A New DEA Cross-Efficiency Method Based on Consensus

Xuepeng Liu; Qing Wang

doi:doi:10.11648/j.ijmea.20221005.13

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A New DEA Cross-Efficiency Method Based on Consensus

Xuepeng Liu, Qing Wang

Published in International Journal of Mechanical Engineering and Applications (Volume 10, Issue 5)

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), 2024. Published by Science Publishing Group

Keywords

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

References

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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

Xuepeng Liu

School of Business, Tianjin University of Commerce, Tianjin City, China
Qing Wang

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

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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}
}

Copy | Download

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  -

Copy | Download