An improvement in DEA cross‐efficiency aggregation based on the Shannon entropy

• Published date: 01 March 2018
• DOI: http://doi.org/10.1111/itor.12361
• Date: 01 March 2018
• Author: Lianlian Song,Fan Liu

Intl. Trans. in Op. Res. 25 (2018) 705–714

DOI: 10.1111/itor.12361

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

An improvement in DEA cross-efficiency aggregation based

on the Shannon entropy

Lianlian Songaand Fan Liub,∗

aCollege of Economics & Management, Nanjing University of Aeronauticsand Astronautics, Nanjing, China

bSchool of Management & Engineering, Nanjing University, Nanjing, China

E-mail: songll@nuaa.edu.cn [Song]; liufan@nju.edu.cn [Liu]

Received 22 January 2016; received in revised form 19 July 2016; accepted 26 September 2016

Abstract

This paper improves a recently proposed Data Envelopment Analysis (DEA) cross-efficiency aggregation

method based on the Shannon entropy. The weights for determining cross-efficiency are derived from mini-

mizing the square distance of weighted cross-efficiencyand weighted CCR efficiency. Our calculationexample

indicates that this method mayproduce inappropriate weights,which is significantly inconsistent with a widely

accepted viewpoint. A variance coefficient method based on the Shannon entropy is presented to overcome

the drawbacks of the DEA cross-efficiency aggregation method. In this study, comparisons of weights and

cross-efficiency scores are provided.

Keywords:cross-efficiency; aggregation; weights; variance coefficient method

1. Introduction

Data Envelopment Analysis (DEA) cross-efficiency was originated by Sexton et al. (1986) and

further investigated by Doyle and Green (1994), the main idea of which is to use DEA in a peer

evaluation rather than a pure evaluation mode. The two prominent advantages of cross-efficiency

evaluation are as follows:

1. cross-efficiency provides an efficiency ranking among all decision-making units (DMUs) to

differentiate between good and poor performances;

2. cross-efficiency can eliminate the requirement of elicitation of weight restrictions from applica-

tion area experts, thereby avoiding unrealistic DEA weighting schemes (Anderson et al., 2002;

Liang et al., 2008).

In line with the classical denotations in DEA, we suppose that there are a set of DMUs and each

DMUjhas mdifferent inputs, xij,i=1,2,...,m,andsdifferent outputs, yrj,r=1,2,...,s.DEA

∗Corresponding author.

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2016 The Authors.

International Transactionsin Operational Research C

2016 International Federation of OperationalResearch Societies

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