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Variable neighborhood search for stochastic linear programming problem with quantile criterion

Author

Listed:
  • Sergey V. Ivanov

    (Moscow Aviation Institute (National Research University))

  • Andrey I. Kibzun

    (Moscow Aviation Institute (National Research University))

  • Nenad Mladenović

    (Emirates College of Technologies
    Ural Federal University)

  • Dragan Urošević

    (Serbian Academy of Sciences and Arts)

Abstract

We consider the stochastic linear programming problem with quantile criterion and continuous distribution of random parameters. Using the sample approximation, we obtain a stochastic programming problem with discrete distribution of random parameters. It is known that the solution to this problem provides an approximate solution to the problem with continuous random parameters if the size of the sample is large enough. Applying the confidence method, we reduce the problem to a mixed integer programming problem, which is linear with respect to continuous variables. Integer variables determine confidence sets, and we describe the structure of the optimal confidence set. This property allows us to take into account only confidence sets that may be optimal. To find an approximate solution to the problem, we suggest a modification of the variable neighborhood search and determine structures of neighborhoods used in the search. Also, we discuss a method to find a good initial solution and give results of numerical experiments. We apply the developed algorithm to solve a problem of optimization of a hospital budget.

Suggested Citation

  • Sergey V. Ivanov & Andrey I. Kibzun & Nenad Mladenović & Dragan Urošević, 2019. "Variable neighborhood search for stochastic linear programming problem with quantile criterion," Journal of Global Optimization, Springer, vol. 74(3), pages 549-564, July.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-019-00773-2
    DOI: 10.1007/s10898-019-00773-2
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    References listed on IDEAS

    as
    1. Peter Kall & János Mayer, 2011. "Stochastic Linear Programming," International Series in Operations Research and Management Science, Springer, edition 2, number 978-1-4419-7729-8, December.
    2. B. K. Pagnoncelli & S. Ahmed & A. Shapiro, 2009. "Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 399-416, August.
    3. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    4. Edward P. C. Kao & Maurice Queyranne, 1985. "Budgeting Costs of Nursing in a Hospital," Management Science, INFORMS, vol. 31(5), pages 608-621, May.
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    Cited by:

    1. Vesna Radonjić Ɖogatović & Marko Ɖogatović & Milorad Stanojević & Nenad Mladenović, 2020. "Revenue maximization of Internet of things provider using variable neighbourhood search," Journal of Global Optimization, Springer, vol. 78(2), pages 375-396, October.

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