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180 Applying simulation to decision problems
be a large or infinite number of combinations of circumstances which
could affect the return on the investment. In such situations it is clearly
impractical to use an approach such as a probability tree to calculate the
probability of each of these combinations of circumstances occurring.
One answer to our problem is to use a versatile and easily understood
technique called Monte Carlo simulation. This involves the use of
a computer to generate a large number of possible combinations of
circumstances which might occur if a particular course of action is
chosen. When the simulation is performed the more likely combination
of circumstances will be generated most often while very unlikely
combinations will rarely be generated. For each combination the payoff
which the decision maker would receive is calculated and, by counting
the frequency with which a particular payoff occurred in the simulation,
a decision maker is able to estimate the probability that the payoff
will be received. Because this method also enables the risk associated
with a course of action to be assessed it is often referred to as risk
analysis (although some authors use the term to include methods other
than simulation such as mathematical assessment of risk). Monte Carlo
simulation is demonstrated in the next section.
Monte Carlo simulation
As we stated earlier, a computer is normally used to carry out Monte
Carlo simulation, but we will use the following simplified problem to
illustrate how the technique works. A company accountant has estimated
that the following probability distributions apply to his company’s
inflows and outflows of cash for the coming month:
Cash inflows
($)
Probability
(%)
Cash outflows
($)
Probability
(%)
50 000 30 50 000 45
60 000 40 70 000 55
70 000 30
100
100
The accountant would like to obtain a probability distribution for the net
cash flow (i.e. cash inflow–cash outflow) over the month. He thinks that
it is reasonable to assume that the outflows and inflows are independent.