Gap Minimization for Peer-Evaluation in DEA Cross-Efficiency

Anrong Yang,Dunliang Chen,Zigang Zhang,Yishi Zhang

doi:10.1155/2014/453749

Abstract

Cross-efficiency evaluation is an effective and widely used method for ranking decision making units (DMUs) in data envelopment analysis (DEA). Gap minimization criterion is introduced in aggressive and benevolent cross-efficiency methods to avoid possible extreme efficiency from peer-evaluation and to get equitable results. On the basis of this criterion, a weighted cross-efficiency method with similarity distance that, respectively, considers the aggressive and the benevolent formulations is proposed to determine cross-efficiency. The weights of the cross-evaluation determined by this method are positively influenced by self-evaluation and thus are propitious to resolving conflict. Numerical demonstration reveals the feasibility of the proposed method.

Highlights

Data envelopment analysis (DEA) is an effective and widely used nonparametric method for assessing the relative efficiency of a set of decision making units (DMUs) with structures of multiple inputs and outputs
Extant research has made efforts to tackle the shortcomings of cross-efficiency but seldom considers how to effectively discriminate DEAefficient from data envelopment analysis (DEA)-inefficient DMUs and to reduce conflict during the cross-evaluation process
Based on two typical cross-efficiency methods, we propose a secondary goal to minimize the gap between the upper and lower bounds of the peer-evaluation scores and a weighted neutral crossefficiency method to determine cross-efficiency of each DMU with a combination of its aggressive and benevolent crossefficiency

Summary

Introduction

Data envelopment analysis (DEA) is an effective and widely used nonparametric method for assessing the relative efficiency of a set of decision making units (DMUs) with structures of multiple inputs and outputs. Doyle and Green [20] propose an aggressive cross-efficiency method and a benevolent one to avoid the problem They introduce secondary objective functions to select the optimal weights minimizing and maximizing the sum of the outputs of other DMUs, respectively. To resolve the problem of having multiple optimal solutions from model (1) so as to keep θj∗p unchanged, Sexton et al [18] introduce a secondary goal to select the optimal input and output weights from multiple optimal solutions while keeping the CCR efficiency θp∗p unchanged. Model (4) with a maxobjective function is known as the benevolent efficiency model, which maximizes the cross-efficiencies of other DMUs while preserving the efficiency of itself under evaluation

A Weighted Neutral Cross-Efficiency Method

An Illustrative Example

Conclusions