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The role of hyperplanes for characterizing suspicious units in DEA

Author

Listed:
  • Amin Mostafaee

    (Islamic Azad University)

  • Sevan Sohraiee

    (Islamic Azad University)

Abstract

In this paper, the suspicious units including anchor, terminal, and exterior units are investigated as important subsets of vertex units. Based on the concept of separating hyperplanes, an alternative definition of vertex units in data envelopment analysis is presented. Moreover, an advanced mathematical model for obtaining the separating hyperplane that splits up a vertex unit from the other units is proposed. Utilizing the core concept of separating hyperplanes, the special geometry of terminal units enables us to introduce a new definition for terminal units. Thus, some theorems have been proved which provide necessary and sufficient conditions for obtaining terminal units. We made use of the concept of supporting hyperplanes to provide a basic definition for exterior units and present a careful model for discovering exterior units. Also, based on the concept of supporting hyperplanes, different definitions of anchor units have been represented. Finally, the relationship between the sets of exterior, terminal and anchor units have been demonstrated in a theorem.

Suggested Citation

  • Amin Mostafaee & Sevan Sohraiee, 2019. "The role of hyperplanes for characterizing suspicious units in DEA," Annals of Operations Research, Springer, vol. 275(2), pages 531-549, April.
    • Handle: RePEc:spr:annopr:v:275:y:2019:i:2:d:10.1007_s10479-018-2997-6
    DOI: 10.1007/s10479-018-2997-6
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    References listed on IDEAS

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    1. Amin Mostafaee & Majid Soleimani-Damaneh, 2016. "Some Conditions for Characterizing Anchor Points," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(02), pages 1-17, April.
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    3. Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2015. "Terminal units in DEA: definition and determination," Journal of Productivity Analysis, Springer, vol. 43(2), pages 151-164, April.
    4. 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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    10. Mostafaee, A. & Soleimani-damaneh, M., 2014. "Identifying the anchor points in DEA using sensitivity analysis in linear programming," European Journal of Operational Research, Elsevier, vol. 237(1), pages 383-388.
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