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Linear programming solutions and distance functions under α-returns to scale

Author

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  • J-P Boussemart

    (University of Lille and LEM-IÉSEG School of Management)

  • W Briec

    (University of Perpignan)

  • H Leleu

    (CNRS-LEM and IÉSEG School of Management)

Abstract

This note generalizes analytical relationships among activity variables of Data envelopment analysis models previously derived in a previous article by the authors of this note. We relax the assumption of constant returns to scale by showing that the key results hold under a weaker assumption of homogeneity. We use the notion of α-returns to scale to extend the analysis to strictly increasing and decreasing returns, covering now the whole range of returns to scale for multi-output homogenous technologies.

Suggested Citation

  • J-P Boussemart & W Briec & H Leleu, 2010. "Linear programming solutions and distance functions under α-returns to scale," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1297-1301, August.
    • Handle: RePEc:pal:jorsoc:v:61:y:2010:i:8:d:10.1057_jors.2009.97
    DOI: 10.1057/jors.2009.97
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    References listed on IDEAS

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    1. Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1999. "Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit," European Journal of Operational Research, Elsevier, vol. 113(1), pages 206-214, February.
    2. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    3. R. Färe & S. Grosskopf & D. Njinkeu, 1988. "Note---On Piecewise Reference Technologies," Management Science, INFORMS, vol. 34(12), pages 1507-1511, December.
    4. J-P Boussemart & W Briec & H Leleu, 2009. "Linear programming solutions and distance functions under a constant returns to scale technology," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 72-78, January.
    5. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    6. Lau, Lawrence J., 1978. "Applications of Profit Functions," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.),Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 3, McMaster University Archive for the History of Economic Thought.
    7. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    8. Jean-Philippe Boussemart & Walter Briec & Nicolas Peypoch & Christophe Tavéra, 2009. "α-Returns to scale and multi-output production technologies," Post-Print halshs-00418883, HAL.
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    Citations

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    Cited by:

    1. Leleu, Hervé & Moises, James & Valdmanis, Vivian, 2012. "Optimal productive size of hospital's intensive care units," International Journal of Production Economics, Elsevier, vol. 136(2), pages 297-305.
    2. Jean-Philippe Boussemart & Walter Briec & Raluca Parvulescu & Paola Ravelojaona, 2022. "$\Lambda$-Returns to Scale and Individual Minimum Extrapolation Principle," Papers 2212.04724, arXiv.org, revised Dec 2023.
    3. Jean-Philippe Boussemart & Walter Briec & Hervé Leleu & Paola Ravelojaona, 2019. "On estimating optimal α-returns to scale," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(1), pages 1-11, January.
    4. Carlos P. Barros & Qi Bin Liang & Nicolas Peypoch, 2014. "Technical Efficiency in the Angolan Banking Sector with the B-convexity Model," South African Journal of Economics, Economic Society of South Africa, vol. 82(3), pages 443-454, September.
    5. Juan Aparicio & José L. Zofío, 2017. "Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach," Journal of Productivity Analysis, Springer, vol. 48(2), pages 133-146, December.

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