Entropy Cross-Efficiency Model for Decision Making Units with Interval Data

Lupei Wang,Ningxi Hong,Lei Li

doi:10.3390/e18100358

Abstract

The cross-efficiency method, as a Data Envelopment Analysis (DEA) extension, calculates the cross efficiency of each decision making unit (DMU) using the weights of all decision making units (DMUs). The major advantage of the cross-efficiency method is that it can provide a complete ranking for all DMUs. In addition, the cross-efficiency method could eliminate unrealistic weight results. However, the existing cross-efficiency methods only evaluate the relative efficiencies of a set of DMUs with exact values of inputs and outputs. If the input or output data of DMUs are imprecise, such as the interval data, the existing methods fail to assess the efficiencies of these DMUs. To address this issue, we propose the introduction of Shannon entropy into the cross-efficiency method. In the proposed model, intervals of all cross-efficiency values are firstly obtained by the interval cross-efficiency method. Then, a distance entropy model is proposed to obtain the weights of interval efficiency. Finally, all alternatives are ranked by their relative Euclidean distance from the positive solution.

Highlights

When decision making units (DMUs) have multiple inputs and outputs, data envelopment analysis (DEA) is a well-known non-parametric programming technique for assessing the efficiency of these DMUs
We propose the introduction of Shannon entropy into the cross-efficiency method
The present study proposes a new cross-efficiency method based on the entropy theory

Summary

Introduction

When decision making units (DMUs) have multiple inputs and outputs, data envelopment analysis (DEA) is a well-known non-parametric programming technique for assessing the efficiency of these DMUs. If the efficiency score of a DMU is equal to 1, it is considered as efficient. Inefficient DMUs are considered as performing worse than efficient ones. DEA is not able to rank the efficient DMUs that all have an efficiency score of 1. In order to solve this problem, the cross-efficiency method was developed by Sexton et al [9]. The cross-efficiency method, as a DEA extension, could obtain the efficiency of each DMU by linking the weights of all DMUs. Its primary advantage is that all DMUs can be completely ranked [10]. The cross-efficiency method could eliminate unrealistic weight results [11]

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