Optimization Letters

, Volume 13, Issue 8, pp 1871–1884 | Cite as

Measuring the smoothness of the DEA frontier

  • Vladimir E. KrivonozhkoEmail author
  • Finn R. Førsund
  • Andrey V. Lychev
Original Paper


Computational experiments with DEA models show that many inefficient units are projected onto the weakly efficient parts of the frontier when efficiency scores are computed. This fact disagrees with the main concept of the DEA approach, since efficiency scores of inefficient units have to be measured relative to efficient units. As a result, inaccurate efficiency scores may be obtained. In our previous work, we developed an algorithm for smoothing the frontier based on using the notion of terminal units. Moreover, it turned out that the smoothness of the frontier can be measured. For this reason, we introduced the notion of a smoothing factor in order to measure the smoothness of the frontier. This factor has to satisfy the following principles: (a) it does not depend on units of variables measurement in DEA models; (b) increased smoothness corresponds to smaller value of the smoothing factor. Our theoretical results are confirmed by computational experiments using a real-life data set.


Data envelopment analysis (DEA) Efficient frontier Terminal units Anchor units Smoothing factor 



This work was supported by the Russian Science Foundation (Project No. 17-11-01353). The authors thank two anonymous referees for their valuable comments.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National University of Science and Technology MISiSMoscowRussia
  2. 2.Department of EconomicsUniversity of OsloBlindernNorway
  3. 3.Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia

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