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Extending the bargaining approach to DEA target setting

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  • Lozano, S.
  • Hinojosa, M.A.
  • Mármol, A.M.

Abstract

This paper extends the approach based on bargaining for computing DEA targets. Thus, for each inefficient Decision Making Unit (DMU), a bargaining problem is defined where the players are the input and output variables that can be improved. In the case of the output players, their utility is an increasing linear function of the corresponding variable. The utility of input players is a decreasing linear function of the input. The disagreement point corresponds to the input and output utilities of the DMU being projected. We show how various well-known bargaining solutions, such as Nash bargaining solution, lexicographic Kalai–Smorodinsky solution, lexicographic egalitarian solution and normalized utilitarian solution, lead to corresponding DEA bargaining models. Some properties of the DEA bargaining models are derived as a consequence of those of the corresponding bargaining solutions. The proposed approach is validated using a container shipping lines application.

Suggested Citation

  • Lozano, S. & Hinojosa, M.A. & Mármol, A.M., 2019. "Extending the bargaining approach to DEA target setting," Omega, Elsevier, vol. 85(C), pages 94-102.
    • Handle: RePEc:eee:jomega:v:85:y:2019:i:c:p:94-102
    DOI: 10.1016/j.omega.2018.05.015
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    4. Chen, Lei & Wang, Ying-Ming, 2020. "DEA target setting approach within the cross efficiency framework," Omega, Elsevier, vol. 96(C).
    5. Yu, Ming-Miin & Rakshit, Ipsita, 2024. "How to establish input and output targets for airlines with heterogeneous production technologies: A nash bargaining DEA approach within the meta-frontier framework," Journal of Air Transport Management, Elsevier, vol. 116(C).
    6. Chang, Tsung-Sheng & Lin, Ji-Gang & Ouenniche, Jamal, 2023. "DEA-based Nash bargaining approach to merger target selection," European Journal of Operational Research, Elsevier, vol. 305(2), pages 930-945.
    7. Yu, Ming-Miin & Rakshit, Ipsita, 2023. "Target setting for airlines incorporating CO2 emissions: The DEA bargaining approach," Journal of Air Transport Management, Elsevier, vol. 108(C).
    8. Zhu, Qingyuan & Aparicio, Juan & Li, Feng & Wu, Jie & Kou, Gang, 2022. "Determining closest targets on the extended facet production possibility set in data envelopment analysis: Modeling and computational aspects," European Journal of Operational Research, Elsevier, vol. 296(3), pages 927-939.
    9. Kadziński, Miłosz & Stamenković, Mladen & Uniejewski, Maciej, 2022. "Stepwise benchmarking for multiple criteria sorting," Omega, Elsevier, vol. 108(C).
    10. Lozano, Sebastián & Khezri, Somayeh, 2021. "Network DEA smallest improvement approach," Omega, Elsevier, vol. 98(C).
    11. Contreras, I. & Lozano, S., 2020. "Allocating additional resources to public universities. A DEA bargaining approach," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    12. 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.
    13. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).
    14. Cui, Yuan & Pan, Hao & Huang, Yi-Di & Yang, Guo-liang, 2024. "How can sociological theories provide legitimacy to eco-efficiency evaluations? Embark on a journey toward understanding," Socio-Economic Planning Sciences, Elsevier, vol. 93(C).

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