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Modelling and Data Analysis
2026. Vol. 16, no. 1, 87–104
doi:10.17759/mda.2026160106
ISSN: 2219-3758 / 2311-9454 (online)

Application of the Monte Carlo method to quantile optimization problems

 
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Abstract

Stochastic programming mathematical models are used in a wide range of problem settings that consider the influence of random factors of various natures. If a loss function dependent on strategy and random parameters is used to describe the system's operation, the value of the loss function becomes random. The quantile criterion utilizes the concept of a quantile function—the smallest value of the loss function that will not be exceeded with a probability no lower than a specified value. Thus, reliability is limited to an acceptable level, and the effectiveness of strategy implementation is optimized. The original problem can be reduced to a minimax problem, where the maximum is taken over the confidence set proposed to be optimized (the so-called confidence method). Using the confidence method, the original problem is approximated by a deterministic minimax problem parameterized by the radius of a sphere inscribed in the polyhedral confidence set. The author's previously proposed algorithm for solving a two-stage facility location problem with a quantile criterion and choice of reliability level has been generalized to the case of an arbitrary unimodal distribution of random parameters. The algorithm's features include the selection of a confidence set bounded by the probability density surface of the random variable. To construct this set, the Monte Carlo method is used to generate and label a random sample in combination with a support vector machine (SVM).

General Information

Keywords: confidence method, quantile criterion, stochastic programming, Monte Carlo method, support vector machine (SVM)

Journal rubric: Optimization Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2026160106

Received 16.02.2026

Revised 20.05.2026

Accepted

Published

For citation: Akmaeva, V.N. (2026). Application of the Monte Carlo method to quantile optimization problems. Modelling and Data Analysis, 16(1), 87–104. (In Russ.). https://doi.org/10.17759/mda.2026160106

© Akmaeva V.N., 2026

License: CC BY-NC 4.0

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Information About the Authors

Valentina N. Akmaeva, Senior Lecturer, Department 804 “Probability Theory and Computer Modeling”, Institute No. 8, Moscow Aviation Institute (national research university) (MAI), Moscow, Russian Federation, ORCID: https://orcid.org/0009-0007-6215-2295, e-mail: akmaevavalentina@yandex.ru

Conflict of interest

The authors declare no conflict of interest.

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