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A New DEA Cross-Efficiency Method Based on Consensus

Received: 25 July 2022     Accepted: 22 September 2022     Published: 28 September 2022
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Abstract

Data Envelopment Analysis (DEA), as a non-parametric technique for evaluating the relative efficiencies of a set of homogenous decision-making units (DMUs) with multi-inputs and multi-outputs, is widely used in the performance evaluation field. This paper develops a new DEA cross-efficiency method based on consensus (CEC-DEA), which can be more reasonably and effectively in evaluating and ranking decision-making units (DMUs). In our proposed method, we firstly attempt to obtain the unique set of weights for each DMU through a second-objective model which can minimize the total variance between the self-evaluated efficiencies and the peer-evaluated efficiencies. Then, based on the acquired weights, the cross-efficiency scores of all DMUs are calculated. Before the cross-efficiency aggregation, we choose a DMU as the Common Reference Point (CRP) based on which all the cross-efficiency scores are rescaled to be comparable for the aggregation. In the aggregation stage, we define the Evaluation Consensus Degrees (ECDs) of all DMUs, which are used as the weights to aggregate the cross-efficiency scores through the weighted geometric mean method. Comprehensively, the proposed CEC-DEA method is developed to increase the rationality and acceptability of the evaluations for all DMUs. Finally, the a numerical example is illustrated to prove the effectiveness of the proposed method.

Published in International Journal of Mechanical Engineering and Applications (Volume 10, Issue 5)
DOI 10.11648/j.ijmea.20221005.13
Page(s) 113-122
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

DEA, Cross-Efficiency, Common Reference Point, Aggregation, Evaluation Consensus Degree

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Cite This Article
  • APA Style

    Xuepeng Liu, Qing Wang. (2022). A New DEA Cross-Efficiency Method Based on Consensus. International Journal of Mechanical Engineering and Applications, 10(5), 113-122. https://doi.org/10.11648/j.ijmea.20221005.13

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    ACS Style

    Xuepeng Liu; Qing Wang. A New DEA Cross-Efficiency Method Based on Consensus. Int. J. Mech. Eng. Appl. 2022, 10(5), 113-122. doi: 10.11648/j.ijmea.20221005.13

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    AMA Style

    Xuepeng Liu, Qing Wang. A New DEA Cross-Efficiency Method Based on Consensus. Int J Mech Eng Appl. 2022;10(5):113-122. doi: 10.11648/j.ijmea.20221005.13

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  • @article{10.11648/j.ijmea.20221005.13,
      author = {Xuepeng Liu and Qing Wang},
      title = {A New DEA Cross-Efficiency Method Based on Consensus},
      journal = {International Journal of Mechanical Engineering and Applications},
      volume = {10},
      number = {5},
      pages = {113-122},
      doi = {10.11648/j.ijmea.20221005.13},
      url = {https://doi.org/10.11648/j.ijmea.20221005.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20221005.13},
      abstract = {Data Envelopment Analysis (DEA), as a non-parametric technique for evaluating the relative efficiencies of a set of homogenous decision-making units (DMUs) with multi-inputs and multi-outputs, is widely used in the performance evaluation field. This paper develops a new DEA cross-efficiency method based on consensus (CEC-DEA), which can be more reasonably and effectively in evaluating and ranking decision-making units (DMUs). In our proposed method, we firstly attempt to obtain the unique set of weights for each DMU through a second-objective model which can minimize the total variance between the self-evaluated efficiencies and the peer-evaluated efficiencies. Then, based on the acquired weights, the cross-efficiency scores of all DMUs are calculated. Before the cross-efficiency aggregation, we choose a DMU as the Common Reference Point (CRP) based on which all the cross-efficiency scores are rescaled to be comparable for the aggregation. In the aggregation stage, we define the Evaluation Consensus Degrees (ECDs) of all DMUs, which are used as the weights to aggregate the cross-efficiency scores through the weighted geometric mean method. Comprehensively, the proposed CEC-DEA method is developed to increase the rationality and acceptability of the evaluations for all DMUs. Finally, the a numerical example is illustrated to prove the effectiveness of the proposed method.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - A New DEA Cross-Efficiency Method Based on Consensus
    AU  - Xuepeng Liu
    AU  - Qing Wang
    Y1  - 2022/09/28
    PY  - 2022
    N1  - https://doi.org/10.11648/j.ijmea.20221005.13
    DO  - 10.11648/j.ijmea.20221005.13
    T2  - International Journal of Mechanical Engineering and Applications
    JF  - International Journal of Mechanical Engineering and Applications
    JO  - International Journal of Mechanical Engineering and Applications
    SP  - 113
    EP  - 122
    PB  - Science Publishing Group
    SN  - 2330-0248
    UR  - https://doi.org/10.11648/j.ijmea.20221005.13
    AB  - Data Envelopment Analysis (DEA), as a non-parametric technique for evaluating the relative efficiencies of a set of homogenous decision-making units (DMUs) with multi-inputs and multi-outputs, is widely used in the performance evaluation field. This paper develops a new DEA cross-efficiency method based on consensus (CEC-DEA), which can be more reasonably and effectively in evaluating and ranking decision-making units (DMUs). In our proposed method, we firstly attempt to obtain the unique set of weights for each DMU through a second-objective model which can minimize the total variance between the self-evaluated efficiencies and the peer-evaluated efficiencies. Then, based on the acquired weights, the cross-efficiency scores of all DMUs are calculated. Before the cross-efficiency aggregation, we choose a DMU as the Common Reference Point (CRP) based on which all the cross-efficiency scores are rescaled to be comparable for the aggregation. In the aggregation stage, we define the Evaluation Consensus Degrees (ECDs) of all DMUs, which are used as the weights to aggregate the cross-efficiency scores through the weighted geometric mean method. Comprehensively, the proposed CEC-DEA method is developed to increase the rationality and acceptability of the evaluations for all DMUs. Finally, the a numerical example is illustrated to prove the effectiveness of the proposed method.
    VL  - 10
    IS  - 5
    ER  - 

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Author Information
  • School of Business, Tianjin University of Commerce, Tianjin City, China

  • School of Business, Tianjin University of Commerce, Tianjin City, China

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