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594 CHAPTER 14 MULTICRITERIA DECISIONS

In previous chapters we have introduced a variety of models to help managers find
the optimal solution to a problem for some defined objective, such as profit, cost,
distance, time. In these cases we have used a single criterion which we seek to
minimize/maximize. However, it is not uncommon for managers to seek the solution
to some problem where there is not one single criterion but rather multiple criteria.
For example, consider a government agency that is planning to build a new hospital.
It has several possible sites under consideration and is trying to determine the
optimal site to choose. Up to now, we have assumed that the agency would use a
single criterion – perhaps minimizing total cost – to choose between the alternatives
(subject of course to any appropriate constraints). However, the agency may be
trying to determine the optimal site using several different criteria. It may want a site
that minimizes total cost. But it also wants the site chosen to be easily accessible
for public transport for patients using the hospital. Another additional criterion
might be that the site has to be close to a major city so as to make staff recruitment
easier. In such cases, we are looking for the optimal solution taking into account all
the decision criteria that are relevant. This makes the solution process more complex
as it is likely that these criteria will conflict – that is, one site might have the lowest
total cost but may not be close to a major city. Another site is close to a major city
but has poor public transport facilities for patients. This type of situation is referred
to as multicriteria decision making. In this chapter we shall be looking at a variety
of approaches to help the decision maker in such situations.
To introduce the topic of multicriteria decision making, we consider a technique
referred to as goal programming. This technique has been developed to handle
multiple-criteria situations within the general framework of linear programming. We
next consider a scoring model as a relatively easy way to identify the best decision
alternative for a multicriteria problem. Finally, we introduce a method known as the
analytical hierarchy process (AHP), which allows the user to make pairwise compar-
isons among the criteria and a series of pairwise comparisons among the decision
alternatives in order to arrive at a prioritized ranking of the decision alternatives.

14.1 Goal Programming: Formulation and Graphical Solution

To illustrate the goal programming approach to multicriteria decision problems, let
us consider a problem facing Nicolo Investment Advisors based in Edinburgh. A
client has £80 000 to invest and, as an initial strategy, would like the investment
Goal programming was portfolio restricted to two stocks:
first used by Charnes,
Cooper and Ferguson in
1955, although the name Estimated Annual Risk
itself first appeared in a Stock Price/Share Return/Share Index/Share
1961 text by Charnes
and Cooper.
UK Oil £25 £3 0.50
Hub Properties £50 £5 0.25

UK Oil, which has a return of £3 on a £25 share price, provides an annual rate of
return of 12 per cent, whereas Hub Properties provides an annual rate of return of
10 per cent. The risk index per share, 0.50 for UK Oil and 0.25 for Hub Properties, is
a rating Nicolo assigned to measure the relative risk of the two investments. Higher
risk index values imply greater risk; hence, Nicolo judged UK Oil to be the riskier
investment. By specifying a maximum portfolio risk index, Nicolo will avoid placing
too much of the portfolio in high-risk investments.

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