IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v76y2020i3d10.1007_s10898-019-00812-y.html
   My bibliography  Save this article

Multidimensional frontier visualization based on optimization methods using parallel computations

Author

Listed:
  • Alexander P. Afanasiev

    (Russian Academy of Sciences
    National University of Science and Technology MISiS
    Lomonosov Moscow State University
    National Research University Higher School of Economics)

  • Vladimir E. Krivonozhko

    (National University of Science and Technology MISiS
    Lomonosov Moscow State University
    Russian Academy of Sciences)

  • Andrey V. Lychev

    (National University of Science and Technology MISiS)

  • Oleg V. Sukhoroslov

    (Russian Academy of Sciences
    National Research University Higher School of Economics)

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.

Suggested Citation

  • Alexander P. Afanasiev & Vladimir E. Krivonozhko & Andrey V. Lychev & Oleg V. Sukhoroslov, 2020. "Multidimensional frontier visualization based on optimization methods using parallel computations," Journal of Global Optimization, Springer, vol. 76(3), pages 563-574, March.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:3:d:10.1007_s10898-019-00812-y
    DOI: 10.1007/s10898-019-00812-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-019-00812-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-019-00812-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    2. Alireza Amirteimoori & Sohrab Kordrostami, 2012. "A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies," Journal of Global Optimization, Springer, vol. 54(1), pages 117-128, September.
    3. V E Krivonozhko & O B Utkin & M M Safin & A V Lychev, 2009. "On some generalization of the DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1518-1527, November.
    4. V E Krivonozhko & O B Utkin & A V Volodin & I A Sablin, 2005. "About the structure of boundary points in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1373-1378, December.
    5. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    6. Finn Førsund & Lennart Hjalmarsson & Vladimir Krivonozhko & Oleg Utkin, 2007. "Calculation of scale elasticities in DEA models: direct and indirect approaches," Journal of Productivity Analysis, Springer, vol. 28(1), pages 45-56, October.
    7. Pitaktong, U. & Brockett, P. L. & Mote, J. R. & Rousseau, J. J., 1998. "Identification of Pareto-efficient facets in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 109(3), pages 559-570, September.
    8. Emrouznejad, Ali & Yang, Guo-liang, 2018. "A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 4-8.
    9. Richard Barr & Matthew Durchholz, 1997. "Parallel and hierarchical decomposition approaches for solving large-scale Data Envelopment Analysis models," Annals of Operations Research, Springer, vol. 73(0), pages 339-372, October.
    10. Yeboon Yun & Hirotaka Nakayama & Min Yoon, 2016. "Generation of Pareto optimal solutions using generalized DEA and PSO," Journal of Global Optimization, Springer, vol. 64(1), pages 49-61, January.
    11. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, October.
    12. Juan Aparicio & Jose J. Lopez-Espin & Raul Martinez-Moreno & Jesus T. Pastor, 2014. "Benchmarking in Data Envelopment Analysis: An Approach Based on Genetic Algorithms and Parallel Programming," Advances in Operations Research, Hindawi, vol. 2014, pages 1-9, February.
    13. V E Krivonozhko & O B Utkin & A V Volodin & I A Sablin & M Patrin, 2004. "Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1049-1058, October.
    14. J.H. Dulá & R.M. Thrall, 2001. "A Computational Framework for Accelerating DEA," Journal of Productivity Analysis, Springer, vol. 16(1), pages 63-78, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Svetlana Ratner & Andrey Lychev & Aleksei Rozhnov & Igor Lobanov, 2021. "Efficiency Evaluation of Regional Environmental Management Systems in Russia Using Data Envelopment Analysis," Mathematics, MDPI, vol. 9(18), pages 1-21, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Førsund, Finn & Krivonozhko, Vladimir W & Lychev, Andrey V., 2016. "Smoothing the frontier in the DEA models," Memorandum 11/2016, Oslo University, Department of Economics.
