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numbers to model the probability distributions of outcomes for uncertain variables
in our problems. This may sound complicated, and it can be, but we will take great
care in understanding the fundamentals—simple, but not too simple.
7.1.1 What is a Model?
So, now back to our original question—what is a model? To answer this question,
let us begin by identifying a broad variety of model types.
1. Physical model : a physical replica that can be operated, tested, and assessed—
e.g. a model of an aircraft that is placed in a wind-tunnel to test its aerodynamic
characteristics and behavior.
2. Analog model : a model that is analogous (shares similarities)—e.g. a map is
analogous to the actual terrestrial location it models.
3. Symbolic model : a model that is more abstract than the two discussed above and
that is characterized by a symbolic representation—e.g. a ﬁnancial model of the
US economy used to predict economic activity in a particular economic sector.
Our focus will be on symbolic models: models constructed of mathematical rela-
tionships that attempt to mimic and describe a process or phenomenon. Of course,
this should be of no surprise since this is exactly what Excel does, besides all its cler-
ical uses like storing, sorting, manipulating, and querying data. Excel, with its vast
array of internal functions, is used to represent phenomenon that can be translated
into mathematical and logical relationships.
Symbolic models also permit us to observe how our decisions will perform under
a particular set of model conditions. We can build models where the conditions
within which the model operates are assumed to be known with certainty. Then
the speciﬁc assumptions we have made can be changed and the changed conditions
applied to the model. Becoming acquainted with these models is the goal of this
We can also build models where the behavior of model elements is uncertain, and
the range of uncertainty is built directly into the model. This is the goal of Chap. 8.
The difference between the two approaches is subtle, but under the ﬁrst approach,
the question that is addressed is—if we impose these speciﬁc conditions, what is the
resulting behavior of our model? It is a very focused approach. In the latter approach
we incorporate the full array of possible conditions into the model and ask—if we
assume these possible conditions, what is the full array of outcomes for the model?
Of course, this latter approach is much broader in its scope.
The models we will build in this chapter will permit us to examine complex
decisions. Imagine you are considering a serious ﬁnancial decision. Your con-
stantly scheming neighbor has a business idea, which for the ﬁrst time you can
recall, appears to have some merit. But the possible outcomes of the idea can result