Technique for optimizing the adaptive control of the output of an enterprise based on a dynamical economic and mathematical model

Occupation: Leading Researcher, Center for Structural Policy, Institute of Economics, the Ural Branch of the Russian Academy of Sciences
Affiliation: Institute of Economics, the Ural Branch of the RAS
Address: Ekaterinburg, Russian Federation

Journal name

Ekonomika i matematicheskie metody

Edition

Volume 58 Issue 4

Pages

102-112

Abstract

The article is devoted to the application of dynamic economic and mathematical models for managing the production of an enterprise based on the use of the feedback principle. Formation of a discrete controllable dynamical system is given, which describes the process of production output by a manufacturing enterprise in the presence of a predictable demand function for products. The phase vector of a dynamical system describes the main parameters of production, and the control action vector (control vector) describes the intensity of the use of technological methods of production that are available to the subject of control. It is assumed that in each period of time the subject of control knows the vector function that describes the volume of demand for the company's products in subsequent periods of time, and the given geometric restrictions on the implementation of the phase vector, control vector and demand vector are also known. As the target function of the problem, the value of the discrepancy between the volumes of output by the enterprise relative to the given predicted value of the demand function in the subsequent control period is considered. Using the generated dynamical system, the paper proposes an economic-mathematical model of the studied problem of optimizing the adaptive control of the enterprise's output, which includes a class of admissible strategies for adaptive control and the formulation of the problem. The paper proposes a method for solving the formulated problem of optimizing the adaptive control of the output of an enterprise, which is implemented as a finite sequence of one-step algebraic operations on vectors of a finite-dimensional vector space, a finite set of solutions to problems of linear and convex mathematical programming. The results obtained can be used in the development of intelligent decision support systems for the actual tasks of managing the production of products at industrial enterprises.

Keywords

economic and mathematical modeling, dynamical systems, control optimization, control strategies, adaptive control, manufacturing enterprise, enterprise output

Acknowledgment

The work was carried out with financial support by the Russian Science Foundation (Project No. 22-28-01868 "Development of an agent-based model of the network industrial complex in the context of digital transformation").

Received

13.03.2022

Publication date

07.12.2022

Number of characters

26522

Cite

GOST	Shorikov A. Technique for optimizing the adaptive control of the output of an enterprise based on a dynamical economic and mathematical model // Ekonomika i matematicheskie metody – 2022. – V. 58. – Issue 4 C. 102-112 [Electronic resource]. URL: https://emm.jes.su/S042473880019196-4-1 (circulation date: 24.04.2024). DOI: 10.31857/S042473880019197-5
MLA	Shorikov, Andrey "Technique for optimizing the adaptive control of the output of an enterprise based on a dynamical economic and mathematical model." Ekonomika i matematicheskie metody 58.4 (2022):102-112. DOI: 10.31857/S042473880019197-5
APA	Shorikov A. (2022). Technique for optimizing the adaptive control of the output of an enterprise based on a dynamical economic and mathematical model. Ekonomika i matematicheskie metody 58(4), pp.102-112 DOI: 10.31857/S042473880019197-5

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1. Kleiner G. B., Rybachuk M. A. (2017). Systemic balance of the economy. Moscow: Nauchnaja biblioteka (in Russian).

2. Makarov V. L., Bakhtizin A. R., Beklaryan G. L., Akopov A. S. (2021). Digital plant: Methods of discrete-event modeling and optimization of production characteristics. Business Informatics, 15, 2, 7–20. DOI: 10.17323/2587-814X.2021.2.7.20 (in Russian).

3. Tyulyukin V. A., Shorikov A. F. (1988). On algorithm for constructing the reachability sets of linear control system. In: Non-smooth optimization problems and control. Sverdlovsk: UB AS USSR, 55–61 (in Russian).

4. Chernikov S. N. (1968). Linear Inequalities. Moscow: Nauka (in Russian).

5. Shorikov A. F. (1997). Minimax estimation and control in discrete-time dynamical systems. Ekaterinburg: Publishing House Ural State University (in Russian).

6. Shorikov A. F. (2006). Methodology for modeling multilevel systems: Hierarchy and dynamics. Applied Informatics, 1, 1, 136–141 (in Russian).

7. Aksyonov K., Bykov E., Aksyonova O., Goncharova N., Nevolina A. (2015). Analysis of simulation modeling systems illustrated with the problem of model design for the subject of technological logistics (WIP). Society for Modeling & Simulation International (SCS). Summer Simulation Multi-Conference (SummerSim’15). Chicago, USA. 26–29 July, 2015. Simulation Series, 47, 10, 345–348.

8. Astolfi A. (2006). Nonlinear and adaptive control: Tools and algorithms for the user. London: Imperial College Press.

9. Astroem K. J., Wittenmark B. (2008). Adaptive control. 2nd ed. N.Y.: Dover Publ., Inc.

10. Bazaraa M. S., Shetty C. M. (1979). Nonlinear programming: Theory and algorithms. 2nd ed. N.Y.: Wiley.

11. Cheng W., Xiao-Bing L. (2013). Integrated production planning and control: A multi-objective optimization model. Journal of Industrial Engineering and Management, 6, 4, 815–830.

12. David S. A., Oliveira C., Derick D., Quintino D. D. (2012). Dynamic model for planning and business optimization. Modern Economy, 3, 4, 384–391. DOI: 10.4236/me.2012.34049

13. Landau I. D., Lozano R., M’Saad M., Karimi A. (2011). Adaptive control: Algorithms, analysis and applications. London: Springer.

14. Margineanu C., Lixndroiu D. (2021). Optimization of industrial management processes. IOP Conf. Ser.: Mater. Sci. Eng, 1009, 012039, 1–9.

15. Olanrele O. O., Olaiya K. A., Aderonmu M. A., Adegbayo O. O., Sanusi B. Y. (2014). Development of a dynamic programming model for optimizing production planning. International Journal of Management Technology, 2, 3, 12–17.

16. Szopa R., Marczyk B. (2011). Optimization of production problems using mathematical programming. Polish Journal of Management Studies, 4, 231–238.

17. Tyulyukin V. A., Shorikov A. F. (1993). Algorithm for solving terminal control problems for a linear discrete system. Automation and Remote Control, 4, 115–127.

18. Zhang Q., Chen Yu., Lin W., Chen Ya. (2021). Optimizing medical enterprise’s operations management considering corporate social responsibility under industry 5.0. Article ID9298166, 1–13. DOI: 10.1155/2021/9298166

19. Wagner H. M., Whitin T. M. (2004). Dynamic version of the economic lot size model. Management Science, 50, 12, 1770–1774.