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The main problem in the microelectronic components production management is the lack of effective decision-making methods with account for the goals, priorities, risks, capabilities and limitations of production. In this work, a mathematical model describing the decision making in the management of microelectronic components production is presented. The production process is represented by an algebraic system consisting of descriptions of production process states and cause-and-effect relations between them. As an alternative for decision making, production process states were used that are available for transition from current state with account for links defined in algebraic system. State transition option selection criterion is maximal time of staying in stationary mode of microelectronic components production management with required characteristics. In addition, the production process was represented as a Markov process, which allows the application of a probabilistic approach to describing its behavior using Kolmogorov differential equations. The study of possible transitions between the states has made it possible to form trajectories accelerating the decision making and adapting the developed mathematical model for use in intelligent production management systems. The mathematical model based on Kolmogorov differential equations allows obtaining not only the probability distribution of processes as a function of time, but also the distribution of the duration of stay in various states in stationary phase. The results obtained contribute to the development of effective and high-quality solutions at all levels of microelectronic component production control.
  • Key words: production management, Markov processes, Kolmogorov equations, probabilistic approach
  • Published in: INFORMATION-COMMUNICATION TECHNOLOGIES
  • Bibliography link: Shevnina Yu. S., Gagarina L. G., Tsarapkin S. F., Semenov M. Yu., Minakov E. I., Portnov E. M. A decision-making model in microelectronics production management based on Markov processes and Kolmogorov equations. Izv. vuzov. Elektronika = Proc. Univ. Electronics. 2025;30(6):754–762. (In Russ.). https://doi.org/10.24151/1561-5405-2025-30-6-754-762.
  • Financial source: the work has been supported by the the Russian Science Foundation (project no. 24-29-00530).
Yulia S. Shevnina
National Research University of Electronic Technology, Russia, 124498, Moscow, Zelenograd, Shokin sq., 1
Larisa G. Gagarina
National Research University of Electronic Technology, Russia, 124498, Moscow, Zelenograd, Shokin sq., 1
Sergey F. Tsarapkin
National Research University of Electronic Technology, Russia, 124498, Moscow, Zelenograd, Shokin sq., 1
Mikhail Yu. Semenov
“NM-Tech” LLC, Russia, 124527, Moscow, Zelenograd, Solnechnaya pkwy, 6
Evgeniy I. Minakov
Tula State University, Russia, 300012, Tula, Lenin ave., 92
Evgeniy M. Portnov
National Research University of Electronic Technology, Russia, 124498, Moscow, Zelenograd, Shokin sq., 1

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