Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix

Qiang Hou,Xue Zhou

doi:10.1155/2015/710264

Abstract

Cross-efficiency evaluation method is an effective and widespread adopted data envelopment analysis (DEA) method with self-assessment and peer-assessment to evaluate and rank decision making units (DMUs). Extant aggressive, benevolent, and neutral cross-efficiency methods are used to evaluate DMUs with competitive, cooperative, and nontendentious relationships, respectively. In this paper, a symmetric (nonsymmetric) compete-cooperate matrix is introduced into aggressive and benevolent cross-efficiency methods and compete-cooperate cross-efficiency method is proposed to evaluate DMUs with diverse (relative) relationships. Deviation maximization method is applied to determine the final weights of cross-evaluation to enhance the differentiation ability of cross-efficiency evaluation method. Numerical demonstration is provided to illustrate the reasonability and practicability of the proposed method.

Highlights

Data envelopment analysis (DEA) is a nonparametric programming method for evaluating the relative efficiencies of a group of decision making units (DMUs) with multiple inputs and outputs
The traditional DEA models, including the CCR and BCC model, are based on self-assessment system; the obtained input and output weights of evaluated DMUs take the aim at maximizing their own efficiency, which will cause problems in three aspects
(1) The traditional DEA models can only distinguish the efficient and inefficient DMUs but cannot rank the merits and with a lower degree of differentiation on CCR-efficient DMUs. (2) The obtained efficiency weights are only beneficial to the single DMU, which is easy to exaggerate its own advantages in some inputs and outputs angles, but circumvent its disadvantages in other input and output angles, resulting in lip-deep efficient phenomena

Summary

Introduction

Data envelopment analysis (DEA) is a nonparametric programming method for evaluating the relative efficiencies of a group of decision making units (DMUs) with multiple inputs and outputs. The traditional DEA models, including the CCR and BCC model, are based on self-assessment system; the obtained input and output weights of evaluated DMUs take the aim at maximizing their own efficiency, which will cause problems in three aspects. (3) Each DMU selects its own favorable weighting scheme, lacking comparability among DMUs. The traditional DEA models, including the CCR and BCC model, are based on self-assessment system; the obtained input and output weights of evaluated DMUs take the aim at maximizing their own efficiency, which will cause problems in three aspects. The typical treatments to avoid the problem include Doyle and Green’s [14] aggressive and benevolent crossefficiency evaluation methods, which introduce secondary objective functions to cross-efficiency evaluation method and can select the optimal weights to minimize and maximize the sum of the outputs of other DMUs, respectively.

Traditional Cross-Efficiency Models

Compete-Cooperate Cross-Efficiency Model

An Illustrative Example

Conclusions