A super-efficiency model for ranking efficient units in data envelopment analysis Shanling Li a , G.R. Jahanshahloo b , M. Khodabakhshi c, * a Management Faculty of McGill University, Montreal, PQ, Canada H3A 1G5 b Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, Tehran, Iran c Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran Abstract Data envelopment analysis (DEA) is a body of research methodologies to evaluate overall efficiencies and identify the sources and estimate the amounts of inefficiencies in inputs and outputs. In DEA, the best performers are called DEA effi- cient and the efficiency score of a DEA efficient unit is denoted by an unity. In the last decade, ranking DEA efficient units has become the interests of many DEA researchers and a variety of models (called super-efficiency models) were developed to rank DEA efficient units. While the models developed in the past are interesting and meaningful, they have the disad- vantages of being infeasible or instable occasionally. In this research, we develop a super-efficiency model to overcome some deficiencies in the earlier models. Both theoretical results and numerical examples are provided. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Data envelopment analysis; Super-efficiency; Ranking; Infeasibility; Instability 1. Introduction Data envelopment analysis was originated in 1978 by Charnes et al. [7] and the first DEA model was called CCR (Charnes, Cooper and Rhodes) model. The objective of DEA models is to evaluate overall efficiencies of decision making units (DMUs) that are responsible to convert a set of inputs into a set of outputs. Efficient DMUs are identified by an unity of 1.0 and inefficient DMUs have efficiency scores less than 1.0. When being evaluated, the efficiency score of a DMU is measured by the combination of a set of DEA efficient DMU(s), which form a part of the segments on the efficiency frontier. The efficient DMUs are not comparable among themselves in the CCR and other DEA models. In the last decade, some DEA researchers initiated a new area called super-efficiency to rank the DEA efficient DMUs and developed various models. Although the devel- oped models are interesting and useful, in general, they have the drawbacks of lacking either stability or feasibility. 0096-3003/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2006.06.063 * Corresponding author. E-mail address: mkhbakhshi@yahoo.com (M. Khodabakhshi). Applied Mathematics and Computation 184 (2007) 638–648 www.elsevier.com/locate/amc