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Measuring the smoothness of the DEA frontier

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. National University of Science and Technology MISiS, Leninsky prs. 4, Moscow, Russia, 119049

    Vladimir E. Krivonozhko & Andrey V. Lychev

  2. Department of Economics, University of Oslo, 0317, Blindern, Norway

    Finn R. Førsund

  3. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilov st. 44-2, Moscow, Russia, 119333

    Vladimir E. Krivonozhko

Authors
  1. Vladimir E. Krivonozhko
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  2. Finn R. Førsund
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  3. Andrey V. Lychev
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Correspondence to Vladimir E. Krivonozhko.

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Krivonozhko, V.E., Førsund, F.R. & Lychev, A.V. Measuring the smoothness of the DEA frontier. Optim Lett 13, 1871–1884 (2019). https://doi.org/10.1007/s11590-018-1329-8

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