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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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. 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.
    11. 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.
    12. 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.
    13. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, July.
    14. 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.
    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. 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.
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    10. F R Førsund & S A C Kittelsen & V E Krivonozhko, 2009. "Farrell revisited–Visualizing properties of DEA production frontiers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1535-1545, November.
    11. José Solana‐Ibáñez & Manuel Caravaca‐Garratón & Ricardo Teruel‐Sánchez, 2020. "Stakeholder perception on corporate reputation and management efficiency: Evidence from the Spanish Defence sector," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 27(5), pages 2381-2399, September.
    12. 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.
    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. 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.
    15. Mehdiloo, Mahmood & Podinovski, Victor V., 2021. "Strong, weak and Farrell efficient frontiers of technologies satisfying different production assumptions," European Journal of Operational Research, Elsevier, vol. 294(1), pages 295-311.
    16. Ioannis E. Tsolas, 2021. "Firm Credit Scoring: A Series Two-Stage DEA Bootstrapped Approach," JRFM, MDPI, vol. 14(5), pages 1-12, May.
    17. Zelenyuk, Valentin, 2020. "Aggregation of inputs and outputs prior to Data Envelopment Analysis under big data," European Journal of Operational Research, Elsevier, vol. 282(1), pages 172-187.
    18. 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.
    19. 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.
    20. 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).

    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.