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Applying simulation to a decision problem 191
Probability
0.5
0.4
0.3
0.1
0.2
Plate
Figurine
−300 −200 −100 0 100 200 300 400 500
Figure 7.5 – A comparison of the profit probability distributions of the commemorative
plate and the figurine
the probabilities that each product would reach a target level of profit.
The two distributions have been plotted in Figure 7.5. Note that to
make the comparison between the distributions easier, their histograms
have been approximated by line graphs (or polygons). Although both
distributions have their highest probabilities for profits in the range $0
to under $100 000 it can be seen that the distribution for the figurine
has a greater spread. Thus while the figurine has a higher probability of
yielding a large loss it also has a higher probability of generating a large
profit. Clearly, the greater spread of the figurine’s distribution implies
that there is more uncertainty about the profit which will actually be
achieved. Because of this, the spread of a distribution is often used as a
measure of the risk which is associated with a course of action.
A distribution’s spread can be measured by calculating its standard
deviation (the larger the standard deviation, the greater the spread – see
the appendix to this chapter if you are unfamiliar with this measure).
For the plate, the standard deviation of profits is $99 080 while for the
figurine it is $163 270.
Determining the option with the highest expected utility
Because the two products offer different levels of risk, utility theory
can be used to identify the option which the decision maker should