"The Impact of Aggregating Benefit and Cost Criteria in Four MCDA Methods"
IEEE Trans. on Engineering Management,
Vol. 52, No. 2, pp. 213-226, 2005 (May of 2005 issue).
by Evangelos Triantaphyllou and Khalid Baig
Abstract:
Multi-criteria decision analysis (MCDA) problems (also known as
multi-criteria decision-making or MCDM) involve the ranking of a
finite set of alternatives in terms of a finite number of decision
criteria. Often times such criteria may be in conflict with each
other. That is, an MCDA problem may involve both benefit and cost
criteria at the same time. Although this is a frequent characteristic
of many real-life MCDA problems, this subject has not received
adequate attention in the literature. This paper examines the use of
four key MCDA methods when two approaches for dealing with conflicting
criteria are used. The two approaches are the benefit to cost ratio
approach and the benefit minus cost approach. The MCDA methods used
in this study are the weighted sum model, the weighted product model,
and the analytic hierarchy process (AHP) along with some of its variants,
including the multiplicative AHP. Not surprisingly, these two approaches
for aggregating conflicting criteria may result in a different indication
of the best alternative or ranking of all alternatives when they are used
on the same problem. As it is demonstrated here, it is also possible for
the two approaches to even result in the opposite ranking of the alternatives.
An extensive empirical analysis of this methodological problem revealed
that the previous phenomena might occur frequently on simulated MCDA problems.
The WSM, the AHP, and the revised AHP performed in an almost identical manner
in these tests. The contradiction rates in these tests were rather
significant and became more dramatic when the number of alternatives was high.
Although it may not be possible to know which ranking is the “correct” one,
this study also theoretically proved that the multiplicative AHP is immune
to these ranking inconsistencies.
Key Words:
Decision criteria, conflicting criteria, preference disaggregation methods,
benefit and cost criteria, reward and loss criteria, decision-making,
multi-criteria decision analysis (MCDA), multi-criteria decision-making (MCDM),
analytic hierarchy process (AHP), weighted sum model, multiplicative AHP.
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