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DEA cross-efficiency evaluation based on Pareto improvement

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  • Wu, Jie
  • Chu, Junfei
  • Sun, Jiasen
  • Zhu, Qingyuan

Abstract

Cross-efficiency evaluation, as an extension tool of data envelopment analysis (DEA), has been widely applied in evaluating and ranking decision making units (DMUs). Unfortunately, the cross-efficiency scores generated may not be Pareto optimal, which has reduced the effectiveness of this method. To solve this problem, we propose a cross-efficiency evaluation approach based on Pareto improvement, which contains two models (Pareto optimality estimation model and cross-efficiency Pareto improvement model) and an algorithm. The Pareto optimality estimation model is used to estimate whether the given set of cross-efficiency scores are Pareto-optimal solutions. If these cross-efficiency scores are not Pareto optimal, the Pareto improvement model is then used to make cross-efficiency Pareto improvement for all the DMUs. In contrast to other cross-efficiency approaches, our approach always obtains a set of Pareto-optimal cross efficiencies under the predetermined weight selection principles for these DMUs. In addition, if the proposed algorithm terminates at its step 3, the evaluation results generated by our approach unify self-evaluation, peer-evaluation, and common-weight-evaluation in DEA cross-efficiency evaluation. Specifically, the self-evaluated efficiency and the peer-evaluated efficiency converge to the same common-weight-evaluated efficiency when the algorithm stops. This will make the evaluation results more likely to be accepted by all the DMUs.

Suggested Citation

  • Wu, Jie & Chu, Junfei & Sun, Jiasen & Zhu, Qingyuan, 2016. "DEA cross-efficiency evaluation based on Pareto improvement," European Journal of Operational Research, Elsevier, vol. 248(2), pages 571-579.
    • Handle: RePEc:eee:ejores:v:248:y:2016:i:2:p:571-579
    DOI: 10.1016/j.ejor.2015.07.042
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    References listed on IDEAS

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    Cited by:

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    2. Chu, Junfei & Wu, Jie & Chu, Chengbin & Zhang, Tinglong, 2020. "DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches," Omega, Elsevier, vol. 94(C).
    3. Hashem Omrani & Khatereh Shafaat & Arash Alizadeh, 2019. "Integrated data envelopment analysis and cooperative game for evaluating energy efficiency of transportation sector: a case of Iran," Annals of Operations Research, Springer, vol. 274(1), pages 471-499, March.
    4. Jie Wu & Junfei Chu & Qingyuan Zhu & Pengzhen Yin & Liang Liang, 2016. "DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 5990-6007, October.
    5. Ma-Lin Song & Ron Fisher & Jian-Lin Wang & Lian-Biao Cui, 2018. "Environmental performance evaluation with big data: theories and methods," Annals of Operations Research, Springer, vol. 270(1), pages 459-472, November.
    6. Fangqing Wei & Junfei Chu & Jiayun Song & Feng Yang, 2019. "A cross-bargaining game approach for direction selection in the directional distance function," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 787-807, September.
    7. Davtalab-Olyaie, Mostafa & Asgharian, Masoud, 2021. "On Pareto-optimality in the cross-efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 288(1), pages 247-257.
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    10. Delimiro Visbal-Cadavid & Mónica Martínez-Gómez & Francisco Guijarro, 2017. "Assessing the Efficiency of Public Universities through DEA. A Case Study," Sustainability, MDPI, vol. 9(8), pages 1-19, August.
    11. Alcaraz, Javier & Aparicio, Juan & Monge, Juan Fco & Ramón, Nuria, 2022. "Weight profiles in cross-efficiency evaluation based on hypervolume maximization," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
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    13. Navas, Lina P. & Montes, Felipe & Abolghasem, Sepideh & Salas, Ricardo J. & Toloo, Mehdi & Zarama, Roberto, 2020. "Colombian higher education institutions evaluation," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    14. Xiaohong Liu & Feng Yang & Jie Wu, 2020. "DEA considering technological heterogeneity and intermediate output target setting: the performance analysis of Chinese commercial banks," Annals of Operations Research, Springer, vol. 291(1), pages 605-626, August.
    15. Shi, Hai-Liu & Chen, Sheng-Qun & Chen, Lei & Wang, Ying-Ming, 2021. "A neutral cross-efficiency evaluation method based on interval reference points in consideration of bounded rational behavior," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1098-1110.
    16. Lei Chen & Fei-Mei Wu & Feng Feng & Fujun Lai & Ying-Ming Wang, 2018. "A Common Set of Weights for Ranking Decision-Making Units with Undesirable Outputs: A Double Frontiers Data Envelopment Analysis Approach," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-25, December.
    17. Lei Chen & Ying-Ming Wang & Yan Huang, 2020. "Cross-efficiency aggregation method based on prospect consensus process," Annals of Operations Research, Springer, vol. 288(1), pages 115-135, May.
    18. Balk, Bert M. & (René) De Koster, M.B.M. & Kaps, Christian & Zofío, José L., 2021. "An evaluation of cross-efficiency methods: With an application to warehouse performance," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    19. Zhu, Weiwei & Yu, Yu & Sun, Panpan, 2018. "Data envelopment analysis cross-like efficiency model for non-homogeneous decision-making units: The case of United States companies’ low-carbon investment to attain corporate sustainability," European Journal of Operational Research, Elsevier, vol. 269(1), pages 99-110.
    20. Rezaeiani, M.J. & Foroughi, A.A., 2018. "Ranking efficient decision making units in data envelopment analysis based on reference frontier share," European Journal of Operational Research, Elsevier, vol. 264(2), pages 665-674.
    21. Feng Li & Han Wu & Qingyuan Zhu & Liang Liang & Gang Kou, 2021. "Data envelopment analysis cross efficiency evaluation with reciprocal behaviors," Annals of Operations Research, Springer, vol. 302(1), pages 173-210, July.
    22. Yeşilyurt, M. Ensar & Şahin, Emre & Elbi, M. Doğan & Kızılkaya, Aydın & Koyuncuoğlu, M. Ulaş & Akbaş-Yeşilyurt, Filiz, 2021. "A novel method for computing single output for DEA with application in hospital efficiency," Socio-Economic Planning Sciences, Elsevier, vol. 76(C).
    23. Junfei Chu & Jie Wu & Qingyuan Zhu & Qingxian An & Beibei Xiong, 2019. "Analysis of China’s Regional Eco-efficiency: A DEA Two-stage Network Approach with Equitable Efficiency Decomposition," Computational Economics, Springer;Society for Computational Economics, vol. 54(4), pages 1263-1285, December.
    24. Li, Yongjun & Xie, Jianhui & Wang, Meiqiang & Liang, Liang, 2016. "Super efficiency evaluation using a common platform on a cooperative game," European Journal of Operational Research, Elsevier, vol. 255(3), pages 884-892.

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