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On some relations between several generalized convex DEA models

Author

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  • Louisa Andriamasy

    (UEVE - Université d'Évry-Val-d'Essonne, LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations - UPVD - Université de Perpignan Via Domitia)

  • Walter Briec

    (LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations - UPVD - Université de Perpignan Via Domitia)

  • Stéphane Mussard

    (CHROME - Détection, évaluation, gestion des risques CHROniques et éMErgents (CHROME) - Université de Nîmes - UNIMES - Nîmes Université)

Abstract

The purpose of this paper is to establish a topological relation between several known production models, precisely a link between -convex and Cobb–Douglas production models. The framework is based on the algebraic structures of the technology sets, issued from data envelopment, respecting either the assumption of constant elasticity of substitution and transformation (CES–CET) or -returns to scale. It is shown that the Painlevé–Kuratowski limit of the CES–CET technology provides either -convex or inverse -convex technologies. Also, -returns to scale models have topological limits relevant with constant return to scale -convex (or inverse -convex) technologies.

Suggested Citation

  • Louisa Andriamasy & Walter Briec & Stéphane Mussard, 2017. "On some relations between several generalized convex DEA models," Post-Print hal-01781483, HAL.
    • Handle: RePEc:hal:journl:hal-01781483
    DOI: 10.1080/02331934.2017.1279159
    Note: View the original document on HAL open archive server: https://hal.science/hal-01781483v1
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    References listed on IDEAS

    as
    1. Podinovski, V. V., 2005. "Selective convexity in DEA models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 552-563, March.
    2. Post, Thierry, 2001. "Transconcave data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 132(2), pages 374-389, July.
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    Cited by:

    1. Walter Briec & Marc Dubois & Stéphane Mussard, 2021. "Technical efficiency in firm games with constant returns to scale and $$\alpha $$ α -returns to scale," Annals of Operations Research, Springer, vol. 304(1), pages 35-62, September.
    2. Ravelojaona, Paola, 2019. "On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions," European Journal of Operational Research, Elsevier, vol. 272(2), pages 780-791.
    3. Briec, Walter & Mussard, Stéphane, 2020. "Improvement of technical efficiency of firm groups," European Journal of Operational Research, Elsevier, vol. 283(3), pages 991-1001.
    4. Walter Briec & Laurent Cavaignac & Kristiaan Kerstens, 2020. "Input Efficiency Measures: A Generalized, Encompassing Formulation," Operations Research, INFORMS, vol. 68(6), pages 1836-1849, November.

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    More about this item

    Keywords

    Non-parametric production models; Painlevé–Kuratowski limit; lattice; CES–CET model; generalized convexity; alpha-returns to scale;
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