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DEA cross-efficiency evaluation under variable returns to scale


  • Sungmook Lim

    (Dongguk Business School, Dongguk University, Seoul, South Korea)

  • Joe Zhu

    (Dongguk Business School, Dongguk University, Seoul, South Korea)


Cross-efficiency evaluation in data envelopment analysis (DEA) has been developed under the assumption of constant returns to scale (CRS), and no valid attempts have been made to apply the cross-efficiency concept to the variable returns to scale (VRS) condition. This is due to the fact that negative VRS cross-efficiency arises for some decision-making units (DMUs). Since there exist many instances that require the use of the VRS DEA model, it is imperative to develop cross-efficiency measures under VRS. We show that negative VRS cross-efficiency is related to free production of outputs. We offer a geometric interpretation of the relationship between the CRS and VRS DEA models. We show that each DMU, via solving the VRS model, seeks an optimal bundle of weights with which its CRS-efficiency score, measured under a translated Cartesian coordinate system, is maximized. We propose that VRS cross-efficiency evaluation should be done via a series of CRS models under translated Cartesian coordinate systems. The current study offers a valid cross-efficiency approach under the assumption of VRS—one of the most common assumptions in performance evaluation done by DEA.

Suggested Citation

  • Sungmook Lim & Joe Zhu, 2015. "DEA cross-efficiency evaluation under variable returns to scale," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(3), pages 476-487, March.
  • Handle: RePEc:pal:jorsoc:v:66:y:2015:i:3:p:476-487

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    Cited by:

    1. Pastor, Jesus T. & Aparicio, Juan & Alcaraz, Javier & Vidal, Fernando & Pastor, Diego, 2015. "An enhanced BAM for unbounded or partially bounded CRS additive models," Omega, Elsevier, vol. 56(C), pages 16-24.
    2. Aparicio, J. & Zofío, J.L., 2019. "Economic Cross-Efficiency," ERIM Report Series Research in Management ERS-2019-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Fei Ma & Fei Liu & Qipeng Sun & Wenlin Wang & Xiaodan Li, 2018. "Measuring and Spatio-Temporal Evolution for the Late-Development Advantage in China’s Provinces," Sustainability, MDPI, Open Access Journal, vol. 10(8), pages 1-27, August.
    4. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2020. "Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA," Omega, Elsevier, vol. 92(C).
    5. Giannis Karagiannis & Georgia Paschalidou, 2017. "Assessing research effectiveness: a comparison of alternative nonparametric models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 456-468, April.
    6. 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.

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