A new case of rank reversal in analytic hierarchy process due to aggregation of cost and benefit criteria. (2021)

• Record Type: Journal Article
• Authors: Majumdar, Abhijit; Tiwari, Manoj Kumar; Agarwal, Aastha; Prajapat, Kanika
• Is Part Of: Operations research perspectives. Volume 8(2021)
• Publication Date: 2021
• Subjects: Analytic hierarchy process (AHP) -- Benefit and cost criteria -- Multi-criteria decision making -- Multiplicative AHP -- Rank reversal -- Revised AHP; Operations research -- Periodicals; Management science -- Periodicals; 658.403405
• DOI: 10.1016/j.orp.2021.100185
• Languages: English
• ISSNs: 2214-7160

Abstract

Highlights: Rank reversal in AHP due to aggregation of benefit and cost criteria has been analysed. Sum 2 approach of aggregation produces irrational ranking of alternatives. Ratio method of aggregation produces the same ranking of alternatives in sum 1 and sum 2 approaches. Multiplicative AHP is also susceptible to rank reversal. Abstract: Rank reversal in Analytic Hierarchy Process (AHP) due to introduction or removal of a new alternative is well documented in literature. However, rank reversal due to the aggregation of benefit and cost criteria has not been addressed with requisite rigour. This paper demonstrates a new type of rank reversal in AHP which can arise due to the method (ratio or difference) and approach (sum 1 or sum 2) used to aggregate the benefit and cost criteria. Numerical examples, mathematical analyses and computer simulations have been used for demonstration of results. It is found that considering the benefit and cost criteria separately (sum 2 approach) while aggregating them can yield irrational ranking. It is also demonstrated that ratio method of aggregation is untenable in additive variants of AHP as it yields identical ranking in sum 1 and sum 2 approaches. Difference method of aggregation considering the benefit and cost criteria together (sum 1 approach) is most logical and sound in additive variants of AHP. The results also counter the notion that multiplicative AHP is immune to rank reversal between ratio and difference methods of aggregation. Besides, sum 1 and sum 2 approaches produce different raking of alternatives in multiplicative AHP irrespective of the method of aggregation. Outcome of this research will be helpful while choosing the appropriate method and approach for aggregation of benefit and cost criteria in different variants of AHP.