A New Measure for Detecting Influential DMUs in DEA

We discuss about influential DMUs and also we review some related studies in the literature. Then we propose a new method to detect influential DMUs, which is based on Euclidean distance and omitting the efficient DMUs by using single case deletion. Our method will be explained with an empirical example. 1. Introduction Data envelopment analysis (DEA) is a nonparametric method for evaluating the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and outputs. In recent years DEA has had important role in application of many fields such as energy [1, 2], banking [3], and sport [4, 5]. DEA is a useful technique to evaluate the performance of DMUs; meanwhile, if a data set contains one or more influential DMUs, obviously calculated results (by DEA) of the performance are changed. Influential DMUs are atypical observations. Some of them are result of recording or measurement errors and should be corrected (if possible) or deleted from data. So detecting influential observations has an important role in DEA [6]. Influential observations for the first time were introduced by Cook [7] in regression analysis as follows: an influential observation causes noticeable effect on the estimation of parameters and fitted values in the regression. He also proposed a practical statistic that is called Cook distance and it is based on Mahalanobis distance. Then several methods and statistics were proposed to detect influential observations in the regression. Most of these methods are based on case deletion approach. Some of these methods and statistics are given by Belsley et al. [8], Cook and Weisberg [9], and Chatterjee and Hadi [10]. General approach for detecting influential observations is the case deletion technique. This technique is applied by single and multiple cases’ deletions [8]. In the single case deletion, th observation is eliminated from data and then the result of computation is compared by the result which is computed using all data. Multiple cases are the generalized form of the single case deletion; namely, these cases are applied by eliminating observations, where and is the number of observations. The main idea about influential observations in DEA is similar to the regression analysis. Indeed, an influential DMU is an efficient DMU, which basically extends the production possibility set according to its own coordinate, and therefore it may cause several problems as follows.(1)The influential DMU may cause that one DMU to be inefficient, while by omitting the influential DMU, it can be an efficient one.(2)The