials is shown in Table 13.1. Note, for example, that if a medium complex is built
other measure and demand turns out to be strong, a return of R14 million will be realized. We will
appropriate for the use the notation V ij to denote the payoff associated with decision alternative i and
decision problem being state of nature j. Using Table 13.1, V 31 ¼ 20 indicates a payoff of R20 million occurs
analyzed.
if the decision is to build a large complex (d 3 ) and the strong demand state of nature
(s 1 ) occurs. Similarly, V 32 ¼ 9 indicates a loss of R9 million if the decision is to
build a large complex (d 3 ) and the weak demand state of nature (s 2 ) occurs.

Decision Trees
A decision tree provides a graphical representation of the decision-making process.
If you have a payoff
table, you can develop a Figure 13.1 presents a decision tree for the PDC problem. Note that the decision
decision tree. Try tree shows the natural or logical progression that will occur over time. The decision
Problem 1(a).

Figure 13.1 Decision Tree for the PDC Project (Payoffs in R Million)

Strong (s 1 )
8
Small (d )
1
2
)
Weak (s 2
7
Strong (s 1 )
14
Medium (d )
2
1 3
Weak (s )
2
5
Strong (s )
1
Large (d ) 20
3
4
Weak (s ) –9
2

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