A Comprehensive Literature Review of the Rank Reversal Phenomenon in the Analytic Hierarchy Process

Abstract

During the last few decades, several multi‐criteria decision analysis methods have been proposed to help in selecting the best compromise alternatives. Among them, analytic hierarchy process (AHP) and its applications have attracted much attention from academics and practitioners. However, since the early 1980s, critics have raised questions regarding its proper use. One of them concerns the unacceptable changes in the ranks of the alternatives, called rank reversal, upon changing the structure of the decision. Several modifications were suggested to preserve ranks. In this paper, a classification scheme and a comprehensive literature review are presented in order to uncover, classify and interpret the current research on AHP methodologies and rank reversals. On the basis of the scheme, 61 scholarly papers from 18 journals are categorized into specific areas. The specific areas include the papers on the topics of adding/deleting alternatives and the papers published in adding/deleting criteria. The scholarly papers are also classified by (1) year of publication, (2) journal of publication, (3) authors' geographic location and (4) using the AHP in association with other methods. It is hoped that the paper can meet the needs of researchers and practitioners for convenient references of AHP methodologies and rank reversals and hence promote the future of rank reversal research. Copyright © 2012 John Wiley & Sons, Ltd.

Aggregation of Priorities in Multi-Criteria Decision Analysis (MCDA): Connecting Decision Spaces in the Cognitive Space

“…It is straightforward to check that the expression of the normalised aggregate priority r q in Equation (11) would remain the same confirming that we did not sacrifice any generality by considering a normalised weight vector at the very beginning in Equation (6).…”

“…It is worth pointing out that, in general, there are arbitrary constants multiplying each term in the expansion of Equation (6). For convenience, we absorbed them in v i s and thus in the corresponding norms i n s .…”

“…This observation brings the Analytic Hierarchy Process (AHP) [4] [5], a familiar MCDM, into focus. It initiated vigorous discussions about the rank reversal problem (see [6] for a comprehensive review and references) during the last few decades. The AHP provides normalised relative priorities for alternatives from pairwise comparison matrices under each criterion and uses method b) for aggregation across criteria.…”

Appropriate criteria set for personnel promotion across organizational levels using analytic hierarchy process (AHP)

“…For the current developments, theoretical extensions, issues and applications of the AHP, see the reviews of Zahedi (1986), Vaidya and Kumar (2006) and Sipahi and Timor (2010) on the overview of applications, Ho (2008) for the integration of other approaches and their applications, Ishizaka and Labib (2011) on its main developments, Subramanian and Ramanathan (2012) for its various applications in operations management, (Schmidt et al, 2015) for healthcare research, Anis and Islam (2015) for applications in higher learning institutions, Chandio et al (2013) on GIS-based integration, Maleki and Zahir (2013) on rank reversal phenomenon issue, and Godinho et al (2011) issues with R&D project selection application, among others.…”

Group Aggregation Techniques for Analytic Hierarchy Process and Analytic Network Process: A Comparative Analysis

“…Owing to the generally known problem of potential rank reversals (see for example Saaty 1994;Forman and Gass 2001;Maleki and Zahir 2013) in the AHP and ANP even for an individual decision maker the fulfillment of the axiom 'independence of irrelevant alternatives' cannot be guaranteed in a GDM context (Van den Honert and Lootsma 1996).…”