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Model Building in Mathematical Programming, 5th Edition by H. Paul Williams

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Chapter 1

Introduction

1.1 The concept of a model

Many applications of science make use of models. The term ‘model’ is usually used for a structure that has been built with the purpose of exhibiting features and characteristics of some other objects. Generally, only some of these features and characteristics will be retained in the model depending upon the use to which it is to be put. Sometimes, such models are concrete, as is a model aircraft used for wind tunnel experiments. More often, in operational research, we will be concerned with abstract models. These models will usually be mathematical in that algebraic symbolism will be used to mirror the internal relationships in the object (often an organization) being modelled. Our attention will mainly be confined to such mathematical models, although the term ‘model’ is sometimes used more widely to include purely descriptive models.

The essential feature of a mathematical model in operational research is that it involves a set of mathematical relationships (such as equations, inequalities and logical dependencies) that correspond to some more down-to-earth relationships in the real world (such as technological relationships, physical laws and marketing constraints).

There are a number of motives for building such models:

1. The actual exercise of building a model often reveals relationships that were not apparent to many people. As a result, a greater understanding is achieved of the object being modelled.
2. Having built a ...

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