Applied statistics 37 Computer Modelling & New Technologies, 2003, Volume 7, No.1, 37-46 Transport and Telecommunication Institute, Lomonosov Str.1, Riga, LV-1019, Latvia DEA SUPER EFFICIENCY MULTISTAGE RANKING Y. HADAD a , L. FRIEDMAN b , Z. SINUANY-STERN b,c , A. MEHREZ + a Department of Industrial Engineering and Management, Negev Academic College of Engineering, Beer Sheva, 84100, Israel, E-Mail:yossi@nace.ac.il b Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel c Academic College of Judea and Samaria, Ariel, 44837, Israel + Professor Mehrez passed away on February 5 th , 2000 after a courageous struggle with cancer In this paper a new ranking method is presented within the Data Envelopment Analysis (DEA). Based on the super efficiency ranking method of Anderson and Peterson, which ranks only the efficient units, we developed here a multistage process which ranks also the inefficient units using a similar procedure at each stage. The model is applied to an example from the literature. Moreover, several ranking methods are compared to the new multistage method and nonparametric statistical tests are utilized to compare the various ranking methods. In this example, as expected, all the ranking methods were significantly correlated. General topics covered by this paper include the following areas: * Data Envelopment Analysis- procedure designed to measure the relative efficiency. * The Technical and Scale Efficiency. * The Technical Efficiency * Ranking Methods. Keywords: Data Envelopment Analysis (DEA), Rank-Scaling, Cross Efficiency Matrix, Multi-Criteria Decision Analysis (MCDA). 1. Introduction Ranking organizational units in the context of Data Envelopment Analysis (DEA) has become an acceptable approach recently, as done in Multi-Criteria Decision Analysis (MCDA). See for example Belton and Stewart [5] and Green and Doyle [9]. If we consider the availability of a model in commercial software as an indication of its popularity then we can point that the super efficiency ranking method developed by Anderson and Peterson (A&P) [2] is the most widespread ranking method. For example, it appears in the Warwick DEA code [23]. Moreover, this ranking method was cited more often than others. In spite of its popularity there were several criticisms about the A&P ranking method. A&P accepts the DEA score as a rank scale for the inefficient units. In order to differentiate between the efficient units (which receive score 1 in DEA), they developed a method to score them with values greater than 1. Cooper and Tone [7] argue that the DEA only classify the units into two dichotomic sets: efficient and inefficient. They do not rank the efficient unit since they claim that they all are on the efficient frontier. Moreover, they do not accept the DEA score as a ranking score for the inefficient units since their weights vary from unit to unit. However, they suggest another ranking method based on the slack variables of the dual problem (the improvements of each variable). Wilson [24] argues that the A&P ranking model does not provide ranking, it mainly identifies outliers; namely, efficient units that receive very high scores by A&P are identified as outliers. In our paper we present a new ranking method, G/DEA, based on the A&P approach, which responds to both criticism mentioned above. G/DEA is a multistage procedure where the A&P method is applied several times on subsets of the units. G/DEA does not receive the DEA score for ranking, it ranks them in stages. Furthermore, we show by example that A&P does not necessarily identify outliers. There are several ranking methods in the DEA literature (see Adler et al. [1]). In this paper we refer to two other ranking methods. The ranking method developed the first is based on the cross efficiency matrix (Sexton, [14]), and a more recent one, the discriminant analysis of ratio (Sinuany-Stern and Friedman, [17]). Both methods rank all the units. In this paper we first present advantages of ranking in the DEA context, then the super efficiency rank scaling method of A&P, is given. Afterwards we present the new super efficiency multistage ranking. In section 5 an example from the literature is presented and analysed. In Section 6 we compare the ranking of several methods. Finally a summary and conclusions are given.