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40 Decisions involving multiple objectives: SMART
Determining the weights of the attributes
In the previous section we derived values to measure how well each
office performed on each attribute. For example, we found that Addison
Square was the best office for image and closeness to customers, but
it was the least-preferred office for providing comfortable working
conditions for staff. Clearly, in order to make a decision the owner now
needs to combine the values for the different attributes in order to gain
a view of the overall benefits which each office has to offer.
An intuitively appealing way of achieving this is to attach weights
to each of the attributes that reflect their importance to the decision
maker. For example, he might consider office floor area to be more
important than distance from customers and therefore give a weight of
5 to floor area and only 1 to distance from customers. Unfortunately,
this approach can lead to serious problems. To see this, consider the
following decision.
Suppose that the choice is between just two offices, X and Y, and that
we are evaluating these on only two attributes: office area and distance
from customers. The table below shows how the offices perform on these
two attributes:
Office Floor area Distance from customers
X 400 ft 2 0 miles
Y 402 ft 2 15 miles
The values assigned to the offices would therefore be:
Office Floor area Distance from customers
X 0 100
Y 100 0
Weights 5 1
If we assume that the weights of 5 and 1 apply then the aggregate
value for each office can be obtained by multiplying each value by its
weight and summing the results, as shown below.
Office X: Aggregate value = (5 × 0) + (1 × 100) = 100
Office Y: Aggregate value = (5 × 100) + (1 × 0) = 500