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Returns to Scale in DEA

In: Handbook on Data Envelopment Analysis

Author

Listed:
  • Rajiv D. Banker

    (Temple University)

  • William W. Cooper

    (University of Texas at Austin)

  • Lawrence M. Seiford

    (University of Michigan at Ann Arbor)

  • Joe Zhu

    (Worcester Polytechnic Institute)

Abstract

This chapter discusses returns to scale (RTS) in data envelopment analysis (DEA). The BCC and CCR models described in Chap. 1 of this handbook are treated in input-oriented forms, while the multiplicative model is treated in output-oriented form. (This distinction is not pertinent for the additive model, which simultaneously maximizes outputs and minimizes inputs in the sense of a vector optimization.) Quantitative estimates in the form of scale elasticities are treated in the context of multiplicative models, but the bulk of the discussion is confined to qualitative characterizations such as whether RTS is identified as increasing, decreasing, or constant. This is discussed for each type of model, and relations between the results for the different models are established. The opening section describes and delimits approaches to be examined. The concluding section outlines further opportunities for research and an Appendix discusses other approaches in DEA treatment of RTS.

Suggested Citation

  • Rajiv D. Banker & William W. Cooper & Lawrence M. Seiford & Joe Zhu, 2011. "Returns to Scale in DEA," International Series in Operations Research & Management Science, in: William W. Cooper & Lawrence M. Seiford & Joe Zhu (ed.), Handbook on Data Envelopment Analysis, chapter 0, pages 41-70, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-6151-8_2
    DOI: 10.1007/978-1-4419-6151-8_2
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    Cited by:

    1. Matthias Klumpp & Dominic Loske, 2021. "Sustainability and Resilience Revisited: Impact of Information Technology Disruptions on Empirical Retail Logistics Efficiency," Sustainability, MDPI, vol. 13(10), pages 1-20, May.
    2. Dalina Dumitrescu & Ionela Costica & Liliana Nicoleta Simionescu & Stefan Cristian Gherghina, 2020. "DEA Approach Towards Exploring the Sustainability of Funding in Higher Education. Empirical Evidence from Romanian Public Universities," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 22(54), pages 593-593, April.
    3. Ströhl, Florian & Borsch, Erik & Souren, Rainer, 2018. "Integration von Gewichtsrestriktionen in das DEA-Modell nach Charnes, Cooper und Rhodes: Exemplarische Optionen und Auswirkungen," Ilmenauer Schriften zur Betriebswirtschaftslehre, Technische Universität Ilmenau, Institut für Betriebswirtschaftslehre, volume 3, number 32018.
    4. Basso, Antonella & Funari, Stefania, 2014. "Constant and variable returns to scale DEA models for socially responsible investment funds," European Journal of Operational Research, Elsevier, vol. 235(3), pages 775-783.
    5. Maryna Tverdostup & Tiiu Paas, 2019. "Economic Performance Analysis Of Selected Blue Economy Sectors In Estonia And Finland," University of Tartu - Faculty of Economics and Business Administration Working Paper Series 115, Faculty of Economics and Business Administration, University of Tartu (Estonia).
    6. Mehdiloo, Mahmood & Podinovski, Victor V., 2019. "Selective strong and weak disposability in efficiency analysis," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1154-1169.
    7. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    8. Podinovski, Victor V., 2019. "Direct estimation of marginal characteristics of nonparametric production frontiers in the presence of undesirable outputs," European Journal of Operational Research, Elsevier, vol. 279(1), pages 258-276.
    9. Konstantinos Petridis & Alexander Chatzigeorgiou & Emmanouil Stiakakis, 2016. "A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units," Annals of Operations Research, Springer, vol. 238(1), pages 475-496, March.
    10. Ricardo Ocaña-Riola & Carmen Pérez-Romero & Mª Isabel Ortega-Díaz & José Jesús Martín-Martín, 2021. "Multilevel Zero-One Inflated Beta Regression Model for the Analysis of the Relationship between Exogenous Health Variables and Technical Efficiency in the Spanish National Health System Hospitals," IJERPH, MDPI, vol. 18(19), pages 1-18, September.
    11. Antonella Basso & Stefania Funari, 2017. "The role of fund size in the performance of mutual funds assessed with DEA models," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 457-473, May.
    12. Loske, Dominic & Klumpp, Matthias, 2021. "Human-AI collaboration in route planning: An empirical efficiency-based analysis in retail logistics," International Journal of Production Economics, Elsevier, vol. 241(C).
    13. Victor V. Podinovski & Robert G. Chambers & Kazim Baris Atici & Iryna D. Deineko, 2016. "Marginal Values and Returns to Scale for Nonparametric Production Frontiers," Operations Research, INFORMS, vol. 64(1), pages 236-250, February.
    14. Konstantinos Petridis & Alexander Chatzigeorgiou & Emmanouil Stiakakis, 2016. "A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units," Annals of Operations Research, Springer, vol. 238(1), pages 475-496, March.
    15. Peixin Duan, 2022. "How large of a grant size is appropriate? Evidence from the National Natural Science Foundation of China," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-14, February.
    16. Masci, Chiara & De Witte, Kristof & Agasisti, Tommaso, 2018. "The influence of school size, principal characteristics and school management practices on educational performance: An efficiency analysis of Italian students attending middle schools," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 52-69.
    17. Seda Busra Sarac & Kazim Baris Atici & Aydin Ulucan, 2022. "Elasticity measurement on multiple levels of DEA frontiers: an application to agriculture," Journal of Productivity Analysis, Springer, vol. 57(3), pages 313-324, June.
    18. Barnabé Walheer, 2020. "Output, input, and undesirable output interconnections in data envelopment analysis: convexity and returns-to-scale," Annals of Operations Research, Springer, vol. 284(1), pages 447-467, January.

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