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Reducing Two-Stage Probabilistic Optimization Problems with Discrete Distribution of Random Data to Mixed-Integer Programming Problems*

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Cybernetics and Systems Analysis Aims and scope

Abstract

We consider two-stage stochastic programming models with quantile criterion as well as models with a probabilistic constraint on the random values of the objective function of the second stage. These models allow us to formalize the requirements for the reliability and safety of the system being optimized and to optimize system’s performance under extreme conditions. We propose a method of equivalent transformation of these models under discrete distribution of random parameters to mixed-integer programming problems. The number of additional integer (Boolean) variables in these problems equals to the number of possible values of the vector of random parameters. The obtained mixed optimization problems can be solved by powerful standard discrete optimization software. To illustrate the approach, the results of numerical experiment for the problem of small dimension are presented.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. I. Norkin

  2. Moscow Aviation Institute, Moscow, Russia

    A. I. Kibzun & A. V. Naumov

Authors
  1. V. I. Norkin
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  2. A. I. Kibzun
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  3. A. V. Naumov
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Corresponding author

Correspondence to V. I. Norkin.

Additional information

*The study was financially supported by the State Fund for Fundamental Research of Ukraine within the framework of the joint Russian-Ukrainian Project F40.1/016 (2011-2012) and the Russian Foundation for Basic Research (Projects 11-07-90407-Ukr-f-a, 11-07-00315-a) and was partially supported by the Norwegian–Ukrainian grant CPEALA-2012/10052.

Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2014, pp. 34–48.

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Norkin, V.I., Kibzun, A.I. & Naumov, A.V. Reducing Two-Stage Probabilistic Optimization Problems with Discrete Distribution of Random Data to Mixed-Integer Programming Problems* . Cybern Syst Anal 50, 679–692 (2014). https://doi.org/10.1007/s10559-014-9658-9

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  • DOI: https://doi.org/10.1007/s10559-014-9658-9

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