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A Revised Inverse Data Envelopment Analysis Model Based on Radial Models

Author

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  • Xiaoyin Hu

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
    School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
    These authors contributed equally to this work.)

  • Jianshu Li

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
    School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
    These authors contributed equally to this work.)

  • 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)

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.

Suggested Citation

  • Xiaoyin Hu & Jianshu Li & Xiaoya Li & Jinchuan Cui, 2020. "A Revised Inverse Data Envelopment Analysis Model Based on Radial Models," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:803-:d:358412
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    References listed on IDEAS

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    1. Puig-Junoy, Jaume, 2000. "Partitioning input cost efficiency into its allocative and technical components: an empirical DEA application to hospitals," Socio-Economic Planning Sciences, Elsevier, vol. 34(3), pages 199-218, September.
    2. M. Eyni & G. Tohidi & S. Mehrabeian, 2017. "Applying inverse DEA and cone constraint to sensitivity analysis of DMUs with undesirable inputs and outputs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 34-40, January.
    3. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "A survey of DEA applications," Omega, Elsevier, vol. 41(5), pages 893-902.
    4. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    5. Hadi-Vencheh, Abdollah & Foroughi, Ali Asghar & Soleimani-damaneh, Majid, 2008. "A DEA model for resource allocation," Economic Modelling, Elsevier, vol. 25(5), pages 983-993, September.
    6. Meng Zhang & Jin-chuan Cui, 2016. "The extension and integration of the inverse DEA method," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(9), pages 1212-1220, September.
    7. Wei, Quanling & Zhang, Jianzhong & Zhang, Xiangsun, 2000. "An inverse DEA model for inputs/outputs estimate," European Journal of Operational Research, Elsevier, vol. 121(1), pages 151-163, February.
    8. Yan, Hong & Wei, Quanling & Hao, Gang, 2002. "DEA models for resource reallocation and production input/output estimation," European Journal of Operational Research, Elsevier, vol. 136(1), pages 19-31, January.
    9. Robert G. Bland, 1977. "New Finite Pivoting Rules for the Simplex Method," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 103-107, May.
    10. Jianqing Zhang & Song Wang & Peilei Yang & Fei Fan & Xueli Wang, 2020. "Analysis of Scale Factors on China’s Sustainable Development Efficiency Based on Three-Stage DEA and a Double Threshold Test," Sustainability, MDPI, vol. 12(6), pages 1-26, March.
    11. Fakarudin Kamarudin & Fadzlan Sufian & Annuar Md. Nassir & Nazratul Aina Mohamad Anwar & Hafezali Iqbal Hussain, 2019. "Bank Efficiency in Malaysia a DEA Approach," Journal of Central Banking Theory and Practice, Central bank of Montenegro, vol. 8(1), pages 133-162.
    12. Feng, Chenpeng & Chu, Feng & Ding, Jingjing & Bi, Gongbing & Liang, Liang, 2015. "Carbon Emissions Abatement (CEA) allocation and compensation schemes based on DEA," Omega, Elsevier, vol. 53(C), pages 78-89.
    13. Lim, Dong-Joon, 2016. "Inverse DEA with frontier changes for new product target setting," European Journal of Operational Research, Elsevier, vol. 254(2), pages 510-516.
    14. Ali Emrouznejad & Guo-liang Yang & Gholam R. Amin, 2019. "A novel inverse DEA model with application to allocate the CO2 emissions quota to different regions in Chinese manufacturing industries," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(7), pages 1079-1090, July.
    15. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, April.
    16. BLAND, Robert G., 1977. "New finite pivoting rules for the simplex method," LIDAM Reprints CORE 315, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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