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

Abstract

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