Full ranking of efficient and inefficient DMUs with the same measure of efficiency in DEA

Abstract

Data envelopment analysis (DEA) is a mathematical programming approach for calculating the relative efficiency of a group of decision making units (DMUs). After efficiency measurement process some DMUs may have the same measure of efficiency, specifically some DMUs may be found efficient. The question is which DMU performs better within a group of DMUs with the same measure of efficiency. The current article aims to answer this question based the DMU's aid not only to the associated group but also its aid to the whole production system. This yields to two ranking indices. The first index is for ranking inefficient DMUs with the same measure of efficiency and the second index is for ranking efficient DMUs. A comparison between the proposed approaches and well-known ranking index in the literature is provided and proposed approaches are explained by many numerical examples and a real life data illustration.