A note on "A new approach for weight derivation using data envelopment analysis in the analytic hierarchy process"

DEAHP as a weight derivation procedure for analytic hierarchy process (AHP) has been found suffering from some significant drawbacks. Recently, Mirhedayatian and Saen (2011) [5] proposed a new procedure entitled Revised DEAHP for AHP weight derivation [S. M. Mirhedayatian, R. F. Saen, A new approach for weight derivation using data envelopment analysis in the analytic hierarchy process, Journal of the Operational Research Society 62 (2011) 1585-1595]. This paper provides a detailed note to reveal that (1) the Revised DEAHP cannot derive true weights from perfectly consistent pairwise comparison matrices, (2) it may produce irrational weights for inconsistent pairwise comparison matrices, (3) it still suffers from rank reversal problem when an efficient decision criterion or alternative is added or removed, (4) the use of the super-efficiency model in data envelopment analysis (DEA) for AHP weight derivation is redundant and meaningless when there exist multiple decision criteria or alternatives that are efficient in a pairwise comparison matrix, and (5) it may produce a completely reversed ranking that is totally opposite to the rank obtained by the eigenvector method in the case of hierarchical structures, leading to a wrong decision being made. (C) 2011 Elsevier Ltd. All rights reserved.