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DEA cross-efficiency evaluation under variable returns to scale

Author

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  • Sungmook Lim

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

  • Joe Zhu

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

Abstract

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. Alcaraz, Javier & Aparicio, Juan & Monge, Juan Fco & Ramón, Nuria, 2022. "Weight profiles in cross-efficiency evaluation based on hypervolume maximization," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    2. Aparicio, Juan & Zofío, José L., 2021. "Economic cross-efficiency," Omega, Elsevier, vol. 100(C).
      • 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. 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.
    4. Minh-Hieu Le & Wen-Min Lu, 2024. "An integrated multiple objective decision making approach for exploring the competitiveness of pharmaceutical multinational enterprises," Annals of Operations Research, Springer, vol. 341(1), pages 401-426, October.
    5. 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, vol. 10(8), pages 1-27, August.
    6. Heydari, Chiman & Omrani, Hashem & Taghizadeh, Rahim, 2020. "A fully fuzzy network DEA-Range Adjusted Measure model for evaluating airlines efficiency: A case of Iran," Journal of Air Transport Management, Elsevier, vol. 89(C).
    7. 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.
    8. Geri L. Dimas & Malak El Khalkhali & Alex Bender & Kayse Lee Maass & Renata A. Konrad & Jeffrey S. Blom & Joe Zhu & Andrew C. Trapp, 2023. "Estimating Effectiveness of Identifying Human Trafficking via Data Envelopment Analysis," Interfaces, INFORMS, vol. 53(6), pages 408-424, November.
    9. Rolf Färe & Giannis Karagiannis, 2023. "Translation efficiency and directionally optimal scale," Journal of Economics, Springer, vol. 140(3), pages 259-273, December.
    10. 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).
    11. 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).
    12. Juan Aparicio & José L. Zofío, 2020. "New Definitions of Economic Cross-efficiency," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor & Joe Zhu (ed.), Advances in Efficiency and Productivity II, pages 11-32, Springer.
    13. 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.
    14. 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.
    15. 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).
    16. Andreas Dellnitz & Elmar Reucher & Andreas Kleine, 2021. "Efficiency evaluation in data envelopment analysis using strong defining hyperplanes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 441-465, June.
    17. 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.
    18. Kao, Chiang & Liu, Shiang-Tai, 2020. "A slacks-based measure model for calculating cross efficiency in data envelopment analysis," Omega, Elsevier, vol. 95(C).
    19. Tao Chen & Muhammad Rizwan & Azhar Abbas, 2022. "Exploring the Role of Agricultural Services in Production Efficiency in Chinese Agriculture: A Case of the Socialized Agricultural Service System," Land, MDPI, vol. 11(3), pages 1-18, February.
    20. Sweksha Srivastava & Abha Aggarwal & Pooja Bansal, 2024. "Efficiency Evaluation of Assets and Optimal Portfolio Generation by Cross Efficiency and Cumulative Prospect Theory," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 129-158, January.

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