Interval efficiency assessment using data envelopment analysis

This paper studies how to conduct efficiency assessment using data envelopment analysis (DEA) in interval and/or fuzzy input–output environments. A new pair of interval DEA models is constructed on the basis of interval arithmetic, which differs from the existing DEA models handling interval data in that the former is a linear CCR model without the need of extra variable alternations and uses a fixed and unified production frontier (i.e. the same constraint set) to measure the efficiencies of decision-making units (DMUs) with interval input and output data, while the latter is usually a nonlinear optimization problem with the need of extra variable alternations or scale transformations and utilizes variable production frontiers (i.e. different constraint sets) to measure interval efficiencies. Ordinal preference information and fuzzy data are converted into interval data through the estimation of permissible intervals and -level sets, respectively, and are incorporated into the interval DEA models. The proposed interval DEA models are developed for measuring the lower and upper bounds of the best relative efficiency of each DMU with interval input and output data, which are different from the interval formed by the worst and the best relative efficiencies of each DMU. A minimax regret-based approach (MRA) is introduced to compare and rank This research was supported by the project on Human Social Science of MOE, P.R.China under the Grant No. 01JA790082, the National Natural Science Foundation of China (NSFC) under the Grant No: 70271056, and also in part by the European Commission under the Grant No: IPS-2000-00030, the UK Engineering and Physical Science Research Council (EPSRC) under the Grant No: GR/R32413/01, and Fok Ying Tung Education Foundation under the Grant No: 71080. ∗ Corresponding author. Manchester Business School East, The University of Manchester, P.O. Box 88, Manchester M60 1QD, UK. Tel.: +44 161 2750788; fax: +44 161 2003505. E-mail addresses: [email protected], [email protected] (Y.-M. Wang). 0165-0114/$ see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2004.12.011 348 Y.-M. Wang et al. / Fuzzy Sets and Systems 153 (2005) 347–370 the efficiency intervals of DMUs. Two numerical examples are provided to show the applications of the proposed interval DEA models and the preference ranking approach. © 2005 Elsevier B.V. All rights reserved.