Ranking of units by positive ideal DMU with common weights

Keywords: Data envelopment analysis (DEA) Common weights analysis (CWA) Ranking The ideal line The special line a b s t r a c t Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. However, DEA does not provide more information about the efficient DMUs. In this research, the researchers will be proposed two ranking methods. In the first method, an ideal line will be defined and determined a common set of weights for efficient DMUs then a new efficiency score will be obtained and ranked them with it. In the second method, a special line will be defined then compared all efficient DMUs with it and ranked them. An example 20 branch banks of Iran illustrates two ranking methods. Charnes, Cooper, and Rhodes (1978) introduce data envelop-ment analysis (DEA) to assess the relative efficiency of a homogeneous group of decision-making units (DMUs), such as schools, hospitals, or sales outlets. DEA successfully divides them into two categories; efficient DMUs and inefficient DMUs. A ranking for inefficient DMUs is given, however, efficient DMUs cannot be ranked. Some of the methods which are proposed for ranking efficient DMUs are mentioned here. Anderson and Petersen (1993) evaluate that a DMUs efficiency possibly exceeds the conventional score 1.0, by comparing the DMU being evaluated with a linear combination of other DMUs, while excluding the observations of the DMU being evaluated. They try to discriminate between these efficient DMUs, by using different efficiency scores larger than 1.0. Cook, Kress, and Seiford (1992) developed prioritization models to rank only the efficient units in DEA. They divide those with equal scores, on the boundary, by imposing the restrictions on the multiplies (weights) in a DEA analysis. Mehrabian, Alirezaee, and Jahanshahloo (1999) (MAJ) presented of the popular of these methods. These methods would have some deficiencies if data have certain structures. There are some methods based on norms. Jahanshahloo, Junior, Hossein-zadeh Lotfi, and Akbarian (2007) introduced an l 1-norm approach that removes some deficiencies arising from AP and MAJ, but that cannot rank non-extreme DMUs. Liu and Peng (2006) searched a common set weights to create the best efficiency score of one group composed of efficient DMUs. Then they use this common set of weights to evaluate the absolute efficiency of each efficient DMUs in order to rank them. The methods that we propose in this …