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Using common weights and efficiency invariance principles for resource allocation and target setting

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  • Feng Li
  • Jian Song
  • Alexandre Dolgui
  • Liang Liang

Abstract

Data envelopment analysis (DEA) has proven to be a useful technique for evaluating the relative performance of comparable and homogeneous decision-making units (DMUs). In recent years, DEA-based resource allocation and target setting approaches have gained more and more attention from both practitioners and academic researchers. In this paper, we propose a new mechanism to simultaneously adopt the principles of common weights and efficiency invariance in allocating multiple resources and setting multiple targets among DMUs. To obtain the final plan, we minimise the deviation between the possible plan based on common weights and another feasible plan emphasising efficiency invariance. If the minimum deviation equals zero, one optimal plan will be determined. In general situations, however, the proposed approach will present two plans that have a non-zero deviation. One is generated using a common set of weights for all DMUs in such a way that the change of efficiencies is minimised, while the other is generated by strictly keeping efficiency scores unchanged yet having similar or even identical weights on input–output measures for each DMU to the utmost extent. The efficacy and usefulness of the proposed approach are demonstrated using a numerical example from previous literature and an empirical application to an urban bus company in China.

Suggested Citation

  • Feng Li & Jian Song & Alexandre Dolgui & Liang Liang, 2017. "Using common weights and efficiency invariance principles for resource allocation and target setting," International Journal of Production Research, Taylor & Francis Journals, vol. 55(17), pages 4982-4997, September.
  • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:17:p:4982-4997
    DOI: 10.1080/00207543.2017.1287450
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    Cited by:

    1. Yongjun Li & Feng Li & Ali Emrouznejad & Liang Liang & Qiwei Xie, 2019. "Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game," Annals of Operations Research, Springer, vol. 274(1), pages 373-394, March.
    2. Qingxian An & Xuyang Liu & Yongli Li & Beibei Xiong, 2019. "Resource planning of Chinese commercial banking systems using two-stage inverse data envelopment analysis with undesirable outputs," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-20, June.
    3. Li, Yongjun & Wang, Lizheng & Li, Feng, 2021. "A data-driven prediction approach for sports team performance and its application to National Basketball Association," Omega, Elsevier, vol. 98(C).
    4. Li, Feng & Zhu, Qingyuan & Chen, Zhi, 2019. "Allocating a fixed cost across the decision making units with two-stage network structures," Omega, Elsevier, vol. 83(C), pages 139-154.
    5. Menghan Chen & Sheng Ang & Lijing Jiang & Feng Yang, 2020. "Centralized resource allocation based on cross-evaluation considering organizational objective and individual preferences," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 529-565, June.
    6. Antunes, Jorge & Tan, Yong & Wanke, Peter & Jabbour, Charbel Jose Chiappetta, 2023. "Impact of R&D and innovation in Chinese road transportation sustainability performance: A novel trigonometric envelopment analysis for ideal solutions (TEA-IS)," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    7. Xiong, Xi & Yang, Guo-liang & Zhou, De-qun & Wang, Zi-long, 2022. "How to allocate multi-period research resources? Centralized resource allocation for public universities in China using a parallel DEA-based approach," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    8. Yang, Jiawei & Li, Dan & Li, Yongjun, 2024. "A generalized data envelopment analysis approach for fixed cost allocation with preference information," Omega, Elsevier, vol. 122(C).
    9. I. Contreras & S. Lozano & M. A. Hinojosa, 2021. "A bargaining approach to determine common weights in DEA," Operational Research, Springer, vol. 21(3), pages 2181-2201, September.
    10. Feng Li & Qingyuan Zhu & Liang Liang, 2019. "A new data envelopment analysis based approach for fixed cost allocation," Annals of Operations Research, Springer, vol. 274(1), pages 347-372, March.
    11. Chao, Shih-Liang & Yu, Ming-Miin, 2022. "Applying data envelopment analysis to allocate incentive bonuses for container terminal operators," Transport Policy, Elsevier, vol. 125(C), pages 231-240.
    12. Mehdi Soltanifar & Farhad Hosseinzadeh Lotfi & Hamid Sharafi & Sebastián Lozano, 2022. "Resource allocation and target setting: a CSW–DEA based approach," Annals of Operations Research, Springer, vol. 318(1), pages 557-589, November.
    13. Afsharian, Mohsen & Ahn, Heinz & Harms, Sören Guntram, 2021. "A review of DEA approaches applying a common set of weights: The perspective of centralized management," European Journal of Operational Research, Elsevier, vol. 294(1), pages 3-15.
    14. Qingxian An & Ping Wang & Honglin Yang & Zongrun Wang, 2021. "Fixed cost allocation in two-stage system using DEA from a noncooperative view," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1077-1102, December.
    15. Ma, Gang & Li, Xu & Zheng, Jianping, 2020. "Efficiency and equity in regional coal de-capacity allocation in China: A multiple objective programming model based on Gini coefficient and Data Envelopment Analysis," Resources Policy, Elsevier, vol. 66(C).
    16. An, Qingxian & Wang, Ping & Emrouznejad, Ali & Hu, Junhua, 2020. "Fixed cost allocation based on the principle of efficiency invariance in two-stage systems," European Journal of Operational Research, Elsevier, vol. 283(2), pages 662-675.

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