Utilizing Monte Carlo Method for Ranking Extreme Efficient Units in Data Envelopment Analysis

Data envelopment analysis (DEA) is a mathematical programming method for calculating efficiency of decision making units (DMU). In calculating the efficiency score of units through DEA we may come up with some efficient units. But the question is among these efficient units which of them is better. As we know, it is possible to rank inefficient units through efficiency score; however, for ranking efficient units it is not helpful and other methods should be developed in these regards. To obviate this problem there have been so many attempts in the literature which have their pros and cons. Cross-efficiency method was first introduced by Sexon et al. for ranking efficient units. The major problem of this method is alternative optimal solutions in each model which must be solved for each DMU. Another problem of this method is dependency of obtained solutions on the solution obtained by other units. Another method which has widely been used is super efficiency, presented by Anderson and Petersen. There are several flaws in their suggested method. Infeasibility, instability, dependency of the model on the input and output orientation and non-zero slack variables are the weaknesses of this method which may occur in specific problems. This article is an attempt to present a method which does not have the aforementioned problems and can be utilized to calculate the rank of extreme efficient units through using the Hit or Miss Monte Carlo method. At the end of the article some examples are made in order to show the efficiency of the presented method.