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A directional distance based super-efficiency DEA model handling negative data

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  • Ruiyue Lin

    (Xi’an Jiaotong University
    Wenzhou University)

  • Zhiping Chen

    (Xi’an Jiaotong University)

Abstract

This paper develops a new radial super-efficiency data envelopment analysis (DEA) model, which allows input–output variables to take both negative and positive values. Compared with existing DEA models capable of dealing with negative data, the proposed model can rank the efficient DMUs and is feasible no matter whether the input–output data are non-negative or not. It successfully addresses the infeasibility issue of both the conventional radial super-efficiency DEA model and the Nerlove–Luenberger super-efficiency DEA model under the assumption of variable returns to scale. Moreover, it can project each DMU onto the super-efficiency frontier along a suitable direction and never leads to worse target inputs or outputs than the original ones for inefficient DMUs. Additional advantages of the proposed model include monotonicity, units invariance and output translation invariance. Two numerical examples demonstrate the practicality and superiority of the new model.

Suggested Citation

  • Ruiyue Lin & Zhiping Chen, 2017. "A directional distance based super-efficiency DEA model handling negative data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1312-1322, November.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:11:d:10.1057_s41274-016-0137-8
    DOI: 10.1057/s41274-016-0137-8
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    References listed on IDEAS

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    Cited by:

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    3. Bansal, Pooja & Kumar, Sunil & Mehra, Aparna & Gulati, Rachita, 2022. "Developing two dynamic Malmquist-Luenberger productivity indices: An illustrated application for assessing productivity performance of Indian banks," Omega, Elsevier, vol. 107(C).
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    8. Tone, Kaoru & Chang, Tsung-Sheng & Wu, Chen-Hui, 2020. "Handling negative data in slacks-based measure data envelopment analysis models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 926-935.
    9. Kanematsu, Simon Y. & Carvalho, Ney P. & Martinhon, Carlos A. & Almeida, Mariana R., 2020. "Ranking using η-efficiency and relative size measures based on DEA," Omega, Elsevier, vol. 90(C).
    10. Lin, Ruiyue & Liu, Yue, 2019. "Super-efficiency based on the directional distance function in the presence of negative data," Omega, Elsevier, vol. 85(C), pages 26-34.
    11. Rajinder Kaur & Jolly Puri, 2024. "Analysing cost-effectiveness in dynamic network DEA: a directional distance function approach," Operational Research, Springer, vol. 24(4), pages 1-31, December.
    12. Tavana, Madjid & Izadikhah, Mohammad & Toloo, Mehdi & Roostaee, Razieh, 2021. "A new non-radial directional distance model for data envelopment analysis problems with negative and flexible measures," Omega, Elsevier, vol. 102(C).
    13. Shiping Mao & Marios Dominikos Kremantzis & Leonidas Sotirios Kyrgiakos & George Vlontzos, 2022. "R&D Performance Evaluation in the Chinese Food Manufacturing Industry Based on Dynamic DEA in the COVID-19 Era," Agriculture, MDPI, vol. 12(11), pages 1-19, November.
    14. Subhadip Sarkar, 2023. "ABC classification using extended R-model, SVM and Lorenz curve," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1433-1455, September.

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