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A secondary goal in DEA cross-efficiency evaluation: A “one home run is much better than two doubles” criterion

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  • Mostafa Davtalab-Olyaie

Abstract

Data Envelopment Analysis (DEA) is a mathematical programming approach for assessing the relative efficiency of decision making units (DMUs). The cross-efficiency evaluation is an extension of DEA that provides a ranking method and eliminates unrealistic DEA weighting schemes on weight restrictions, without requiring a prior information. The cross-efficiency evaluation may have some shortages, e.g. the cross-efficiency scores may not be unique due to the presence of several optima. To rectify this issue, several secondary goals have been proposed in the literature. Some scholars have proposed several cross-efficiency evaluations based on maximising (minimising) the total deviation from their ideal point as an aggressive (benevolent) perspective. In some cases, minimising (maximising) the number of DMUs that achieve their target efficiencies, is more important than maximising (minimising) the total deviation from the ideal point. We propose some alternative models for the cross-efficiency evaluation based on the cardinality of the set of “satisfied DMUs”, i.e. the DMUs that achieve their maximum efficiencies. For aggressive (benevolent) cross-efficiency evaluation, among all the optimal weights for a specific unit, we choose the weights which can maximise its efficiency, and at the same time minimise (maximise) the number of satisfied units. We demonstrate how the proposed method can be implemented and illustrate the method using two examples.

Suggested Citation

  • Mostafa Davtalab-Olyaie, 2019. "A secondary goal in DEA cross-efficiency evaluation: A “one home run is much better than two doubles” criterion," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(5), pages 807-816, May.
    • Handle: RePEc:taf:tjorxx:v:70:y:2019:i:5:p:807-816
    DOI: 10.1080/01605682.2018.1457482
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    Cited by:

    1. Davtalab-Olyaie, Mostafa & Asgharian, Masoud, 2021. "On Pareto-optimality in the cross-efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 288(1), pages 247-257.
    2. Borrás, Fernando & Ruiz, José L. & Sirvent, Inmaculada, 2023. "Peer evaluation through cross-efficiency based on reference sets," Omega, Elsevier, vol. 114(C).
    3. Ebrahimi, Bohlool & Dhamotharan, Lalitha & Ghasemi, Mohammad Reza & Charles, Vincent, 2022. "A cross-inefficiency approach based on the deviation variables framework," Omega, Elsevier, vol. 111(C).
    4. Kao, Chiang & Liu, Shiang-Tai, 2020. "A slacks-based measure model for calculating cross efficiency in data envelopment analysis," Omega, Elsevier, vol. 95(C).
    5. Mostafa Davtalab-Olyaie & Hadis Mahmudi-Baram & Masoud Asgharian, 2023. "Measuring individual efficiency and unit influence in centrally managed systems," Annals of Operations Research, Springer, vol. 321(1), pages 139-164, February.
    6. Feng Li & Han Wu & Qingyuan Zhu & Liang Liang & Gang Kou, 2021. "Data envelopment analysis cross efficiency evaluation with reciprocal behaviors," Annals of Operations Research, Springer, vol. 302(1), pages 173-210, July.

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