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Local and global returns to scale in performance measurement

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  • V V Podinovski

    (University of Warwick)

Abstract

In data envelopment analysis, the type of local returns to scale (RTS) exhibited by a technically efficient unit indicates whether an increase or reduction of the scale of operations could improve the productivity of the unit. One of the approaches to testing RTS is based on the comparison of the efficiency of the unit in specially constructed reference technologies. It has been suggested that this approach is equally suitable for convex and non-convex, including the free disposal hull, technologies. In this paper, we construct examples that show that this suggestion in the case of non-convex technologies is not correct. We show that the type of RTS obtained by this approach is not a local, but global, characteristic of the technology, as it indicates the direction to the most productive scale size of the unit. In non-convex technologies, the local and global classifications of RTS are generally different.

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  • V V Podinovski, 2004. "Local and global returns to scale in performance measurement," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 170-178, February.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:2:d:10.1057_palgrave.jors.2601680
    DOI: 10.1057/palgrave.jors.2601680
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    Citations

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    Cited by:

    1. Kristiaan Kerstens & Ignace Van de Woestyne, 2021. "Cost functions are nonconvex in the outputs when the technology is nonconvex: convexification is not harmless," Annals of Operations Research, Springer, vol. 305(1), pages 81-106, October.
    2. Gitto, Simone & Mancuso, Paolo, 2010. "Airport efficiency: a DEA two stage analysis of the Italian commercial airports," MPRA Paper 34366, University Library of Munich, Germany, revised 10 Oct 2010.
    3. Walheer, Barnabé, 2018. "Aggregation of metafrontier technology gap ratios: the case of European sectors in 1995–2015," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1013-1026.
    4. Subhash C. Ray, 2014. "Data Envelopment Analysis: An Overview," Working papers 2014-33, University of Connecticut, Department of Economics.
    5. K. Tone & M. Tsutsui, 2015. "How to Deal with Non-Convex Frontiers in Data Envelopment Analysis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1002-1028, September.
    6. Leleu, Herve, 2006. "A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models," European Journal of Operational Research, Elsevier, vol. 168(2), pages 340-344, January.
    7. Kaoru Tone & Miki Tsutsui, 2013. "How to deal with S-shaped curve in DEA," GRIPS Discussion Papers 13-10, National Graduate Institute for Policy Studies.
    8. Laurens Cherchye & Bram De Rock & Veerle Hennebel, 2017. "Coordination efficiency in multi-output settings: a DEA approach," Annals of Operations Research, Springer, vol. 250(1), pages 205-233, March.
    9. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs," Annals of Operations Research, Springer, vol. 318(1), pages 383-423, November.
    10. Hennebel, Veerle & Simper, Richard & Verschelde, Marijn, 2017. "Is there a prison size dilemma? An empirical analysis of output-specific economies of scale," European Journal of Operational Research, Elsevier, vol. 262(1), pages 306-321.
    11. Dellnitz, Andreas & Tavana, Madjid, 2024. "Data envelopment analysis: From non-monotonic to monotonic scale elasticities," European Journal of Operational Research, Elsevier, vol. 318(2), pages 549-559.
    12. Podinovski, Victor V., 2017. "Returns to scale in convex production technologies," European Journal of Operational Research, Elsevier, vol. 258(3), pages 970-982.
    13. Emrouznejad, Ali & De Witte, Kristof, 2010. "COOPER-framework: A unified process for non-parametric projects," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1573-1586, December.
    14. Subhash C. Ray, 2010. "A One-Step Procedure for Returns to Scale Classification of Decision Making Units in Data Envelopment Analysis," Working papers 2010-07, University of Connecticut, Department of Economics.
    15. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2019. "Cone extensions of polyhedral production technologies," European Journal of Operational Research, Elsevier, vol. 276(2), pages 736-743.
    16. Mahmood Mehdiloo & Jafar Sadeghi & Kristiaan Kerstens, 2024. "Top Down Axiomatic Modeling of Metatechnologies and Evaluating Directional Economic Efficiency," Working Papers 2024-EQM-03, IESEG School of Management.
    17. 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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