A Review of Ranking Models in Data Envelopment Analysis <s> Ranking Techniques by Multivariate Statistics in the DEA <s> Abstract This paper presents a case study where academic departments at Ben-Gurion University were evaluated via the Data Envelopment Analysis using the CCR model. Extensive post analyses were performed in several directions. First various sets of data were used to identify efficient and inefficient departments. New efficiency measures are suggested in relation to the reference set included in the analyses of academic departments. We measured the efficiency of departments to other departments within the same school. We applied cluster analyses to divide the departments into several sets; and the discriminant analysis to test the match of the efficiency/inefficiency division of the CCR ratio. We further tested organizational changes where an inefficient department was closed and joins other departments. Finally we compared the CCR model to the pure economic approach—the cost per student ratio. <s> BIB001 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Ranking Techniques by Multivariate Statistics in the DEA <s> Abstract This paper deals with the evaluation of decision making units which have multiple inputs and outputs. A new method (CCA/DEA) is developed where the Canonical Correlation Analysis (CCA) is utilized to provide a full rank scaling for all the units rather than a categorical classification (for efficient and inefficient units) as done by the Data Envelopment Analysis (DEA). The CCA/DEA approach is an attempt to bridge the gap between the frontier approach of DEA and the average tendencies of statistics (econometrics). Nonparametric statistical tests are employed to validate the consistency between the classification from the DEA and the postclassification that was generated by the CCA/DEA. <s> BIB002 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Ranking Techniques by Multivariate Statistics in the DEA <s> Abstract Within data envelopment analysis (DEA) is a sub-group of papers in which many researchers have sought to improve the differential capabilities of DEA and to fully rank both efficient, as well as inefficient, decision-making units. The ranking methods have been divided in this paper into six, somewhat overlapping, areas. The first area involves the evaluation of a cross-efficiency matrix, in which the units are self and peer evaluated. The second idea, generally known as the super-efficiency method, ranks through the exclusion of the unit being scored from the dual linear program and an analysis of the change in the Pareto Frontier. The third grouping is based on benchmarking, in which a unit is highly ranked if it is chosen as a useful target for many other units. The fourth group utilizes multivariate statistical techniques, which are generally applied after the DEA dichotomic classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The last approach requires the collection of additional, preferential information from relevant decision-makers and combines multiple-criteria decision methodologies with the DEA approach. However, whilst each technique is useful in a specialist area, no one methodology can be prescribed here as the complete solution to the question of ranking. <s> BIB003
As described in DEA literature in DEA technique frontier is taken into consideration rather than central tendency considered in regression analysis. DEA technique considers that an envelope encompasses through all the observations as tight as possible and does not try to fit regression planes in center of data. In DEA methodology each unit is considered initially and compared to the efficient frontier, but in regression analysis a procedure is considered in which a single function fits to the data. DEA uses different weights for different units but does not let the units use weights of other units. Canonical correlation analysis, as Friedman and SinuanyStern BIB002 noted, can be used for ranking units. This method is somehow the extension of regression analysis, Adler et al. BIB003 . The aim in canonical correlation analysis is to find a single vector common weight for the inputs and outputs of all units. Consider , as the composite input and output and ,́as corresponding weights, respectively. The presented model by Tatsuoka and Lohnes  is as follows: where , , and are respectively defined as the matrices of the sums of squares and sums of products of the variables. Friedman and Sinuany-Stern BIB002 while defining the ratio of linear combinations of the inputs and outputs, = / used canonical correlation analysis. As they noted that scaling ratio of the canonical correlation analysis/DEA is unbounded. Sinuany-Stern et al. BIB001 used linear discriminant analysis for ranking units. They defined DMU is said to be efficient if > where is a critical value based on the midpoint of the means of the discriminant function value of the two groups, Morrison  . The larger the amount of is the better rank DMU will have. Friedman and Sinuany-Stern BIB002 noted that as crossefficiency/DEA, canonical correlation analysis/DEA and discriminant analysis/DEA, ranking orders may vary from each other, thus it seems necessary to introduce the combined ranking (CO/DEA). Combined ranking, for each unit, considered all the ranks obtained from the above-mentioned rankings. Moreover, statistical tests are; one for goodness of fit between DEA and a specific ranking and the other for testing correlation between variety of ranking orders, Siegel and Castellan  .