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DEA-based proportional-sharing fixed cost allocation considering bi-objective optimization

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Abstract

This paper proposes a new proportional-sharing approach for fixed cost allocation (FCA) among a group of decision-making units (DMUs) based on data envelopment analysis (DEA). We first prove the proportional invariance in DEA-based FCA. Then, we show that the “all-efficient” assumption in existing models usually leads to the use of unrealistic weights in efficiency analysis. To address this issue, we relax this assumption and adopt a weight constraint approach. Further, we illustrate that some DMUs would always be allocated with zero fixed cost if only the goal of efficiency maximizing is considered. Therefore, some weight constraints are added, and a new bi-objective model is proposed to allocate the fixed cost among the DMUs in order to simultaneously maximize the efficiencies of the DMUs and make the allocation as close as possible to the one generated according to the DMUs’ operation sizes. A mono-objective nonlinear program, which can be solved using dichotomy and a linear program solver, is used to obtain a non-dominated or Pareto-optimal trade-off solution for the bi-objective model. With the use of our approach, neither unrealistic weights nor zero fixed cost appears in the result. Finally, the proposed approach is applied to a numerical example and a commercial bank case study.

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Acknowledgements

The authors are sincerely grateful for the suggestions and comments given by the two anonymous reviewers. The research is supported by the National Natural Science Foundation of China (Nos. 72271247, 72102234, and 71901225), the Natural Science Foundation of Hunan Province (No. 2021JJ40800), and Zhejiang General Soft Science Research Project (No. 2023C35078).

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Authors and Affiliations

  1. School of Business, Central South University, Hunan, 410083, People’s Republic of China

    Junfei Chu & Wang Su

  2. School of Management, University of Science and Technology of China, Anhui, 230026, People’s Republic of China

    Jie Wu

  3. Research Center, Léonard de Vinci Pôle Universitaire, 92 916, Paris La Défense, France

    Zhe Yuan

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  1. Junfei Chu
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  2. Wang Su
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  3. Jie Wu
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  4. Zhe Yuan
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Correspondence to Junfei Chu.

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Chu, J., Su, W., Wu, J. et al. DEA-based proportional-sharing fixed cost allocation considering bi-objective optimization. OR Spectrum 45, 1333–1360 (2023). https://doi.org/10.1007/s00291-023-00727-x

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