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332 Resource allocation and negotiation problems
Stage 6: Use a computer to calculate the costs and benefits for every
package and identify the efficient frontier.
Stage 7: Propose a package which appears to achieve the desired objectives
within the constraints of the resources available.
Stage 8: Use the computer to find if there are packages on the efficient
frontier which offer higher benefits for the same cost as the
proposed package (or the same benefits at a lower cost).
Stage 9: Perform a sensitivity analysis on the results to identify which
other packages would be worth considering if more or less
resources are available and to examine the effects of changes in
the data used in the model.
Determining the variables, resources and benefits
The first question the group faced was the determination of the variables
involved in the problem. The term ‘variable’, in this context, refers to an
area to which resources might be directed. Typical variables might be
different research and development projects, different functional areas
of a business or different product lines.
In this problem the group soon decided that the four sales regions were
the variables, but in some problems the identification of the variables
is not so easy. The key point to bear in mind is that, apart from the
fact that they are competing for resources, the areas should be regarded
as separate compartments with a decision in one area having virtually
no effect on a decision in another. Statements such as ‘If department
X chooses that option, then we ought to do this’ may reveal a lack of
independence.
Having identified the variables, the managers of the furniture company
had to think about the nature of the resources which they would be
allocating to the different sales regions. Again this proved to be easy,
since their main concern was the efficient use of the company’s money.
Of course, in some problems there may be several resources which are
to be allocated such as personnel, equipment and production facilities.
Next, the group was asked to identify the benefits which they hoped
would result from the allocation of money between the regions. After
some discussion it was agreed that there were three main objectives:
(i) To sustain the profitability of the company in the short term (we will
refer to the benefit associated with this objective simply as ‘Profit’);
(ii) To increase the company’s turnover and national market share by
expanding the number of outlets (we will call the associated benefit
‘Market share’);