The relationship between Extreme Efficient and Most Efficient Unit(s) in Data Envelopment Analysis

Abstract

Although data envelopment analysis models are able to divide decision-making units (DMUs) into efficient and inefficient sets, choosing the best efficient unit has always been a challenge in decision-making issues. Also, various methods have been introduced to find the most efficient unit, most of which are based on solving linear and nonlinear problems, and also according to the related logic, different units are found as the most efficient unit. The relationship between the most efficient and the extreme efficient units has not been discussed yet. In this paper, we show that each extreme efficient unit can be taken as the most efficient one and vice versa. As a result, the properties of an extreme efficient unit are the same as the most efficient ones. Therefore, since the ways of finding extreme efficient units are simpler, we can utilize these methods to find the most efficient DMU.  We also show how to use the proposed method on a popular example used in most studies.