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

作     者：Alcaraz, Javier Anton-Sanchez, Laura Aparicio, Juan Monge, Juan F. Ramon, Nuria 

作者机构：Miguel Hernandez Univ Elche Ctr Operat Res Avda Univ S-N Elche 03202 Alicante Spain 

出 版 物：《EUROPEAN JOURNAL OF OPERATIONAL RESEARCH》 (欧洲运筹学杂志)

年 卷 期：2021年第292卷第2期

页      面：663-674页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Spanish Ministry of Science and Innovation State Research Agency [PID2019-105952GB-I00/AEI/10.13039/501100011033] Spanish Ministry for Economy and Competitiveness State Research Agency European Regional Development Fund [MTM2016-76530-R] 

主　　题：Data envelopment analysis Russell Graph Measures Properties Second order cone programming 

摘      要：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 accounted 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 Russell 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 introduced approaches is empirically illustrated through a data set taken from the literature. (C) 2020 Elsevier B.V. All rights reserved.