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206 Applying simulation to decision problems
While computers excel at the rapid calculation of a large number
of simulation results, we should not forget that the judgments of the
decision maker are still the crucial inputs to the decision model. This
means that, as always, care should be taken in the design of the model
and in the elicitation of probabilities and utilities. The process of initially
dividing the problem into small parts should help the decision
maker in this task. Nevertheless, it is important to be aware of any
assumptions and simplifications which are inherent in the model which
is being used.
Exercises
(1) A small retail store sells a particular brand of monochrome and
color television sets. Each monochrome set that is sold earns a profit
of $100, while each color set earns $200 profit. The manager of
the store estimates that the weekly demands for each type of set
follow the probability distributions shown below. It can be assumed
that the demands for each type of set are independent, as is the
week-to-week demand.
Demand Probability
per week Monochrome sets Color sets
0 0.2 0.4
1 0.5 0.6
2 0.3
(a) Determine the possible total profits that can be earned in any
given week by selling television sets and calculate the probability
of each of these profits being earned.
(b) The following two-digit random numbers have been generated
by a computer. Use these numbers to simulate the demand for
the two types of set for a 10-week period and hence calculate the
profit that will be earned in each week. (The first set of numbers
should be used for monochrome sets and the second for color.)
Monochrome 71 82 19 50 67 29 95 48 84 32
Color 36 44 64 92 39 21 18 55 77 73