Enaleeva-Bandura I., Lozovoy D., Litvinov D., Baranov A., Kunitskaya O., Zadrauskaite N. Matrix method of modeling production lines of the timber industry complex // Resources and Technology. 2026. №1, Vol. 23. P. 1‒25.

Matrix method of modeling production lines of the timber industry complex

Enaleeva-Bandura
Irina

Siberian State University of Science and Technology named after Academician M. F. Reshetnev, melnikov1978@inbox.ru

Lozovoy
Dmitry

Siberian State University of Science and Technology named after Academician M. F. Reshetnev, dvl92@mail.ru

Litvinov
Daniil

Siberian State University of Science and Technology named after Academician M. F. Reshetnev, chess96@mail.ru

Baranov
Alexander

Siberian State University of Science and Technology named after Academician M. F. Reshetnev, aleksandr-baranov-55@mail.ru

Kunitskaya
Olga

Arctic State Agrotechnological University, ola.ola07@mail.ru

Zadrauskaite
Natalia

Northern (Arctic) Federal University named after M.V. Lomonosov, n.zadrauskaite@narfu.ru

Key words:
timber industry complex streaming technologies
continuity model
graphoanalytical modeling

Summary: Continuous production lines at the enterprises of the forestry complex and the network of transport mechanisms, assemblies and machines provide specified volumes and quality of products in accordance with the requirements of the market. It should be noted that a significant part of transport operations is associated with the primary conversion of wood raw materials on an individual basis. That is, there is a close relationship between the continuous production lines, for example, a crosscutting line, with operations of wood saw material sorting, debarking, infeeding, etc. At the same time, not only crosscutting lines should be designed individually, but also adjacent equipment, which generally does not meet standard parameters and may be combined in a separate line. The article proposes a generalizing approach to describing the structure of continuous production lines with transitional matrices 4 × 4 and 5×5 in abbreviated (analytical) and expanded forms of recording by transitional single diagonal matrices to describe different levels of equipment location. For clarity, the modeling method is considered for the sequence of a continuous production line of five units located at three levels (x, y, z). In this case, the structure is described by analytically diagonal single matrices of 4 × 4 with the subsequent interpretation in the form of a vector equation with a graphic solution in the form of a spatial number of vectors. The vector equation allows obtaining the values of the speed characteristics of the subject of labor during consecutive operations. The transition from the vector model to the continuity one is performed by transforming the structure of the model from matrices of the four -dimensional format to the five –dimensional one by addition of the fifth measurement in the form of an axis of time. The authors consider a variation of continuous production line (for simplicity, consisting of three units) with a description of the structure with transition matrices 5 × 5, which ensure the transition to the continuity of the modeling process. Further, the graphic compliance of the 5 × 5 transition matrices is considered in detail by the dependence of the movements on the time that ensures the visualization of the continual model of the technological process of the continuous production line with the sequential location of more than two units of the equipment. In conclusion, a graphic model of an ideal continuous production line in 4D format is presented. The basis of the model is the dependence graph of the object of labor movements on time on machines (units), obtained when the four -dimensional model is transformed into the five -dimensional one based on transitional matrices.

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Resources and Technology

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Matrix method of modeling production lines of the timber industry complex