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340 Resource allocation and negotiation problems
which they felt would lead to the best use of the company’s funds. (It
was thought that around $70–80 million would be available to support
the company’s strategies in the four regions.) The package that they
suggested was a fairly cautious one. It simply involved maintaining
the status quo in every region except the East, where an expansion
of operations to four outlets would take place. From Table 13.2 it can
be seen that this package would cost $80 million (i.e. $28 million +
$7 million + $25 million + $20 million). It would result in profit benefits
which would have a total value of 203.2 (i.e. 0 + 21.27 + 91 + 90.91),
market share benefits of 110 and risk benefits of 112. Now that the
across-criteria weights had been elicited, the overall benefits could be
calculated by taking a weighted average of the individual benefits (using
the normalized weights) as shown below:
Value of benefits
= 0.167 × (value for profit) + 0.556 × (value for market share)
+ 0.278 × (value for risk)
= (0.167 × 203.2) + (0.556 × 110) + (0.278 × 112)
= 126.2
If similar calculations were carried out for the least beneficial package
(as identified by a computer) the value of benefits would be found to
be 87.49. The corresponding figure for the most beneficial package is
159.9. The results of the analysis are easier to interpret if these values
are rescaled, so that the worst and best packages have values of 0 and
100, respectively. Since 126.2 is about 53.4% of the way between 87.49
and 159.8, the benefits of this package would achieve a value of 53.4 on
the 0–100 scale (i.e. this package would give 53.4% of the improvement
in benefits which could be achieved by moving from the worst to the
best package).
A computer can be used to perform similar calculations for all the
other packages and the results can be displayed on a graph such as
Figure 13.5. On this graph the efficient frontier links those packages
which offer the highest value of benefits for a given cost (or the lowest
costs for a given level of benefits).
Note, however, that the packages marked 1 and 2 on the graph do not
appear on the efficient frontier, despite the fact that they offer the highest
benefits for their respective costs. This is because the analysis assumes a
constant rate of trade-off between costs and benefits (i.e. each additional
point on the benefits scale is worth the same number of dollars). It can
be shown that, if this is the case, then the efficient frontier will either be