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48 Decisions involving multiple objectives: SMART
mean that Elton Street (E), for example, would have benefits with a
value of 81.7. At the other extreme, if turnover had a weight of 100 (and
therefore working conditions a weight of zero) the value of benefits for
Elton Street would have been 60.4. The line joining these points shows the
value of benefits for Elton Street for turnover weights between 0 and 100.
It can be seen that Elton Street gives the highest value of benefits as
long as the weight placed on turnover is less than 52.1. If the weight
is above this figure then Addison Square (A) has the highest value of
benefits. Since the owner assigned a weight of 81 to turnover, it will
take a fairly large change in this weight before Elton Street is worth
considering, and the owner can be reasonably confident that Addison
Square should appear on the efficient frontier.
Figure 3.7 also shows that no change in the weight attached to turnover
will make the other offices achieve the highest value for benefits. Filton
Village (F), in particular, scores badly on any weight. If we consider the
other two offices on the efficient frontier we see that Gorton Square (G)
always has higher-valued benefits than Carlisle Walk (C).
Similar analysis could be carried out on the lower-level weights. For
example, the owner may wish to explore the effect of varying the weights
attached to ‘closeness to customers’ and ‘visibility’ while keeping the
weight attached to ‘image’ constant. Carrying out sensitivity analysis
should contribute to the decision maker’s understanding of his problem
and it may lead him to reconsider some of the figures he has supplied. In
many cases sensitivity analysis also shows that the data supplied do not
need to be precise. As we saw above, large changes in these figures are
often required before one option becomes more attractive than another:
a phenomenon referred to as ‘flat maxima’ by von Winterfeldt and
Edwards. 10
Theoretical considerations
The axioms of the method
In our analysis of the office location problem we implicitly made a
number of assumptions about the decision maker’s preferences. These
assumptions, which are listed below, can be regarded as the axioms of
the method. They represent a set of postulates which may be regarded
as reasonable. If the decision maker accepts these axioms, and if he is
rational (i.e. if he behaves consistently in relation to the axioms), then he