The impact of aggregating benefit and cost criteria in four MCDA methods

Multicriteria decision analysis (MCDA) problems (also known as multicriteria 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.