Page 572 -

552 CHAPTER 13 DECISION ANALYSIS

Figure 13.4 Risk Profile for the Large Complex Decision Alternative for the PDC
Project

1.0

.8
Probability .6

.4

.2

–10 0 10 20
Profit ($ millions)

Sensitivity Analysis

Sensitivity analysis can be used to determine how changes in the probabilities for the
states of nature or changes in the payoffs affect the recommended decision alter-
native. In many cases, the probabilities for the states of nature and the payoffs are
based on subjective assessments. Sensitivity analysis helps the decision maker under-
stand which of these inputs are critical to the choice of the best decision alternative.
If a small change in the value of one of the inputs causes a change in the recom-
mended decision alternative, the solution to the decision analysis problem is sensi-
tive to that particular input. Extra effort and care should be taken to make sure the
input value is as accurate as possible. On the other hand, if a modest to large change
in the value of one of the inputs does not cause a change in the recommended
decision alternative, the solution to the decision analysis problem is not sensitive to
that particular input. No extra time or effort would be needed to refine the esti-
mated input value.
One approach to sensitivity analysis is to select different values for the proba-
bilities of the states of nature and the payoffs and then solve the decision analysis
problem again. If the recommended decision alternative changes, we know that the
solution is sensitive to the changes made. For example, suppose that in the PDC
problem the probability for a strong demand is revised to 0.2 and the probability for
a weak demand is revised to 0.8. Would the recommended decision alternative
change? Using P(s 1 ) ¼ 0.2, P(s 2 ) ¼ 0.8, and Equation (13.4), the revised expected
values for the three decision alternatives are:
EVðd 1 Þ¼ 0:2ð8Þþ 0:8ð7Þ¼ 7:2
EVðd 2 Þ¼ 0:2ð14Þþ 0:8ð5Þ¼ 6:8
EVðd 3 Þ¼ 0:2ð20Þþ 0:8ð 9Þ¼ 3:2

With these probability assessments the recommended decision alternative is to
construct a small complex (d 1 ), with an expected value of R7.2 million. The prob-
ability of strong demand is only 0.2, so constructing the large complex (d 3 ) is the
least preferred alternative, with an expected value of R3.2 million (a loss).
Thus, when the probability of strong demand is large, PDC should build the large
complex; when the probability of strong demand is small, PDC should build the
small complex. Obviously, we could continue to modify the probabilities of the states

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.