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A simple MILP to determine closest targets in non-oriented DEA model satisfying strong monotonicity

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  • Zhu, Qingyuan
  • Wu, Jie
  • Ji, Xiang
  • Li, Feng

Abstract

The benchmarking information targets based on Data envelopment analysis (DEA) are commonly classified into two groups: the farthest targets and the closest targets. Many methods have been introduced to derive the closest projection to the strongly efficienct frontier, most of them merely based on the computation of closest efficient targets. Although there are several measures that satisfy a set of interesting properties from an economic and mathematical point of view, they are based on output-oriented models with a multi-stage procedure and cannot be extended easily to the situation of non-orientation, or they are mostly based on a conceptual framework which could not be solved easily. In this paper, we provide an easy, well-defined efficiency measure based on non-oriented closest targets that satisfies strong monotonicity and that is calculated by a simple mixed integer linear program (MILP). A real case of industrial production processes of 30 provincial level regions in mainland China was analyzed to verify the applicability of our proposed approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jomega:v:79:y:2018:i:c:p:1-8
    DOI: 10.1016/j.omega.2017.07.003
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    5. 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.
    6. Javad Vakili & Hanieh Amirmoshiri & Rashed Khanjani Shiraz & Hirofumi Fukuyama, 2020. "A modified distance friction minimization approach in data envelopment analysis," Annals of Operations Research, Springer, vol. 288(2), pages 789-804, May.
    7. Monge, Juan F. & Ruiz, José L., 2023. "Setting closer targets based on non-dominated convex combinations of Pareto-efficient units: A bi-level linear programming approach in Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1084-1096.
    8. Mohammad Amirkhan & Hosein Didehkhani & Kaveh Khalili-Damghani & Ashkan Hafezalkotob, 2018. "Measuring Performance of a Three-Stage Network Structure Using Data Envelopment Analysis and Nash Bargaining Game: A Supply Chain Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1429-1467, September.
    9. An, Qingxian & Tao, Xiangyang & Xiong, Beibei, 2021. "Benchmarking with data envelopment analysis: An agency perspective," Omega, Elsevier, vol. 101(C).
    10. Fukuyama, Hirofumi & Matousek, Roman & Tzeremes, Nickolaos G., 2022. "Bank production with nonperforming loans: A minimum distance directional slack inefficiency approach," Omega, Elsevier, vol. 113(C).
    11. Hirofumi Fukuyama & Yong Tan, 2023. "Estimating market power under a nonparametric analysis: evidence from the Chinese real estate sector," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(2), pages 599-622, June.
    12. 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.
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    15. Kao, Chiang, 2022. "Closest targets in the slacks-based measure of efficiency for production units with multi-period data," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1042-1054.

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