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Applying simulation to a decision problem 195
Of course, there are bound to be situations where the CDFs intersect
each other several times. In these cases we would have to add areas
together to establish the extent to which one option dominates the other.
The mean–standard deviation approach
When a decision problem involves a large number of alternative courses
of action it is helpful if inferior options can be screened out at an early
stage. In these situations the mean–standard deviation approach can
be useful. This has mainly been developed in connection with portfolio
theory, where a risk-averse decision maker has to choose between a
large number of possible investment portfolios (see Markowitz 4 ).
To illustrate the approach let us suppose that a company is considering
five alternative products which are code-named A to E. For each product
a simulation has been carried out and the mean and standard deviation
of that product’s profits have been calculated. The results are plotted
in Figure 7.8. The company’s manager would like to maximize the
expected (or mean) return, and being risk averse, she would also like
Standard deviation of profit ($000)
250
200
150
100
50
B
A
E
−200 0 200 400 600 800
Expected (mean) profit ($000)
D
Efficient frontier
Figure 7.8 – The mean–standard deviation screening method
C