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42 Decisions involving multiple objectives: SMART
We can now give ‘closeness to customers’ a weight of 100. The other
weights are assessed as follows. The owner is asked to compare a
swing from the least visible location to the most visible, with a swing
from the most distant location from customers to the closest location.
After some thought, he decides that the swing in ‘visibility’ is 80% as
important as the swing in ‘closeness to customers’, so visibility is given
a weight of 80. Similarly, a swing from the worst ‘image’ to the best
is considered to be 70% as important as a swing from the worst to the
best location for ‘closeness to customers’, so ‘image’ is assigned a weight
of 70. The procedure is repeated for all the other lower-level attributes
and Figure 3.5 illustrates the results. As shown below, the six weights
obtained sum to 310, and it is conventional to ‘normalize’ them so that
they add up to 100 (this will make later stages of the analysis easier to
understand). Normalization is achieved by simply dividing each weight
by the sum of the weights (310) and multiplying by 100.
Attribute Original weights
Normalized weights
(to nearest
whole number)
Closeness to customers 100 32
Visibility 80 26
Image 70 23
Size 30 10
Comfort 20 6
Car-parking facilities 10 3
310 100
The weights for the higher-level attributes in the value tree, ‘turnover’
and ‘working conditions’, are now found by summing the appropriate
lower-level weights, so the weight for turnover is 81 (i.e. 32 + 26 + 23)
and the weight for working conditions is 19 (i.e. 10 + 6 + 3). Note that
experiments by Pöyhönen et al. 11 have indicated that the weight people
attach to a given attribute is sensitive to whether or not the attribute
has been split in the value tree into lower-level attributes. For example,
the weight attached to ‘car-parking facilities’ in the office value tree
might have been different if the decision maker had decided to split
this attribute into three sub-attributes: ‘quality of car park surface’,
‘security of car park’ and ‘distance of car park from office’. Because
of this Pöyhönen et al. suggest that it is also worth asking decision
makers what weight they would attach to an attribute if it is split into