Стохастическое планирование производственных процессов

S I Velikiy; M M Gorokhov; V A Tenenev

doi:10.22213/2410-9304-2025-1-54-64

Authors

S. I. Velikiy Kalashnikov Izhevsk State Technical University
M. M. Gorokhov Kalashnikov Izhevsk State Technical University; Federal State Institution Research Institute of the Federal Penitentiary Service of Russia
V. A. Tenenev Kalashnikov Izhevsk State Technical University

DOI:

https://doi.org/10.22213/2410-9304-2025-1-54-64

Keywords:

production schedule, statistical testing method, genetic algorithm, optimization problems, Stochastic planning

Abstract

Uncertainty is an unavoidable element in many practical production planning and scheduling environments. The problem is formulated as follows. There are many tasks. The task is understood as any type of work within the technological process. Many machines must be used to complete a particular task. The execution of each task on a machine is characterized by indefinite time. In accordance with the technological process, a technological route representing a sequence of machines is prescribed for each or for some works. For practical use, methods using genetic algorithms are used to support planning within the production system. The genetic algorithm belongs to the category of artificial intelligence. This is a very effective algorithm to find optimal or close to optimal solutions of an optimization problem. Due to the fact that discrete optimization methods, such as the branch and boundary method, are NP difficult, it is proposed to use a genetic algorithm that includes elements of the statistical test method to solve production planning problems withtiming uncertainty of tasks on process equipment. The genetic algorithm uses a flexible chromosome coding scheme. This scheme allows generation of valid solutions in all genetic operators: crosses, mutations and selection. This made it possible to obtain a solution with a lower value of the objective function compared to the method of encoding using Petri nets. The application of the normal distribution law of random work time values on machines leads to a distribution close to normal for finite time of the final operation. There is a linear relationship between the calculatedand given deviation levels. Final operation mean time is increased 1.54 times when deviation is being set as as .

Author Biographies

S. I. Velikiy, Kalashnikov Izhevsk State Technical University

Post-graduate

M. M. Gorokhov, Kalashnikov Izhevsk State Technical University; Federal State Institution Research Institute of the Federal Penitentiary Service of Russia

Doctor of Physics and Mathematics, Professor; Chief Researcher

V. A. Tenenev, Kalashnikov Izhevsk State Technical University

Doctor of Physics and Mathematics, Professor

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