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50 Decisions involving multiple objectives: SMART
To demonstrate preference independence let us suppose that our office
location problem only involves two attributes: ‘distance from customers’
and ‘office size’. Our decision maker is now offered two offices, X and
Y. These are both the same size (1000 ft 2 ) but X is closer to customers, as
shown below:
Office Distance from customers Office floor area
X 3 miles 1000 ft2 Y 5 miles 1000 ft2 Not surprisingly, the decision maker prefers X to Y. Now suppose that we
change the size of both offices to 400 ft 2 . If, as is likely, the decision maker
still prefers X to Y his preference for a distance of 3 miles over a distance of
5 miles has clearly been unaffected by the change in office size. This might
remain true if we change the size of both offices to any other possible
floor area. If this is the case, we can say that ‘distance from customers’
is preference independent of ‘office size’ because the preference for one
distance over another does not depend on the size of the offices.
If we also found that ‘size of office’ is preference independent of ‘distance
from customers’ then we can say that the two attributes are mutually
preference independent. Note that mutual preference independence does
not automatically follow. When choosing a holiday destination, you
may prefer a warmer climate to a cooler one, irrespective of whether or
not the hotel has an open-air or indoor swimming pool. However, your
preference between hotels with open-air or indoor swimming pools will
probably depend on whether the local climate is warm or cool.
To see what can happen when the additive model is applied to a
problem where mutual preference independence does not exist, consider
the following problem. Suppose now that our office location decision
depends only on the attributes ‘image’ and ‘visibility’ and the owner has
allocated weights of 40 and 60 to these two attributes. Two new offices,
P and Q, are being compared and the values assigned to the offices for
each of these attributes are shown below (0 = worst, 100 = best).
Office Visibility Image
P 0 100
Q 100 0
Using the additive model, the aggregate value of benefits for P will be:
(40 × 0) + (60 × 100) = 6000, i.e. 60 after dividing by 100