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Variable neighborhood search for stochastic linear programming problem with quantile criterion

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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.

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Acknowledgements

The second author’s work has been supported by the Ministry of Education and Science of the Russian Federation (State Assignment 2.2461.2017/4.6). The third author’s work is partially covered by the framework of the Grant No. BR05236839 “Development of information technologies and systems for stimulation of personality’s sustainable development as one of the bases of development of digital Kazakhstan”.

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Authors and Affiliations

  1. Department of Probability Theory and Computer Modeling, Moscow Aviation Institute (National Research University), Volokolamskoe shosse 4, A-80, GSP-3, Moscow, Russia, 125993

    Sergey V. Ivanov & Andrey I. Kibzun

  2. Emirates College of Technologies, P.O. Box 15551, Al Ain, Abu Dhabi, United Arab Emirates

    Nenad Mladenović

  3. Ural Federal University, 19 Mira Street, Ekaterinburg, Russia, 620002

    Nenad Mladenović

  4. Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36/III, Belgrade, 11001, Serbia

    Dragan Urošević

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  1. Sergey V. Ivanov
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  2. Andrey I. Kibzun
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  3. Nenad Mladenović
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  4. Dragan Urošević
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Correspondence to Sergey V. Ivanov.

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Ivanov, S.V., Kibzun, A.I., Mladenović, N. et al. Variable neighborhood search for stochastic linear programming problem with quantile criterion. J Glob Optim 74, 549–564 (2019). https://doi.org/10.1007/s10898-019-00773-2

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  • DOI: https://doi.org/10.1007/s10898-019-00773-2

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