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Multidimensional frontier visualization based on optimization methods using parallel computations

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Abstract

In data envelopment analysis, methods for constructing sections of the frontier have been recently proposed to visualize the production possibility set. The aim of this paper is to develop, prove and test the methods for the visualization of production possibility sets using parallel computations. In this paper, a general scheme of the algorithms for constructing sections (visualization) of production possibility set is proposed. In fact, the algorithm breaks the original large-scale problems into parallel threads, working independently, then the piecewise solution is combined into a global solution. An algorithm for constructing a generalized production function is described in detail.

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Acknowledgements

This work was supported by the Russian Science Foundation (Project No. 17-11-01353).

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Authors and Affiliations

  1. Centre for Distributed Computing, Institute for Information Transmission Problems, Russian Academy of Sciences, Nakhimovsky Prospekt 36-1, Moscow, Russia, 117218

    Alexander P. Afanasiev & Oleg V. Sukhoroslov

  2. National University of Science and Technology MISiS, Leninskiy Prospekt 4, Moscow, Russia, 119049

    Alexander P. Afanasiev, Vladimir E. Krivonozhko & Andrey V. Lychev

  3. Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, Russia, 119991

    Alexander P. Afanasiev & Vladimir E. Krivonozhko

  4. National Research University Higher School of Economics, Myasnitskaya str., 20, Moscow, Russia, 101000

    Alexander P. Afanasiev & Oleg V. Sukhoroslov

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

    Vladimir E. Krivonozhko

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  1. Alexander P. Afanasiev
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  2. Vladimir E. Krivonozhko
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  3. Andrey V. Lychev
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  4. Oleg V. Sukhoroslov
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Correspondence to Vladimir E. Krivonozhko.

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Afanasiev, A.P., Krivonozhko, V.E., Lychev, A.V. et al. Multidimensional frontier visualization based on optimization methods using parallel computations. J Glob Optim 76, 563–574 (2020). https://doi.org/10.1007/s10898-019-00812-y

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