A Revised Model of the Neutral DEA Model and Its Extension

Peng Liu,Li-Fang Wang,Jian Chang

doi:10.1155/2017/1619798

Abstract

The neutral data envelopment analysis (DEA) model is an alternative way to determine the weights in DEA cross-efficiency evaluation, while avoiding the difficulty in making a choice between the aggressive and benevolent formulations. However, the weights determined by the neutral model merely make the efficiency of part output bigger than other sets of weights. The neutral model is not able to make the efficiency of each output of the DMU biggest among the favorable weights. This neutral model is not purely “neutral” and not most favorable to the DMU. We proposed a revised model for the neutral model. Based on the idea that the DMU should choose a set of weights to maximize its own efficiency, this paper proposes a new cross-efficiency model. The weights determined by the two models are neutral, neither aggressive nor benevolent.

Highlights

Data envelopment analysis proposed by Charnes et al [1] is a nonparametric method to identify the production frontier and to measure the efficiency of homogenous decisionmaking units (DMUs) with multiple inputs and multiple outputs
To avoid the difficulty in making a choice between the aggressive and benevolent formulations in data envelopment analysis (DEA) crossefficiency evaluation, Wang and Chin [18] put forward a neutral DEA model for the cross-efficiency evaluation, which maximinimizes the relative efficiency of each output
The neutral DEA model was proposed on the idea that “when a DMU is given an opportunity to decide a set of input and output weights, what the DMU is concerned most about is whether the weights can be as favorable as possible to itself.”

Summary

Introduction

Data envelopment analysis proposed by Charnes et al [1] is a nonparametric method to identify the production frontier and to measure the efficiency of homogenous decisionmaking units (DMUs) with multiple inputs and multiple outputs. The aggressive (benevolent) model minimizes (maximizes) the average efficiency of other DMUs. The neutral DEA cross-efficiency model suggested by Ying-Ming Wang (2010) offers the new idea to solve this question. To avoid the difficulty in making a choice between the aggressive and benevolent formulations in DEA crossefficiency evaluation, Wang and Chin [18] put forward a neutral DEA model for the cross-efficiency evaluation, which maximinimizes the relative efficiency of each output. The neutral DEA model was proposed on the idea that “when a DMU is given an opportunity to decide a set of input and output weights, what the DMU is concerned most about is whether the weights can be as favorable as possible to itself.”. We further propose a new model based on the idea that according to self-interest principle the DMU will select a set of input and output weights among the favorable weights to maximize its own efficiency.

The Cross-Efficiency Evaluation

The New DEA Model

Numerical Examples

Conclusions