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7
Applying simulation
to decision problems
Introduction
When the payoff of a decision depends upon a large number of factors,
estimating a probability distribution for the possible values of this payoff
can be a difficult task. Consider, for example, the problem of estimating
a probability distribution for the return that might be generated by a
new product. The return on the investment will depend upon factors
such as the size of the market, the market share which the product
will achieve, the costs of launching the product, manufacturing and
distribution costs, and the life of the product. We could, of course, ask
the decision maker to estimate the probability distribution directly (for
example, we might ask questions such as: ‘What is the probability that
the investment will achieve a return of over 10% per annum?’). However,
it is likely that many decision makers would have difficulty in making
this sort of judgment since all the factors which might influence the
return on the investment, and the large number of ways in which they
could interrelate, would have to be considered at the same time.
The decision analysis approach to this problem is to help the decision
maker by initially dividing the probability assessment task into smaller
parts (a process sometimes referred to as ‘credence decomposition’).
Thus we might ask the decision maker to estimate individual probability
distributions for the size of the market, the market share which will be
achieved, the launch costs and so on.
The problem is, that having elicited these distributions, we then need
to determine their combined effect in order to obtain a probability
distribution for the return on the investment. In most practical problems
there will be a large number of factors, and also the possible values which
each of the factors can assume may be very large or infinite. Consider, for
example, the possible levels of the costs of launch, manufacturing and
distribution which we might experience. All of this means that there will