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Some Conditions for Characterizing Anchor Points

Author

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  • Amin Mostafaee

    (Department of Mathematics, College of Science, Tehran North Branch, Islamic Azad University, Tehran, Iran)

  • Majid Soleimani-Damaneh

    (School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Enghelab Avenue, Tehran, Iran)

Abstract

The set of anchor points is an important subset of the set of extreme efficient points of the production possibility set (PPS) in data envelopment analysis (DEA). In this paper, some new results, under variable returns to scale (VRS) assumption, are given which characterize these points from different points of view. First, we prove two necessary and sufficient conditions leading to geometrical characterizations. Afterwards, four sufficient conditions are given with respect to the level values of the supporting hyperplanes, infeasibility of the super efficiency models, maximum/minimum data, and zero data. Some of the given conditions can be checked without solving any mathematical programming problems. Also, some of them can be tested by solving standard DEA models. The investigated conditions are useful in designing pre-processors and heuristics.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:02:n:s0217595916500135
    DOI: 10.1142/S0217595916500135
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    References listed on IDEAS

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    Cited by:

    1. 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.

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