Downloadable - About University

Utility functions for non-monetary attributes 111
Expected
utility = 0.65
Continue with existing
method
Switch to new approach
Expected
utility = 0.58
0.4
0.6
0.2
0.4
0.4
Development
time
6 years
4 years
1 year
2 years
8 years
Utilities
Figure 5.8 – A decision tree for the drug company research department problem
that there is a 0.4 probability that the drug will take 6 years to develop
and a 0.6 probability that development will take 4 years. However,
recently a ‘short-cut’ method has been proposed which might lead to
significant reductions in the development time, and the company, which
has limited resources available for research, has to decide whether to
take a risk and switch completely to the proposed new method. The
head of research estimates that, if the new approach is adopted, there
is a 0.2 probability that development will take a year, a 0.4 probability
that it will take 2 years and a 0.4 probability that the approach will not
work and, because of the time wasted, it will take 8 years to develop
the product.
Clearly, adopting the new approach is risky, so we need to derive
utilities for the development times. The worst development time is
8years,sou(8 years) = 0andthebesttimeis1year,sou(1 year) = 1.0.
After being asked a series of questions, based on the variable probability
method, the head of research is able to say that she is indifferent between
a development time of 2 years and engaging in a lottery which will give
her a 0.95 probability of a 1-year development and a 0.05 probability of
an 8-year development time. Thus:
0.5
0.75
1.0
0.95
u(2years) = 0.95 u(1 year) + 0.05 u(8 years)
= 0.95(1.0) + 0.05(0) = 0.95
0