A Revised Inverse Data Envelopment Analysis Model Based on Radial Models

Xiaoyin Hu, Jianshu Li, Xiaoya Li and Jinchuan Cui
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Xiaoyin Hu: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Jianshu Li: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Xiaoya Li: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Jinchuan Cui: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Mathematics, 2020, vol. 8, issue 5, 1-17

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.

Keywords: data envelopment analysis; efficiency index; multi-objective programing; slacks (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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