Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach

Abstract

The measurement of technical efficiency is a topic of great interest. Since the beginning, many researchers have developed new approaches to gauge technical efficiency, mainly in the non-parametric area of Data Envelopment Analysis (DEA). However, the first measures in DEA, the well-known radial models, only ac- counted for radial inefficiency, which motivated the introduction in the literature of the so-called Global Efficiency Measures (GEMs); non-oriented and non-radial in nature. Two famous GEMs are the Russell Graph Measure and the Enhanced Russell Graph Measure, also known as the Slacks-Based Measure. These approaches aggregate input and output specific efficiencies through the arithmetic mean, which may not be the most appropriate aggregator function when input and output efficiency ratios are considered, as will be shown. In this paper, in contrast, we propose aggregating input and output specific inefficiencies by applying the geometric average, which will allow us to define new multiplicative versions of the Rus- sell Graph Measures. We also prove some theoretical results and introduce an iterative algorithm, based upon Second Order Cone Programming, to solve the new models. Finally, the implementation of the in- troduced approaches is empirically illustrated through a data set taken from the literature.