African Journal of Business Management Vol. 6(1), pp. 459-473,11 January, 2012 Available online at http://www.academicjournals.org/AJBM DOI: 10.5897/AJBM11.060 ISSN 1993-8233 ©2012 Academic Journals Full Length Research Paper Comparison of the REMBRANDT system with the Wang and Elhag approach: A practical example of the rank reversal problem Hamed Maleki 1 * and Amir Hassan Zadeh 2 1 Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran. 2 Department of Industrial Engineering, Amir Kabir University of Technology, Tehran, Iran. Accepted 24 October, 2011 Analytic hierarchy process (AHP) has been considerably criticized for possible rank reversal phenomenon caused by: i, when new alternatives are added or old ones deleted; and ii, when new criteria are added or old ones deleted with the caveat that the priorities of alternatives would be tied under these criteria and hence argued that the criteria should be irrelevant when ranking the alternatives. While in many cases this is a perfectly valid phenomenon, there are also many cases where rank should be preserved. This paper deals with rank reversal due to the inconsistency of the inputs. The preference intensities on REMBRANDT scale are more compatible than AHP scale. The REMBRANDT system is therefore proposed to avoid rank reversal phenomenon. We have provided a practical example to show that the rank reversal phenomenon did not occur with the REMBRANDT system, but did occur with the Wang and Elhag approach. Key words: Analytic hierarchy process (AHP), REMBRANDT system, rank reversal, multiple-attribute decision making (MADM), uncertainty. INTRODUCTION Analytic hierarchy process (AHP), as a very popular multiple criteria decision making (MCDM) tool, has been considerably criticized for its possible rank reversal phenomenon, which means changes of the relative rankings of the other alternatives after an alternative is added or deleted. Such a phenomenon was first noticed and pointed out by Belton and Gear (1983), which leads to a long-lasting debate about the validity of AHP (Dyer, 1990a, b; Harker and Vargas, 1987; Leung and Cao, 2001; Perez, 1995; Saaty, 1990a; Saaty, 1986, 1990,1994; Saaty et al., 1983; Schoner et al., 1989; Stewart, 1992; Troutt, 1988; Vargas, 1994; Wang and Elhag, 2006; Watson and Freeling, 1982, 1983), especially about the legitimacy of rank reversal (Forman, 1990; Millet and Saaty, 2000; Saaty, 1987a,b; Saaty and Vargas, 1984; Schoner et al.,1992). *Corresponding author. E-mail: st_h_maleki@azad.ac.ir. In order to avoid the rank reversal, Belton and Gear (1983) suggested normalizing the eigenvector weights of alternatives using their maximum rather than their sum, which was usually called B–G modified AHP. Saaty and Vargas (1984) provided a counterexample to show that B– G modified AHP was also subject to rank reversal. Belton and Gear (1985) argued that their procedure was misunderstood and insisted that their approach would not result in any rank reversal if criteria weights were changed accordingly. Schoner and Wedley (1989) presented a referenced AHP to avoid rank reversal phenomenon, which requires the modification of criteria weights when an alternative is added or deleted. Schoner et al. (1993) also suggested a method of normalization to the minimum and a linking pin AHP [see also (Schoner et al., 1997)], in which one of the alternatives under each criterion is chosen as the link for criteria comparisons and the values in the linking cells are assigned a value of one, with proportional values in