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RISK ANALYSIS AND SENSITIVITY ANALYSIS 555

Using P(s 1 ) ¼ 0.8 and P(s 2 ) ¼ 0.2, the general expression for EV(d 3 ) is:

EVðd 3 Þ¼ 0:8S þ 0:2W (13:10)

Assuming that the payoff for d 3 stays at its original value of R9 million when
demand is weak, the large complex decision alternative will remain optimal as
long as:

EVðd 3 Þ¼ 0:8S þ 0:2ð 9Þ 12:2 (13:11)

Solving for S, we have:
0:8S 1:8 12:2
0:8S 14
S 17:5
Recall that when demand is strong, decision alternative d 3 has an estimated payoff
of R20 million. The preceding calculation shows that decision alternative d 3 will
remain optimal as long as the payoff for d 3 when demand is strong is at least R17.5
million.
Assuming that the payoff for d 3 when demand is strong stays at its original value
of R20 million, we can make a similar calculation to learn how sensitive the optimal
solution is with regard to the payoff for d 3 when demand is weak. Returning to the
expected value calculation of Equation (13.10), we know that the large complex
decision alternative will remain optimal as long as:

EVðd 3 Þ¼ 0:8ð20Þþ 0:2W 12:2 (13:12)

Solving for W, we have:

16 þ 0:2W 12:2
0:2W 3:8
W 19

Sensitivity analysis can Recall that when demand is weak, decision alternative d 3 has an estimated
assist management in payoff of R9 million. The preceding calculation shows that decision alternative
deciding whether more d 3 will remain optimal as long as the payoff for d 3 when demand is weak is at
time and effort should be
spent obtaining better least R19 million.
estimates of payoffs and Based on this sensitivity analysis, we conclude that the payoffs for the large
probabilities. complex decision alternative (d 3 ) could vary considerably and d 3 would remain the
recommended decision alternative. Thus, we conclude that the optimal solution for
the PDC decision problem is not particularly sensitive to the payoffs for the large
complex decision alternative. We note, however, that this sensitivity analysis has
been conducted based on only one change at a time. That is, only one payoff was
changed and the probabilities for the states of nature remained P(s 1 ) ¼ 0.8 and
P(s 2 ) ¼ 0.2. Note that similar sensitivity analysis calculations can be made for the
payoffs associated with the small complex decision alternative d 1 and the medium
complex decision alternative d 2 . However, in these cases, decision alternative d 3
remains optimal only if the changes in the payoffs for decision alternatives d 1 and d 2
meet the requirements that EV(d 1 ) 14.2 and EV(d 2 ) 14.2.

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