Crowding distance development for ranking efficient units in DEA

Abstract

Data Envelopment Analysis models have proven ability to classify decision making units into two efficient and inefficient sets. Although inefficient ones can be sorted by the value of efficiency score, ranking the efficient units has always been a challenging subject in DEA. Various methods, in terms of implementation and nature, have been proposed to rank efficient DMUs. A novel method based on diversity and variety of units on the efficient frontier is presented in this study. Firstly, the crowding distance definition from the multi-objective evolutionary optimization is developed and then a linear programming model is introduced to detect and rank the efficient units at the same time. This means that by solving the proposed model for each DMU separately, ranking efficient units is fulfilled meaning there is no prior need to detect efficient ones. Furthermore, this model can be applied to rank inefficient units with the same logic of the efficient ones which leads to a homogenous ranking of all DMUs. To check the validity and compatibility of this method, it is analyzed through its application on a case study.