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interchangeably; that is, simulation as modeling and vice versa. We will make a
distinction between the two terms and we will see that in order to simulate a process
we must ﬁrst create a model of the process. Thus, modeling precedes simulation,
and simulation is an activity that depends on exercising a model. This may sound
like a great deal of concern about the minor distinctions between the two terms,
but as we discussed in Chap. 7, being systematic and rigorous in our approach to
modeling helps insure that we don’t overlook critical aspects of a problem. Over
many years of teaching and consulting, I have observed very capable people make
serious modeling errors, simply because they felt that they could approach modeling
in a casual manner, thereby abandoning a systematic approach.
So why do we make the distinction between modeling and simulation? In Chap. 7
we developed deterministic models and then exercised the model to generate out-
comes based on simple what - if changes. We did so with the understanding that not
all models require sophisticated simulation. For example, Fr. Eﬁa’s problem was a
very simple form of simulation. We exercised the model by imposing a number of
conditions: weather, an expected return on bets, and an expected number of atten-
dees. Similarly, we imposed requirements (rate, term, principal) in the modeling of
mortgage payments. But models are often not this simple, and can require consider-
able care in conducting simulations; for example, modeling the process of patients
visiting a hospital emergency department. The arrival of many types of injury and
illness, the stafﬁng required to deal with the cases, and the updating of current bed
and room capacity based on the state of conditions in the emergency department
make this a complex model to simulate.
The difference between the mortgage payment and a hospital emergency depart-
ment simulation, aside from the model complexity, is how we deal with uncertainty.
For the mortgage payment model, we used a manual approach to managing uncer-
tainty by changing values and asking what-if questions individually: what-if the
interest rate is 7% rather than 6%, what if I change the principal amount I bor-
row, etc. In the OLPS model we reduced uncertainty to point estimates (speciﬁc
values) and then used a manual approach to exercise a speciﬁc model conﬁgura-
tion; for example, we set the number of attendees for Cloudy weather to exactly
2500 people and we considered a what-if change to Entry Fee from \$10 to \$50. This
approach was sufﬁcient for our simple what-if analysis, but with models contain-
ing more elements of uncertainty and even greater complexity due to the interaction
of uncertainty elements, we will have to devise complex simulation approaches for
managing uncertainty.
The focus of this chapter will be on a form of simulation that is often used in
modeling of complex problems—a methodology called Monte Carlo Simulation .
Monte Carlo simulation has the capability of handling the more complex models
that we will encounter in this chapter. This does not suggest that all problems are
destined to be modeled as Monte Carlo simulations, but many can and should. In
the next section, I will brieﬂy discuss several types of simulation. Emphasis will
be placed on the differences between approaches and on the appropriate use of
techniques. Though there are many commercially available simulation software
packages for a variety of applications, remarkably, Excel is a very capable tool
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