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44 Decisions involving multiple objectives: SMART
that attribute. The resulting products are then summed and divided by
100 to obtain the overall value of benefits at that location.
Attribute
Addison Square
values Weight Value × weight
Closeness to customers 100 32 3200
Visibility 60 26 1560
Image 100 23 2300
Size 75 10 750
Comfort 0 6 0
Car-parking facilities 90 3 270
8080
Therefore the aggregate value for Addison Square is 8080/100, i.e. 80.8.
Table 3.2 gives a summary of the values obtained for all the offices and
their aggregate values. It can be seen that Addison Square has the highest
value for benefits and Filton Village the lowest. However, so far we have
ignored the costs associated with the offices and the next section shows
how these can be taken into account.
Trading benefits against costs
You will recall that until now we have ignored the costs of the offices
because of the difficulties which decision makers often have in making
judgments about the trade-off between costs and benefits. If our decision
maker had not found this to be a problem then we could have treated
cost as just another attribute. We could therefore have allocated values to
the various costs, with a value of 100 being given to the office which had
the lowest costs and 0 to the office with the highest. Weights could then
have been derived to compare swings from the least-preferred to the
most-preferred level of benefits with swings from the worst to the best
cost. This would have enabled the value for cost to have been included
when we used the additive model to derive an overall value to measure
the attractiveness of the different offices. The office achieving the highest
overall value would have been the one the owner should choose. This
approach has been used in problems where decision makers experienced
no difficulty in assigning weights to all the attributes.
However, because our owner does have difficulties in judging the
cost–benefit trade-off, we can proceed as follows. In Figure 3.6 the