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12 CHAPTER 1 INTRODUCTION

Figure 1.2 Revised MS approach

Problem
recognition
Implementation

Problem
Solution(s) and Structuring and
recommendation(s) Definition

Modelling
and Analysis

1.5 Models

Management science makes considerable use of models. Models are representations of
real objects or situations and can be presented in various forms. For example, Airbus
may make a scale model of an aeroplane that they’re thinking of producing. VW may
make a model of a new vehicle prototype. The model aeroplane and vehicle are
examples of models that are physical replicas of real objects. In modelling terminology,
physical replicas are referred to as iconic models. Another classification of models – the
type we will primarily be studying – includes representations of a problem by a system
of symbols and quantitative relationships or expressions. Such models are referred to as
mathematical models and are a critical part of any quantitative approach to decision
making. For example, the total profit from the sale of a product can be determined by
multiplying the profit per unit by the quantity sold. If we let x represent the number of
units sold and P the total profit, then, with a profit of E10 per unit, the following
mathematical model defines the total profit earned by selling x units:

P ¼ 10x (1:1)

The symbols P and x are known as variables – their exact numerical value can vary,
it is not predetermined or fixed. The variable P, profit, is known as a dependent
variable since its value depends on x, the number of units sold. x is referred to as an
independent variable since its value in this equation is not dependent on another
variable. The whole equation is referred to as a functional relationship. We are
relating profit, P, to the number of units sold, x, and we are saying that profit is a
function of sales. The value of E10 in equation (1.1) is known as a parameter.
Parameters are known, constant values. Unlike variables their value does not change.
The values for parameters in a model are usually obtained from observed data. In this
case the data is likely to be readily available and reliable and accurate, after all, we
know the price we’re selling the product for. In other cases, however, the value of a
parameter may have to be estimated using the best available data and may be less
reliable. Consider a different model, for example, where we are relating the number of

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