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Characterizing and finding full dimensional efficient facets in DEA: a variable returns to scale specification

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  • Mostafa Davtalab Olyaie

    (Kharazmi University, Tehran, Iran)

  • Israfil Roshdi

    (Islamic Azad University, Semnan, Iran)

  • Gholamreza Jahanshahloo

    (Kharazmi University, Tehran, Iran)

  • Masoud Asgharian

    (McGill University, Montreal, Canada)

Abstract

The full dimensional efficient facets (FDEFs) of a production possibility set (PPS) play a key role in data envelopment analysis (DEA). Finding the FDEFs has been the subject of intensive research over the past decade. The available algorithms for finding the FDEFs in the current DEA literature either require information about the position of all the extreme efficient decision-making units on the facets of the PPS or knowledge of all extreme optimal solutions of the multiplier form of the BCC model. In this article, we develop an algorithm that does not require such crucial information that may not be easily available. To this purpose, we first carefully analyse the structure of the FDEFs of PPS with BCC technology, using basic concepts of polyhedral set theory. We then utilize this information to devise an algorithm for finding the FDEFs, using mixed integer linear programming. We illustrate our algorithm using a set of real data.

Suggested Citation

  • Mostafa Davtalab Olyaie & Israfil Roshdi & Gholamreza Jahanshahloo & Masoud Asgharian, 2014. "Characterizing and finding full dimensional efficient facets in DEA: a variable returns to scale specification," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(9), pages 1453-1464, September.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:9:p:1453-1464
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    Cited by:

    1. K Hervé Dakpo & Philippe Jeanneaux & Laure Latruffe & Claire Mosnier & Patrick Veysset, 2018. "Three decades of productivity change in French beef production: a Färe‐Primont index decomposition," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 62(3), pages 352-372, July.
    2. Panagiotis Ravanos & Giannis Karagiannis, 2022. "In search for the most preferred solution in value efficiency analysis," Journal of Productivity Analysis, Springer, vol. 58(2), pages 203-220, December.
    3. Andreas Dellnitz & Elmar Reucher & Andreas Kleine, 2021. "Efficiency evaluation in data envelopment analysis using strong defining hyperplanes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 441-465, June.
    4. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2020. "Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA," Omega, Elsevier, vol. 92(C).
    5. Mehdiloozad, Mahmood & Mirdehghan, S. Morteza & Sahoo, Biresh K. & Roshdi, Israfil, 2015. "On the identification of the global reference set in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(3), pages 779-788.
    6. Mostafa Davtalab-Olyaie & Hadis Mahmudi-Baram & Masoud Asgharian, 2023. "Measuring individual efficiency and unit influence in centrally managed systems," Annals of Operations Research, Springer, vol. 321(1), pages 139-164, February.
    7. Dakpo, K Herve & Jeanneaux, Philippe & Latruffe, Laure & Mosnier, Claire & Veysset, Patrick, 2018. "Three decades of productivity change in French beef production: a F€are-Primont index decomposition," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 62(3), July.
    8. Panagiotis Ravanos & Giannis Karagiannis, 2022. "In search for the Most Preferred Solution in Value Efficiency Analysis," Discussion Paper Series 2022_05, Department of Economics, University of Macedonia, revised Jul 2022.
    9. Hasannasab, Maryam & Margaritis, Dimitris & Roshdi, Israfil & Rouse, Paul, 2019. "Hyperbolic efficiency measurement: A conic programming approach," European Journal of Operational Research, Elsevier, vol. 278(2), pages 401-409.
    10. Ando, Kazutoshi & Minamide, Masato & Sekitani, Kazuyuki & Shi, Jianming, 2017. "Monotonicity of minimum distance inefficiency measures for Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 260(1), pages 232-243.
    11. Kao, Chiang & Liu, Shiang-Tai, 2020. "A slacks-based measure model for calculating cross efficiency in data envelopment analysis," Omega, Elsevier, vol. 95(C).

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