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Data envelopment analysis cross efficiency evaluation with reciprocal behaviors

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Abstract

Data envelopment analysis (DEA) has proven to be a powerful technique for performance evaluation since its inception. Since the traditional DEA approaches lack discrimination power among efficient decision-making units (DMUs), the cross efficiency method has been proposed for peer appraisal in the literature. However, the previous cross efficiency approaches imposed a single and identical evaluation strategy across all DMUs simultaneously. In addition, all the related studies have considered a static issue without the dynamic alternation of evaluation strategies. In this paper, the reciprocal behaviors among DMUs are considered to address the cross efficiency evaluation, and a novel threshold value is used to determine positive or negative reciprocal behaviors by comparing the peer-evaluated efficiency with the threshold value based efficiency. This study assumes that a DMU would show positive behavior and apply a benevolent strategy toward other DMUs that evaluate it friendly, while it also shows negative behavior and apply an aggressive strategy toward DMUs that evaluate it hostilely. Furthermore, a game-like iteration process is developed for each DMU to determine and further adjust its evaluation strategy toward other DMUs in the evaluation process. Afterward, we calculate the optimal ultimate cross efficiency score with reciprocal behaviors. Finally, the proposed approach is applied to both a numerical example and an empirical study of 31 Chinese manufacturing industries to demonstrate its usefulness and efficacy.

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Acknowledgements

The authors would like to thank the editor and three anonymous reviewers for their kind work and insightful comments and suggestions for improving this paper. An earlier version of this paper entitled “DEA cross-efficiency model with reciprocal behavior” was presented at the INFORMS 2018 Annual Meeting in Phoenix, Arizona, USA, during November 4–7, 2018. This research was financially supported by the National Natural Science Foundation of China (Nos. 71901178, 71904084, 71910107002 and 71725001), the Sichuan Provincial Social Science Foundation (No. SC20C052), the Natural Science Foundation for Jiangsu Province (No. BK20190427) and the Social Science Foundation of Jiangsu Province (No. 19GLC017).

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  1. School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130, Sichuan Province, China

    Feng Li, Han Wu & Gang Kou

  2. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, Jiangsu Province, China

    Qingyuan Zhu

  3. Research Centre for Soft Energy Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, Jiangsu Province, China

    Qingyuan Zhu

  4. School of Management, Hefei University of Technology, Hefei, 230009, Anhui Province, China

    Liang Liang

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Li, F., Wu, H., Zhu, Q. et al. Data envelopment analysis cross efficiency evaluation with reciprocal behaviors. Ann Oper Res 302, 173–210 (2021). https://doi.org/10.1007/s10479-021-04027-x

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