NUMERICAL CALCULATION ALGORITHM FOR EFFECTIVE RESOURCE ALLOCATION IN AN OPEN ECONOMIC SYSTEM

One of the pressing issues in the field of economic process automation is the complexity of finding an analytical solution to optimal control problems in nonlinear economic models. This is due to complex interdependencies between variables, constraints on resource allocation, and external influences. In such conditions, traditional analytical methods become ineffective, requiring the application of numerical algorithms. This paper presents a numerical algorithm for optimal resource allocation in an open economic system. The method is based on the use of Lagrange multipliers and the golden section method to determine the stationary state of the system under labor and investment resource constraints. The proposed approach automates computational processes and ensures high calculation accuracy. The mathematical package Maple was used to implement the algorithm. The paper discusses the features of the algorithm’s software implementation and provides numerical experiments demonstrating its stability and accuracy. The developed algorithm can be applied in resource management information systems, automated planning, and decision-making systems in enterprises. It enables modeling of economic processes and forecasting optimal resource allocation trajectories considering external factors. The obtained results confirm the effectiveness of the approach for automation and information technologies in economic analysis and management.

1. Moradikashkooli A. An efficient optimization algorithm for nonlinear 2D fractional optimal control problems / A. Moradikashkooli, H. Haj Seyyed Javadi, S. Jabbehdari // J Supercomput. – 2024. – Vol. 80 – Р. 7906-7930. https://doi.org/10.1007/s11227-023-05732-z.

2. Mohamed A.W. A novel differential evolution algorithm for solving constrained engineering optimization problems / A.W. Mohamed // J Intell Manuf. – 2018. – Vol. 29. – Р. 659-692. https://doi.org/10.1007/s10845-017-1294-6.

3. Mohamed A.W. Adaptive guided differential evolution algorithm with novel mutation for numerical optimization / A.W. Mohamed, A.K. Mohamed // Int. J. Mach. Learn. & Cyber. – 2019. – Vol. 10. – Р. 253-277. https://doi.org/10.1007/s13042-017-0711-7.

4. Mukesh K.R. А novel hybrid approach for computing numerical solution of the time-fractional nonlinear one and two-dimensional partial integro-differential equation / K.R. Mukesh, K.V. Amit, C. Carlo // Communications in Nonlinear Science and Numerical Simulation. – 2023. – Vol.118. – Р. 106986. https://doi.org/10.1016/j.cnsns.2022.106986.

5. Dehghan R.A numerical solution of variable order fractional functional differential equation based on the shifted Legendre polynomials / R. Dehghan // SeMA. – 2019. – Vol. 76. – Р. 217-226. https://doi.org/10.1007/s40324-018-0173-1.

6. Farzaneh S. A numerical approach for solving a class of two-dimensional variable-order fractional optimal control problems using Gegenbauer operational matrix / S. Farzaneh, S. Fahimeh, M. Kamal // IMA Journal of Mathematical Control and Information. – 2023. – Vol. 40(1). – Р. 1-19. https://doi.org/10.1093/imamci/dnac031.

7. Software Engineering for Optimal Control Problems / А. Gornov et al // MANCS. – 2021. – Vol. 424. – H. 416-426.

8. Framework of Decision Support System for Effective Resource Management / I.N. Muhammad et al // Dubai, United Arab Emirates. – 2023. – Р. 1-7. https://doi.org/10.1109/ICBATS57792.2023.10111307.

9. Murzabekov Z.N. Solution of steady state search problem in three-sector economic model of a cluster / Z.N. Murzabekov, M. Milosz, K.B. Tussupova // Actual Problems of Economics. – 2015. – Vol. 165(3). – Р. 443-452.

10. Development of an algorithm for solving the problem of optimal control on a finite interval for a nonlinear system of a three-sector economic cluster / Z. Murzabekov et al // Eastern-European Journal of Enterprise Technologies. – 2022. – Vol. 1(3-115). – Р. 43-52. https://doi.org/10.15587/1729-4061.2022.252866.

11. Murzabekov Z. The optimal control problem with fixed-end trajectories for a three-sector economic model of a cluster / Z. Murzabekov, M. Milosz, К. Tussupova // ACIIDS, 2018, Dong Hoi City, Vietnam. – 2018. – Vol.10751 LNAI. – Р. 382-391. https://doi.org/10.1007/978-3-319-75417-8_36

12. Problems of Optimal Control for a Class of Linear and Nonlinear Systems of the Economic Model of a Cluster / Z. Murzabekov et al // Vietnam Journal of Computer Science. – 2020. – Vol.7(2). – Р. 109-127. https://doi.org/10.1142/S2196888820500062.

13. Murzabekov З. Development of a model of efficient resource allocation in an open three-sector economy for balanced growth / З. Murzabekov, К. Tussupova // Journal of Mathematics, Mechanics and Computer Science. – 2025. – № 124(4). – Р. 59-70. https://doi.org/10.26577/JMMCS2024-v124-i4-a5.