Downloadable - About University

182 Applying simulation to decision problems
Cash outflow
($)
Probability
(%)
Random
numbers
50 000 45 00–44
70 000 55 45–99
We are now ready to perform the simulation run. Each simulation
will involve the generation of two random numbers. The first of these
will be used to determine the cash inflow and the second, the cash
outflow. Suppose that a computer generates the random numbers 46
and 81. This implies a cash inflow of $60 000 and an outflow of $70 000,
leading to a net cash flow for the month of −$10 000. If we repeat
this process a large number of times then it is to be expected that the
more likely combinations of cash flows will occur most often, while
the unlikely combinations will occur relatively infrequently. Thus the
probability of a particular net cash flow occurring can be estimated
from the frequency with which it occurs in the simulations. Table 7.1
shows the results of ten simulations. This number of repetitions is far
too small for practical purposes, but the experiment is designed simply
to illustrate the basic idea.
If we assume for the moment that this small number of repetitions
is sufficient to give us estimates of the probabilities of the various net
cash flows occurring then we can derive the probability distribution
shown in Table 7.2. For example, since a new cash flow of −$20 000
occurred in four of our ten simulations we estimate that the probability
Table 7.1 – Ten simulations of monthly cash flows
Random
number
Cash inflow
($)
Random
number
Cash outflow
($)
Net cash flow
($)
46 60 000 81 70 000 −10 000
30 60 000 08 50 000 10 000
14 50 000 88 70 000 −20 000
35 60 000 21 50 000 10 000
09 50 000 73 70 000 −20 000
19 50 000 77 70 000 −20 000
72 70 000 01 50 000 20 000
20 50 000 46 70 000 −20 000
75 70 000 97 70 000 0
16 50 000 43 50 000 0