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A new approach for achievement of the equilibrium efficient frontier with fixed-sum outputs

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  • Lei Fang

    (Nankai University, Tainjin City, People’s Republic of China)

Abstract

In a recent paper, Yang et al developed an algorithm based on the extended minimal adjustment strategy and the equilibrium competition strategy to achieve a common equilibrium efficient frontier. However, the computational burden of their algorithm is challenging when a sample contains many inefficient decision-making units (DMUs). In this paper, we propose a linear programming model that can achieve a common equilibrium efficient frontier in a single step, regardless of the number of inefficient DMUs. Furthermore, we demonstrate the existence and the non-uniqueness of the equilibrium efficient frontier and identify its shortcomings through an example. Next, we extend our approach to incorporate weight restrictions to indicate the relative importance of the different inputs and outputs and introduce the secondary goal of minimizing the maximal relative deviation for each fixed-sum output, which can result in a unique equilibrium efficient frontier.

Suggested Citation

  • Lei Fang, 2016. "A new approach for achievement of the equilibrium efficient frontier with fixed-sum outputs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(3), pages 412-420, March.
  • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:3:p:412-420
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    Citations

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    Cited by:

    1. Ding, Tao & Zhang, Yun & Zhang, Danlu & Li, Feng, 2023. "Performance evaluation of Chinese research universities: A parallel interactive network DEA approach with shared and fixed sum inputs," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    2. Zhu, Qingyuan & Li, Xingchen & Li, Feng & Wu, Jie & Zhou, Dequn, 2020. "Energy and environmental efficiency of China's transportation sectors under the constraints of energy consumption and environmental pollutions," Energy Economics, Elsevier, vol. 89(C).
    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. Xifan Chen & Qingyuan Zhu & Chengzhen Xu & Zhiyang Shen & Malin Song, 2024. "Energy and environmental efficiency of China's regional electric power industry by considering renewable energy constraints," Energy & Environment, , vol. 35(2), pages 927-949, March.
    5. 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).
    6. Lozano, Sebastián, 2023. "Bargaining approach for efficiency assessment and target setting with fixed-sum variables," Omega, Elsevier, vol. 114(C).
    7. Li, Yongjun & Liu, Jin & Ang, Sheng & Yang, Feng, 2021. "Performance evaluation of two-stage network structures with fixed-sum outputs: An application to the 2018winter Olympic Games," Omega, Elsevier, vol. 102(C).
    8. 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).
    9. 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.
    10. 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.
    11. Li, Feng & Zhang, Danlu & Zhang, Jinyu & Kou, Gang, 2022. "Measuring the energy production and utilization efficiency of Chinese thermal power industry with the fixed-sum carbon emission constraint," International Journal of Production Economics, Elsevier, vol. 252(C).

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