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Input, output and graph technical efficiency measures on non-convex FDH models with various scaling laws: An integrated approach based upon implicit enumeration algorithms

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  • Walter Briec
  • Kristiaan Kerstens

Abstract

In a recent article, Briec, Kerstens and Vanden Eeckaut (2004) develop a series of nonparametric, deterministic non-convex technologies integrating traditional returns to scale assumptions into the non-convex FDH model. They show, among other things, how the traditional technical input efficiency measure can be analytically derived for these technology specifications. In this paper, we develop a similar approach to calculate output and graph measures of technical efficiency and indicate the general advantage of such solution strategy via enumeration. Furthermore, several analytical formulas are established and some algorithms are proposed relating the three measurement orientations to one another.
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Suggested Citation

  • Walter Briec & Kristiaan Kerstens, 2006. "Input, output and graph technical efficiency measures on non-convex FDH models with various scaling laws: An integrated approach based upon implicit enumeration algorithms," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 135-166, June.
    • Handle: RePEc:spr:topjnl:v:14:y:2006:i:1:p:135-166
    DOI: 10.1007/BF02579006
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    Cited by:

    1. Kerstens, Kristiaan & Sadeghi, Jafar & Toloo, Mehdi & Van de Woestyne, Ignace, 2022. "Procedures for ranking technical and cost efficient units: With a focus on nonconvexity," European Journal of Operational Research, Elsevier, vol. 300(1), pages 269-281.
    2. Kristiaan Kerstens & Ignace Van de Woestyne, 2018. "Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions," Annals of Operations Research, Springer, vol. 271(2), pages 1067-1078, December.
    3. Antonio Peyrache & Maria C. A. Silva, 2022. "A Comment on Decomposition of Efficiency in Network Production Models," CEPA Working Papers Series WP072022, School of Economics, University of Queensland, Australia.
    4. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    5. Antonio Peyrache, 2024. "A Homothetic and Additively Separable Production Frontier," CEPA Working Papers Series WP012024, School of Economics, University of Queensland, Australia.
    6. Tavakoli, Ibrahim M. & Mostafaee, Amin, 2019. "Free disposal hull efficiency scores of units with network structures," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1027-1036.
    7. Peyrache, Antonio & Silva, Maria C.A., 2024. "The decomposition of efficiency in parallel network production models," Omega, Elsevier, vol. 127(C).
    8. Antonio Peyrache, 2024. "Homothetic Data Generated Production Metatechnologies," CEPA Working Papers Series WP022024, School of Economics, University of Queensland, Australia.
    9. Antonio Peyrache, 2022. "A Homothetic Data Generated Technology," CEPA Working Papers Series WP042022, School of Economics, University of Queensland, Australia.
    10. Peyrache, Antonio, 2024. "A homothetic data generated technology," European Journal of Operational Research, Elsevier, vol. 316(1), pages 255-267.
    11. 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.
    12. Soleimani-damaneh, Majid & Mostafaee, Amin, 2015. "Identification of the anchor points in FDH models," European Journal of Operational Research, Elsevier, vol. 246(3), pages 936-943.

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