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DEA Cross Efficiency Under Variable Returns to Scale

In: Data Envelopment Analysis

Author

Listed:
  • Sungmook Lim

    (Dongguk Business School, Dongguk University—Seoul)

  • Joe Zhu

    (School of Business, Worcester Polytechnic Institute)

Abstract

While cross-efficiency evaluation has been used in a wide variety of DEA applications due to its attractive mechanism, so has it been for DEA models mostly with constant returns to scale (CRS) assumption. This is due to the fact that negative VRS cross-efficiency arises for some 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. This chapter introduces a recent development of DEA cross-efficiency evaluation approach under VRS, which is motivated by the observation that cross-efficiency evaluation is closely related to the issue of incorporation of weight restrictions and that negative VRS cross-efficiency is related to free production of outputs. The new approach is based upon a geometric interpretation of the relationship between the CRS and VRS DEA models that the VRS model can be cast as a series of CRS models under translated Cartesian coordinate systems. We illustrate this approach using a simple example and show how the VRS negative cross-efficiency problem is addressed under the new framework.

Suggested Citation

  • Sungmook Lim & Joe Zhu, 2015. "DEA Cross Efficiency Under Variable Returns to Scale," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 3, pages 45-66, Springer.
    • Handle: RePEc:spr:isochp:978-1-4899-7553-9_3
    DOI: 10.1007/978-1-4899-7553-9_3
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    Citations

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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. 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).
    3. Meng, Fanyong & Xiong, Beibei, 2021. "Logical efficiency decomposition for general two-stage systems in view of cross efficiency," European Journal of Operational Research, Elsevier, vol. 294(2), pages 622-632.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Kao, Chiang & Liu, Shiang-Tai, 2020. "A slacks-based measure model for calculating cross efficiency in data envelopment analysis," Omega, Elsevier, vol. 95(C).
    9. 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).
    10. Afsharian, Mohsen & Bogetoft, Peter, 2023. "Limiting flexibility in nonparametric efficiency evaluations: An ex post k-centroid clustering approach," European Journal of Operational Research, Elsevier, vol. 311(2), pages 633-647.
    11. 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.
    12. 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.
    13. 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).
    14. 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.
    15. 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.
    16. Balk, B.M. & de Koster, M.B.M. & Kaps, C. & Zofío, J.L., 2017. "An Evaluation of Cross-Efficiency Methods, Applied to Measuring Warehouse Performance," ERIM Report Series Research in Management ERS-2017-015-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.
    17. 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).
    18. 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.
    19. 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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