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138 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

In the previous chapters linear programming was introduced and a method of
determining the solution to such a simple problem provided. In subsequent chapters
we shall examine a more rigorous and general purpose solution method and discuss
the management information that can be obtained from the application of the
technique. Before doing so, however, it is worthwhile examining a variety of typical
applications of LP. This will serve two purposes. The first is that it will provide an
overview of the tremendous diversity of business applications to which the technique
has been applied. LP has turned out to be one of the most successful quantitative
models in decision making. Applications have been reported in almost every indus-
try and sector. The second is that it will provide further insight into the process of LP
problem formulation. In previous chapters it was apparent that an LP problem
typically falls into three parts: problem formulation, solution and interpretation.
The solution of an LP problem is generally straightforward, particularly when a
suitable computer package is used, and the interpretation of that solution is equally
straightforward, at least to a management scientist familiar with the technique. Both
these stages, however, are totally dependent upon the correct and appropriate
formulation of the problem.
This chapter focuses on a number of detailed examples of typical management
applications. Over time, LP applications have come to be classed or categorized
by their type and we shall look at examples in each category. The purpose
of such categorization is primarily to help the management scientist at the
problem formulation stage. By looking at other examples of the same type of
LP problem, it may be easier and quicker to come up with an appropriate
problem formulation.

4.1 The Process of Problem Formulation

The process of formulating an LP application requires the management scientist to
In Section 2.1 we
provided some general be able to ‘translate’ the business problem under investigation into a form suitable
guidelines for modelling for solution by the technique. Over the years such formulation has developed into
linear programming almost an art form and it is only fair to point out that it is this stage that will provide
problems. You may want
to review Section 2.1 most difficulty in virtually every LP application. The methods of solution and
before proceeding with interpretation are, fortunately, fairly similar no matter what the problem. The
the linear programming formulation, however, is likely to be almost unique to the problem under consid-
applications in this
chapter. eration. Fortunately, many problems do fall into general application categories that
provide some guidance to the practitioner on the basic formulation approach to be
adopted. It is also worthwhile pointing out that there is no magic formula that can be
provided to ease the burden of this process. The development of appropriate LP
formulation skills only comes with time and practise and the more examples and
case studies you are able to access the quicker these skills will be developed.
However, adopting a logical and consistent process when attempting to formulate
a problem can be a big help. Naturally, like all such processes, it will not conform
exactly to every problem that is examined but it does provide a useful general
framework and is detailed below:

1 Provide a detailed verbal description of the problem under consideration,
ensuring that related information is unambiguous and sufficiently precise. It is
essential that we have a clear and adequate understanding of the problem
under investigation before we seek to apply the technique itself. In practice,
the management scientist may find themselves going back to the client several
times to clarify some aspect of the problem that is not clear or to check on
some of the data provided.

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