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the question—what is a model? This might appear to be a simple question, but as is

often the case, simple questions can often lead to complex answers. Additionally, we

need to walk a ﬁne line between an answer that is simple, and one that does not over-

simplify our understanding. Albert Einstein was known to say—“Things should be

made as simple as possible, but not any simpler.” We will heed his advice.

Throughout the initial chapters, we have discussed models in various forms.

Early on, we broadly viewed models as an attempt to capture the behavior of a

system. The presentation of quantitative and qualitative data in Chaps. 2 and 4 pro-

vided visual models of the behavior of a system for a number of examples: sales

data of products over time, payment data in various categories, and auto sales for

sales associates. Each graph, data sort, or ﬁlter modeled the outcome of a focused

question. For example, we determined which sales associates sold automobiles in a

speciﬁed time period and we determined the types of expenditures a college student

made on particular days of the week. In Chaps. 3 and 5 we performed data analysis

on both quantitative and qualitative data leading to models of general and speciﬁc

behavior, like summary statistics and
PivotTables
. Each of these analyses relied on

the creation of a model to determine behavior. For example, our paired t-Test for

determining the changes in average page views of teens modeled the number of

views before and after website changes. In all these cases, the model was the way

we
arranged
,
viewed
, and
examined
data.

Before we proceed with a formal answer to our question, let’s see where this

chapter will lead. The world of modeling can be described and categorized in many

ways. One important way to categorize models is related to the circumstances of

their
data availability
. Some modeling situations are
data rich
; that is, data for

modeling purposes exists and is readily available for model development. The data

on teens viewing a website was such a situation, and in general, the models we

examined in Chaps. 2, 3, 4, 5, and 6 were all data rich. But what if there is little

data available for a particular question or problem—a
data poor
circumstance? For

example, what if we are introducing a new product that has no reasonable equivalent

in a particular sales market? How can we model the potential success of the product

if the product has no sales history and no related product exists that is similar in

potential sales? In these situations modelers rely on models that
generate
data based

on a set of underlying assumptions. Chaps. 7 and 8 will focus on these models that

can be analyzed by the techniques we have discussed in our early chapters.

Since the academic area of Modeling and Simulation is very broad, it will be

necessary to divide the topics into two chapters. Chapter 7 will concentrate on the

basics of modeling. We will learn how models can be used and how to construct

them. Also, since this is our ﬁrst formal view of models, we will concentrate on

models that are less complex in their content and structure. Although uncertainty

will be modeled in both Chaps. 7 and 8, we will deal explicitly with uncertainty

in Chap. 8. Yet, for both chapters, considering the uncertainty associated with a

process will help us analyze the risk associated with overall model results.

Chapter 8 will also introduce methods for constructing
Monte Carlo
simulations,

a powerful method for modeling uncertainty. Monte Carlo simulation uses random

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