Annals of Operations Research

, Volume 275, Issue 2, pp 531–549 | Cite as

The role of hyperplanes for characterizing suspicious units in DEA

  • Amin Mostafaee
  • Sevan SohraieeEmail author
Original Research


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.


Data envelopment analysis Variable returns to scale technology Anchor units Terminal units Exterior units Separating hyperplane 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences, Tehran North BranchIslamic Azad UniversityTehranIran

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