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126 Decision making under uncertainty
considering problems which involve uncertainty. If project cost is also
utility independent of overrun time (this will not automatically be the
case) then we can say that overrun time and project cost are mutually
utility independent.
The great advantage of mutual utility independence, if it exists, is that
it enables the decision maker to concentrate initially on deriving utility
function for one attribute at a time without the need to worry about the
other attributes. If this independence does not exist then the analysis
can be extremely complex (see Keeney and Raiffa 16 ), but in very many
practical situations it is usually possible to define the attributes in such
a way that they do have the required independence.
Deriving the multi-attribute utility function
Assuming that mutual utility independence does exist, we now derive
the multi-attribute utility function as follows.
Stage 1: Derive single-attribute utility functions for overrun time and
project cost.
Stage 2: Combinethesingle-attributefunctionstoobtainamulti-attribute
utility function so that we can compare the alternative courses of
action in terms of their performance over both attributes.
Stage 3: Perform consistency checks, to see if the multi-attribute utility
function really does represent the decision maker’s preferences,
and sensitivity analysis to examine the effect of changes in the
figures supplied by the decision maker.
Stage 1
First we need to derive a utility function for project overrun. Using the
approach which we discussed earlier in the context of single-attribute
utility, we give the best overrun (0 weeks) a utility of 1.0 and the
worst (6 weeks) a utility of 0. We then attempt to find the utility of the
intermediate values, starting with an overrun of 3 weeks. After being
asked a series of questions, the project manager indicates that he is
indifferent between:
A: A project which will certainly overrun by 3 weeks; and
B: A gamble offering a 60% chance of a project with 0 weeks overrun
and a 40% chance of a 6 week overrun.