A Revised Inverse Data Envelopment Analysis Model Based on Radial Models

Xiaoyin Hu,Xiaoya Li,Jinchuan Cui,Jianshu Li

doi:10.3390/math8050803

Abstract

In recent years, there has been an increasing interest in applying inverse data envelopment analysis (DEA) to a wide range of disciplines, and most applications have adopted radial-based inverse DEA models. However, results given by existing radial based inverse DEA models can be unreliable as they neglect slacks while evaluating decision-making units’ (DMUs) overall efficiency level, whereas classic radial DEA models measure the efficiency level through not only radial efficiency index but also slacks. This paper points out these disadvantages with a counterexample, where current inverse DEA models give results that outputs shall increase when inputs decrease. We show that these unreasonable results are the consequence of existing inverse DEA models’ failure in preserving DMU’s efficiency level. To rectify this problem, we propose a revised model for the situation where the investigated DMU has no slacks. Compared to existing radial inverse DEA models, our revised model can preserve radial efficiency index as well as eliminating all slacks, thus fulfilling the requirement of efficiency level invariant. Numerical examples are provided to illustrate the validity and limitations of the revised model.

Highlights

Data envelopment analysis (DEA) is a linear programming (LP) based method to assess the efficiency level of decision-making units (DMUs) with multiple inputs and outputs
The radial inefficiency is measured by a scalar named radial efficiency index, while the mix inefficiency is identified by slacks of the corresponding LP
This paper points out possible failures of existing radial inverse DEA models and provides a remedy for some situations

Summary

Introduction

Data envelopment analysis (DEA) is a linear programming (LP) based method to assess the efficiency level of decision-making units (DMUs) with multiple inputs and outputs. The first DEA model, the Charnes, Cooper, and Rhodes (CCR) model [10], evaluates the efficiency level of each DMU in two aspects, radial inefficiency and mix inefficiency. The radial inefficiency is measured by a scalar named radial efficiency index, while the mix inefficiency is identified by slacks of the corresponding LP. This evaluation process indicates that radial efficiency index and slacks should be considered to measure the efficiency level. The CCR model and other DEA models with similar evaluation process are referred to as radial

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Conclusion