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554 CHAPTER 13 DECISION ANALYSIS

Figure 13.5 Expected Value for the PDC Decision Alternatives as a Function of p

d 3 provides
the highest EV
20
EV(d 3 )

d provides
15 2
the highest EV EV(d 2 )
d 1 provides
the highest EV
Expected Value (EV) 5 EV(d 1 )
10

0 p
0.2 0.4 0.6 0.8 1.0

–5

–10

Graphical sensitivity Hence, when p ¼ 0.25, decision alternatives d 1 and d 2 provide the same expected
analysis shows how value. Repeating this calculation for the value of p corresponding to the intersection
changes in the
probabilities for the states of the EV(d 2 ) and EV(d 3 ) lines, we obtain p ¼ 0.70.
of nature affect the Using Figure 13.5, we can conclude that decision alternative d 1 provides the
recommended decision largest expected value for p 0.25, decision alternative d 2 provides the largest
alternative. Try Problem 6.
expected value for 0.25 p 0.70, and decision alternative d 3 provides the largest
expected value for p 0.70. Because p is the probability of state of nature s 1 and
(1 p) is the probability of state of nature s 2 , we now have the sensitivity analysis
information that tells us how changes in the state-of-nature probabilities affect the
recommended decision alternative.
Sensitivity analysis calculations can also be made for the values of the payoffs. In
the original PDC problem, the expected values for the three decision alternatives
were as follows: EV(d 1 ) ¼ 7.8, EV(d 2 ) ¼ 12.2 and EV(d 3 ) ¼ 14.2. Decision alter-
native d 3 (large complex) was recommended. Note that decision alternative d 2 with
EV(d 2 ) ¼ 12.2 was the second best decision alternative. Decision alternative d 3 will
remain the optimal decision alternative as long as EV(d 3 ) is greater than or equal to
the expected value of the second best decision alternative. Thus, decision alternative
d 3 will remain the optimal decision alternative as long as:

EVðd 3 Þ 12:2 (13:9)

Let
S ¼ the payoff of decision alternative d 3 when demand is strong
W ¼ the payoff of decision alternative d 3 when demand is weak

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