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130 Decision making under uncertainty
Expected
utility = 0.757
Work normally
Hire extra labor, etc.
Expected
utility = 0.872
0.1
0.6
0.3
0.8
0.2
Overrun
time
0 weeks
3 weeks
6 weeks
Project
cost
$50000
$60000
$80000
0 weeks $120000
1 week $140000
Figure 5.21 – The project manager’s decision tree with utilities
Utility
1.0
0.8256
0.54
0.91
0.72
u(3 weeks overrun) = 0.6 and u($60 000 cost) = 0.96. Therefore:
u(3 weeks overrun, $60 000 cost)
= 0.8 u(3 weeks overrun) + 0.6 u($60 000 cost)
− 0.4 u(3 weeks overrun)u($60 000 cost)
= 0.8(0.6) + 0.6(0.96) − 0.4(0.6)(0.96) = 0.8256
Figure 5.21 shows the decision tree again with the multi-attribute
utilities replacing the original attribute values. By multiplying the probabilities
of the outcomes by their utilities we obtain the expected utility
of each option. The results shown on the tree indicate that the project
manager should hire the extra labor and operate 24-hour working, as
this yields the highest expected utility.
Stage 3
It is important that we should check that the results of the analysis
have faithfully represented the project manager’s preferences. This can
involve tracking back through the analysis and explaining why one