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A unique equilibrium efficient frontier with fixed-sum outputs in data envelopment analysis

Author

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  • Qingyuan Zhu

    (University of Science and Technology of China
    University of Illinois at Urbana-Champaign)

  • Jie Wu

    (University of Science and Technology of China)

  • Malin Song

    (Anhui University of Finance and Economics)

  • Liang Liang

    (Hefei University of Technology)

Abstract

Based on the equilibrium efficient frontier data envelopment analysis (EEFDEA) approach, Fang (J Oper Res Soc 67:412–420, 2015a) developed an equivalent linear programming model to improve and strengthen the EEFDEA approach. Furthermore, Fang (2015a) indicated that his secondary goal approach can achieve a unique equilibrium efficient frontier. However, through a simple counterexample we demonstrate that Fang’s secondary goal approach cannot always achieve uniqueness of the equilibrium efficient frontier. In this paper, we propose an algorithm based on the secondary goal approach to address the problem. The proposed algorithm is proven mathematically to be an effective approach to guaranteeing the uniqueness of the equilibrium efficient frontier.

Suggested Citation

  • Qingyuan Zhu & Jie Wu & Malin Song & Liang Liang, 2017. "A unique equilibrium efficient frontier with fixed-sum outputs in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1483-1490, December.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:12:d:10.1057_s41274-017-0181-z
    DOI: 10.1057/s41274-017-0181-z
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    Cited by:

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    3. Bouzidis, Thanasis & Karagiannis, Giannis, 2022. "An alternative ranking of DMUs performance for the ZSG-DEA model," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    4. Yu, Shasha & Lei, Ming & Deng, Honghui, 2023. "Evaluation to fixed-sum-outputs DMUs by non-oriented equilibrium efficient frontier DEA approach with Nash bargaining-based selection," Omega, Elsevier, vol. 115(C).
    5. Lozano, Sebastián, 2023. "Bargaining approach for efficiency assessment and target setting with fixed-sum variables," Omega, Elsevier, vol. 114(C).
    6. Lozano, Sebastián & Contreras, Ignacio, 2022. "Centralised resource allocation using Lexicographic Goal Programming. Application to the Spanish public university system," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    7. Jie Wu & Panpan Xia & Qingyuan Zhu & Junfei Chu, 2019. "Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output," Annals of Operations Research, Springer, vol. 275(2), pages 731-749, April.
    8. Yongjun Li & Wenhui Hou & Weiwei Zhu & Feng Li & Liang Liang, 2021. "Provincial carbon emission performance analysis in China based on a Malmquist data envelopment analysis approach with fixed-sum undesirable outputs," Annals of Operations Research, Springer, vol. 304(1), pages 233-261, September.
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    10. Thanasis Bouzidis & Giannis Karagiannis, 2021. "An Alternative Ranking of DMUs Performance for the ZGS-DEA Model," Discussion Paper Series 2021_12, Department of Economics, University of Macedonia, revised Oct 2021.
    11. Zhu, Qingyuan & Wu, Jie & Ji, Xiang & Li, Feng, 2018. "A simple MILP to determine closest targets in non-oriented DEA model satisfying strong monotonicity," Omega, Elsevier, vol. 79(C), pages 1-8.

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