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Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions

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  • Kristiaan Kerstens

    (Department of Economics - IESEG School of Managementg, LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • Ignace van de Woestyne

    (Department of Economics - IESEG School of Managementg)

Abstract

Computing directional distance functions for a free disposal hull (FDH) technology in general requires solving nonlinear mixed integer programs. Cherchye et al. (J Product Anal 15(3):201–215, 2001) provide an enumeration algorithm for the FDH directional distance function in case of a variable returns to scale technology. In this contribution, we provide fast enumeration algorithms for the FDH directional distance functions under constant, nonincreasing, and nondecreasing returns to scale assumptions. Consequently, enumeration algorithms are now available for all commonly used returns to scale assumptions.

Suggested Citation

  • Kristiaan Kerstens & Ignace van de Woestyne, 2018. "Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions," Post-Print hal-01733347, HAL.
    • Handle: RePEc:hal:journl:hal-01733347
    DOI: 10.1007/s10479-018-2791-5
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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. 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.
    3. François Mairesse & Philippe Vanden Eeckaut, 2002. "Museum Assessment and FDH Technology: Towards a Global Approach," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 26(4), pages 261-286, November.
    4. Afriat, Sidney N, 1972. "Efficiency Estimation of Production Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(3), pages 568-598, October.
    5. Per Agrell & Jørgen Tind, 2001. "A Dual Approach to Nonconvex Frontier Models," Journal of Productivity Analysis, Springer, vol. 16(2), pages 129-147, September.
    6. 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.
    7. Podinovski, V. V., 2004. "On the linearisation of reference technologies for testing returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 152(3), pages 800-802, February.
    8. Walter Briec & Kristiaan Kerstens & Philippe Venden Eeckaut, 2004. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, Springer, vol. 81(2), pages 155-192, February.
    9. Giovanni Cesaroni & Kristiaan Kerstens & Ignace Van de Woestyne, 2017. "A New Input-Oriented Plant Capacity Notion: Definition and Empirical Comparison," Pacific Economic Review, Wiley Blackwell, vol. 22(4), pages 720-739, October.
    10. Kevin Cullinane & Dong-Wook Song & Tengfei Wang, 2005. "The Application of Mathematical Programming Approaches to Estimating Container Port Production Efficiency," Journal of Productivity Analysis, Springer, vol. 24(1), pages 73-92, September.
    11. J. Cummins & Hongmin Zi, 1998. "Comparison of Frontier Efficiency Methods: An Application to the U.S. Life Insurance Industry," Journal of Productivity Analysis, Springer, vol. 10(2), pages 131-152, October.
    12. Green, R. H., 1996. "DIY DEA: Implementing data envelopment analysis in the mathematical programming language AMPL," Omega, Elsevier, vol. 24(4), pages 489-494, August.
    13. De Borger, Bruno & Kerstens, Kristiaan, 1996. "Cost efficiency of Belgian local governments: A comparative analysis of FDH, DEA, and econometric approaches," Regional Science and Urban Economics, Elsevier, vol. 26(2), pages 145-170, April.
    14. Henry Tulkens, 2006. "On FDH Efficiency Analysis: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 311-342, Springer.
    15. Fried, Harold O. & Knox Lovell, C. A. & Eeckaut, Philippe Vanden, 1993. "Evaluating the performance of US credit unions," Journal of Banking & Finance, Elsevier, vol. 17(2-3), pages 251-265, April.
    16. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    17. Balaguer-Coll, Maria Teresa & Prior, Diego & Tortosa-Ausina, Emili, 2007. "On the determinants of local government performance: A two-stage nonparametric approach," European Economic Review, Elsevier, vol. 51(2), pages 425-451, February.
    18. David J. Mayston, 2014. "Effectiveness analysis of quality achievements for university Departments of Economics," Applied Economics, Taylor & Francis Journals, vol. 46(31), pages 3788-3797, November.
    19. 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.
    20. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    21. Kerstens, Kristiaan & Van de Woestyne, Ignace, 2014. "Comparing Malmquist and Hicks–Moorsteen productivity indices: Exploring the impact of unbalanced vs. balanced panel data," European Journal of Operational Research, Elsevier, vol. 233(3), pages 749-758.
    22. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    23. H Leleu, 2009. "Mixing DEA and FDH models together," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1730-1737, December.
    24. Dominique Deprins & Léopold Simar & Henry Tulkens, 2006. "Measuring Labor-Efficiency in Post Offices," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 285-309, Springer.
    25. Kristof Witte & Rui Marques, 2011. "Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies," Journal of Productivity Analysis, Springer, vol. 35(3), pages 213-226, June.
    26. H. A. Eiselt & C. -L. Sandblom, 2007. "Linear Programming and its Applications," Springer Books, Springer, number 978-3-540-73671-4, September.
    27. Fare, Rolf & Grosskopf, Shawna & Zaim, Osman, 2002. "Hyperbolic efficiency and return to the dollar," European Journal of Operational Research, Elsevier, vol. 136(3), pages 671-679, February.
    28. Sergio Destefanis & Vania Sena, 2005. "Public capital and total factor productivity: New evidence from the Italian regions, 1970-98," Regional Studies, Taylor & Francis Journals, vol. 39(5), pages 603-617.
    29. Laurens Cherchye & Timo Kuosmanen & Thierry Post, 2001. "FDH Directional Distance Functions with an Application to European Commercial Banks," Journal of Productivity Analysis, Springer, vol. 15(3), pages 201-215, January.
    30. Alam, Ila M Semenick & Sickles, Robin C, 2000. "Time Series Analysis of Deregulatory Dynamics and Technical Efficiency: The Case of the U.S. Airline Industry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 203-218, February.
    31. K. Kerstens & S. Managi, 2012. "Total Factor Productivity Growth and Convergence in the Petroleum Industry: Empirical Analysis Testing for Convexity," Post-Print hal-00720616, HAL.
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    2. Xiao, Helu & Zhou, Zhongbao & Ren, Teng & Liu, Wenbin, 2022. "Estimation of portfolio efficiency in nonconvex settings: A free disposal hull estimator with non-increasing returns to scale," Omega, Elsevier, vol. 111(C).
    3. Ning Zhu & Xiang Dai & Tomas Baležentis & Dalia Streimikiene & Zhiyang Shen, 2022. "Estimating production gains from international cooperation: Evidence from countries along the Belt and Road," Economic Change and Restructuring, Springer, vol. 55(2), pages 715-736, May.
    4. Mehdiloo, Mahmood & Podinovski, Victor V., 2021. "Strong, weak and Farrell efficient frontiers of technologies satisfying different production assumptions," European Journal of Operational Research, Elsevier, vol. 294(1), pages 295-311.
    5. Peixin Duan, 2022. "How large of a grant size is appropriate? Evidence from the National Natural Science Foundation of China," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-14, February.
    6. 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.

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