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The closest strong efficient targets in the FDH technology: an enumeration method

Author

Listed:
  • J. Vakili

    (University of Tabriz)

  • R. Sadighi Dizaji

    (University of Tabriz)

Abstract

This paper is concerned with the identification of the closest strong efficient target of a Decision Making Unit (DMU) in the Free Disposal Hull (FDH) technology in Data Envelopment Analysis (DEA). The paper uses the geometrical properties of the FDH Production Possibility Set (PPS) to design and test an enumeration algorithm to obtain the minimum distance from a DMU to the strong efficient frontier of the PPS, corresponding to each of the various returns to scale assumptions. The proposed method solves some simple optimization problems whose optimal solutions are obtained by calculating a limited number of ratios. Then, an attempt will be made to mitigate the problem of the lack of unit and translation invariance of the selected distances by considering weighted norms. Finally, the applicability of the presented method is illustrated by a numerical example using real data.

Suggested Citation

  • J. Vakili & R. Sadighi Dizaji, 2021. "The closest strong efficient targets in the FDH technology: an enumeration method," Journal of Productivity Analysis, Springer, vol. 55(2), pages 91-105, April.
    • Handle: RePEc:kap:jproda:v:55:y:2021:i:2:d:10.1007_s11123-020-00594-6
    DOI: 10.1007/s11123-020-00594-6
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    References listed on IDEAS

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    1. G. R. Jahanshahloo & J. Vakili & S. M. Mirdehghan, 2012. "USING THE MINIMUM DISTANCE OF DMUs FROM THE FRONTIER OF THE PPS FOR EVALUATING GROUP PERFORMANCE OF DMUs IN DEA," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(02), pages 1-25.
    2. 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.
    3. G. R. Jahanshahloo & J. Vakili & M. Zarepisheh, 2012. "A Linear Bilevel Programming Problem For Obtaining The Closest Targets And Minimum Distance Of A Unit From The Strong Efficient Frontier," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(02), pages 1-19.
    4. Tone, Kaoru & Sahoo, Biresh K., 2003. "Scale, indivisibilities and production function in data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 84(2), pages 165-192, May.
    5. 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.
    6. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    7. Ila Alam & Robin Sickles, 1998. "The Relationship Between Stock Market Returns and Technical Efficiency Innovations: Evidence from the US Airline Industry," Journal of Productivity Analysis, Springer, vol. 9(1), pages 35-51, January.
    8. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    9. M C A Silva Portela & E Thanassoulis & G Simpson, 2004. "Negative data in DEA: a directional distance approach applied to bank branches," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1111-1121, October.
    10. Cherchye, Laurens & Van Puyenbroeck, Tom, 2001. "Product mixes as objects of choice in non-parametric efficiency measurement," European Journal of Operational Research, Elsevier, vol. 132(2), pages 287-295, July.
    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. 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.
    13. Frances Frei & Patrick Harker, 1999. "Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA," Journal of Productivity Analysis, Springer, vol. 11(3), pages 275-300, June.
    14. repec:adr:anecst:y:1999:i:55-56:p:19 is not listed on IDEAS
    15. Gonzalez, Eduardo & Alvarez, Antonio, 2001. "From efficiency measurement to efficiency improvement: The choice of a relevant benchmark," European Journal of Operational Research, Elsevier, vol. 133(3), pages 512-520, September.
    16. Niels Christian Petersen, 1990. "Data Envelopment Analysis on a Relaxed Set of Assumptions," Management Science, INFORMS, vol. 36(3), pages 305-314, March.
    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. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
    19. Sergio Destefanis, 2002. "The Verdoorn Law: Some Evidence from Non-Parametric Frontier Analysis," Palgrave Macmillan Books, in: John McCombie & Maurizio Pugno & Bruno Soro (ed.), Productivity Growth and Economic Performance, chapter 6, pages 136-164, Palgrave Macmillan.
    20. 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.
    21. J. Vakili, 2017. "New Models for Computing the Distance of DMUs to the Weak Efficient Boundary of Convex and Nonconvex PPSs in DEA," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-20, December.
    22. W. Briec & J. B. Lesourd, 1999. "Metric Distance Function and Profit: Some Duality Results," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 15-33, April.
    23. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    24. Yair Mundlak & Donald F. Larson & Rita Butzer, 1999. "Rethinking Within and Between Regressions: The Case of Agricultural Production Functions," Annals of Economics and Statistics, GENES, issue 55-56, pages 475-501.
    25. Fukuyama, Hirofumi & Maeda, Yasunobu & Sekitani, Kazuyuki & Shi, Jianming, 2014. "Input–output substitutability and strongly monotonic p-norm least distance DEA measures," European Journal of Operational Research, Elsevier, vol. 237(3), pages 997-1007.
    26. Sergio Destefanis & Giuseppe Storti, 2002. "Measuring cross-country technological catch-up through variable-parameter FDH," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(1), pages 109-125, February.
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