Vestnik КRAUNC. Fiz.-Mat. Nauki. 2025. vol. 51. no. 2. P. 73 – 84. ISSN 2079-6641

MATHEMATICAL MODELING
https://doi.org/10.26117/2079-6641-2025-51-2-73-84
Research Article
Full text in Russian
MSC 90C05, 49M37

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The Existence Theorem for a Solution to the Problem of Optimal Control of the Customs Clearance Process

J. O. Takhirov^{\ast}, T. T. Abdurakhmonov, A. A. Saidov

V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 100174, Tashkent, University street, 9, Uzbekistan

Abstract. The article examines the issue of modeling the process of customs clearance of foreign trade goods. A mathematical model for managing the considered process has been developed in the form of linear programming with variable coefficients in the objective function. The multi-stage nature of the customs clearance process for foreign trade goods is justified, as well as the necessity of using the customs risk function as coefficients in the objective function of the linear programming problem. The stages of the customs clearance process for foreign trade goods have been formed, and the customs risks associated with these stages have been identified. An analysis has been conducted of methods for solving the linear programming problem with variable coefficients in the objective function, such as the parametric programming method, the piecewise constant functions method, the differential transform method, the interval conditions method, the “small parameter” method, and others. It has been proven that it is impossible to solve the optimal control problem of the customs clearance process using the aforementioned methods. Problematic issues in solving similar problems are discussed, and directions for further research are proposed. A theorem on the existence of a solution to the optimal control problem of the customs clearance process has been proven. As a result, the optimal control problem of the customs clearance process is reduced to the problem of minimizing customs risks.

Key words: customs clearance, mathematical modeling, linear optimization, objective function with variable coefficient, customs risks.

Received: 25.05.2025; Revised: 19.06.2025; Accepted: 28.08.2025; First online: 17.09.2025

For citation. Takhirov J. O., Abdurakhmonov T. T., Saidov A. A. The existence theorem for a solution to the problem of optimal control of the customs clearance process. Vestnik KRAUNC. Fiz.-mat. nauki. 2025, 51: 2, 73-84. EDN: VGLGFD. https://doi.org/10.26117/2079-6641-2025-51-2-73-84.

Funding. The work was carried out without the support of funds.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^{\ast}Correspondence: E-mail: prof.takhirov@yahoo.com

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Takhirov J. O., Abdurakhmonov T. T., Saidov A. A., 2025

© Institute of Cosmophysical Research and Radio Wave Propagation, 2025 (original layout, design, compilation)

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Takhirov Jozil Ostanovich – DSc. (Phy. & Math.), Professor, Head of the Laboratory of Mathematical Modeling of Nonlinear Systems, V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan, ORCID 0000-0002-0023-5673.

Abdurakhmonov Tokhir Tokhtasinovich – PhD student, V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan, ORCID 0000-0002-4611-3831

Saidov Abdusobir Abdurakhmonovich – DSc. (Tech.), Professor, Leading researcher at the Laboratory of Mathematical Modeling of Nonlinear Systems, V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan, ORCID 0000-0003-3596-7468.

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