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DEA Cobb–Douglas frontier and cross-efficiency

Author

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  • W D Cook

    (Schulich School of Business, York University, Toronto, Canada)

  • J Zhu

    (School of Business, Worcester Polytechnic Institute, Worcester, USA)

Abstract

The current paper examines the cross-efficiency concept in data envelopment analysis (DEA). While cross-efficiency has appeal as a peer evaluation approach, it is often the subject of criticism, due mainly to the use of DEA weights that are often non-unique. As a result, cross-efficiency scores are routinely viewed as arbitrary in that they depend on a particular set of optimal DEA weights generated by the computer code in use at the time. While imposing secondary goals can reduce the variability of cross-efficiency scores, such approaches do not completely solve the problem of non-uniqueness, and meaningful secondary goals can lead to computationally intractable non-linear programs. The current paper proposes to use the units-invariant multiplicative DEA model to calculate the cross-efficiency scores. This allows one to calculate the maximum cross-efficiency score for each DMU in a converted linear model, and eliminates the need for imposing secondary goals.

Suggested Citation

  • W D Cook & J Zhu, 2014. "DEA Cobb–Douglas frontier and cross-efficiency," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(2), pages 265-268, February.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:2:p:265-268
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    Citations

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    Cited by:

    1. Liquan Guo & Zhongzhen Yang, 2019. "Relationship Between Shipping Accessibility and Maritime Transport Demand: the Case of Mainland China," Networks and Spatial Economics, Springer, vol. 19(1), pages 149-175, March.
    2. Qiang Hou & Meiou Wang & Xue Zhou, 2018. "Improved DEA Cross Efficiency Evaluation Method Based on Ideal and Anti-Ideal Points," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, April.
    3. Balk, Bert M. & (René) De Koster, M.B.M. & Kaps, Christian & Zofío, José L., 2021. "An evaluation of cross-efficiency methods: With an application to warehouse performance," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    4. Hamid Kiaei & Reza Farzipoor Saen & Reza Kazemi Matin, 2023. "Cross-efficiency evaluation and improvement in two-stage network data envelopment analysis," Annals of Operations Research, Springer, vol. 321(1), pages 281-309, February.
    5. Qingxian An & Fanyong Meng & Beibei Xiong, 2018. "Interval cross efficiency for fully ranking decision making units using DEA/AHP approach," Annals of Operations Research, Springer, vol. 271(2), pages 297-317, December.
    6. Ghasemi, Mohammad Reza & Ignatius, Joshua & Rezaee, Babak, 2019. "Improving discriminating power in data envelopment models based on deviation variables framework," European Journal of Operational Research, Elsevier, vol. 278(2), pages 442-447.
    7. Jie Wu & Junfei Chu & Qingyuan Zhu & Pengzhen Yin & Liang Liang, 2016. "DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 5990-6007, October.

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