    2. Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2015. "Terminal units in DEA: definition and determination," Journal of Productivity Analysis, Springer, vol. 43(2), pages 151-164, April.
    3. Wen-Chih Chen & Sheng-Yung Lai, 2017. "Determining radial efficiency with a large data set by solving small-size linear programs," Annals of Operations Research, Springer, vol. 250(1), pages 147-166, March.
    4. Vladimir Krivonozhko & Finn Førsund & Andrey Lychev, 2012. "Returns-to-scale properties in DEA models: the fundamental role of interior points," Journal of Productivity Analysis, Springer, vol. 38(2), pages 121-130, October.
    5. Førsund, Finn R. & Kittelsen, Sverre A. & Krivonozhko, Vladimir E., 2007. "Farrell Revisited: Visualising the DEA Production Frontier," Memorandum 15/2007, Oslo University, Department of Economics.
    6. Vladimir E. Krivonozhko & Finn R. Førsund & Andrey V. Lychev, 2017. "On comparison of different sets of units used for improving the frontier in DEA models," Annals of Operations Research, Springer, vol. 250(1), pages 5-20, March.
    7. Krivonozhko, Vladimir E. & Førsund, Finn R. & Lychev, Andrey V., 2012. "Identifying Suspicious Efficient Units in DEA Models," Memorandum 30/2012, Oslo University, Department of Economics.
    8. Svetlana Ratner & Andrey Lychev & Aleksei Rozhnov & Igor Lobanov, 2021. "Efficiency Evaluation of Regional Environmental Management Systems in Russia Using Data Envelopment Analysis," Mathematics, MDPI, vol. 9(18), pages 1-21, September.
    9. Victor V. Podinovski & Finn R. Førsund, 2010. "Differential Characteristics of Efficient Frontiers in Data Envelopment Analysis," Operations Research, INFORMS, vol. 58(6), pages 1743-1754, December.
    10. Khezrimotlagh, Dariush & Zhu, Joe & Cook, Wade D. & Toloo, Mehdi, 2019. "Data envelopment analysis and big data," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1047-1054.
    11. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    12. Rafael Benítez & Vicente Coll-Serrano & Vicente J. Bolós, 2021. "deaR-Shiny: An Interactive Web App for Data Envelopment Analysis," Sustainability, MDPI, vol. 13(12), pages 1-19, June.
    13. Hahn, G.J. & Brandenburg, M. & Becker, J., 2021. "Valuing supply chain performance within and across manufacturing industries: A DEA-based approach," International Journal of Production Economics, Elsevier, vol. 240(C).
    14. Mahmood Mehdiloozad & Mohammad Bagher Ahmadi & Biresh K. Sahoo, 2017. "On classifying decision making units in DEA: a unified dominance-based model," Annals of Operations Research, Springer, vol. 250(1), pages 167-184, March.
    15. K. Tone & M. Tsutsui, 2015. "How to Deal with Non-Convex Frontiers in Data Envelopment Analysis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1002-1028, September.
    16. Mehdiloozad, Mahmood & Mirdehghan, S. Morteza & Sahoo, Biresh K. & Roshdi, Israfil, 2015. "On the identification of the global reference set in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(3), pages 779-788.
    17. Violeta Cvetkoska & Katerina Fotova Čiković & Marija Tasheva, 2021. "Efficiency of Commercial Banking in Developing Countries," Mathematics, MDPI, vol. 9(14), pages 1-21, July.
    18. Falavigna, G. & Ippoliti, R., 2020. "The socio-economic planning of a community nurses programme in mountain areas: A Directional Distance Function approach," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    19. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo, 2019. "Is Social Capital Green? Cultural Features and Environmental Performance in the European Union," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(3), pages 795-822, March.
    20. Fragoudaki, Alexandra & Giokas, Dimitrios, 2020. "Airport efficiency in the dawn of privatization: The case of Greece," Journal of Air Transport Management, Elsevier, vol. 86(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:76:y:2020:i:3:d:10.1007_s10898-019-00812-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.