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Solution Methods For Nonconvex Free Disposal Hull Models: A Review And Some Critical Comments

Author

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  • KRISTIAAN KERSTENS

    (CNRS-LEM (UMR 8179), IESEG School of Management, 3 rue de la Digue, F-59000 Lille, France)

  • IGNACE VAN DE WOESTYNE

    (KU Leuven, Research Unit MEES, Warmoesberg 26, B-1000 Brussels, Belgium)

Abstract

This note first succinctly summarizes the currently available methods to solve the various nonconvex free disposal hull (FDH) models for technical efficiency as well as for minimum costs. It also offers some empirical illustration as to their computational efficiency. Second, this note briefly points out that the recent article by (26) and its correction by (4) proposing an extended enumeration method to solve for technical efficiency evaluated relative to this family of FDH models contain no original results.

Suggested Citation

  • Kristiaan Kerstens & Ignace Van De Woestyne, 2014. "Solution Methods For Nonconvex Free Disposal Hull Models: A Review And Some Critical Comments," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-13.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:01:n:s0217595914500109
    DOI: 10.1142/S0217595914500109
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    Cited by:

    1. 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.
    2. Branda, Martin, 2015. "Diversification-consistent data envelopment analysis based on directional-distance measures," Omega, Elsevier, vol. 52(C), pages 65-76.
    3. 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.
    4. Frederic Ang & Kristiaan Kerstens & Jafar Sadeghi, 2023. "Energy productivity and greenhouse gas emission intensity in Dutch dairy farms: A Hicks–Moorsteen by‐production approach under non‐convexity and convexity with equivalence results," Journal of Agricultural Economics, Wiley Blackwell, vol. 74(2), pages 492-509, June.
    5. Cesaroni, Giovanni & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2017. "Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration," European Journal of Operational Research, Elsevier, vol. 259(2), pages 576-586.
    6. 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.
    7. 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.
    8. Kerstens, Kristiaan & Sadeghi, Jafar & Van de Woestyne, Ignace, 2019. "Convex and nonconvex input-oriented technical and economic capacity measures: An empirical comparison," European Journal of Operational Research, Elsevier, vol. 276(2), pages 699-709.
    9. Xiaoqing Chen & Kristiaan Kerstens & Qingyuan Zhu, 2021. "Exploring Horizontal Mergers in Swedish District Courts Using Convex and Nonconvex Technologies: Usefulness of a Conservative Approach," Working Papers 2021-EQM-05, IESEG School of Management.
    10. Fukuyama, Hirofumi & Shiraz, Rashed Khanjani, 2015. "Cost-effectiveness measures on convex and nonconvex technologies," European Journal of Operational Research, Elsevier, vol. 246(1), pages 307-319.
    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. Wang, Yizhong & Jeong, Sujong & Hang, Ye & Wang, Qunwei, 2024. "Multi-sector environmental efficiency and productivity: A general Leontief optimization method," Omega, Elsevier, vol. 126(C).

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    Keywords

    Free disposal hull; enumeration method;

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