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Economics and Finances
ArticleName Graph-matrix modeling of production systems as a basis for managing the production capacity of metal working enterprises
DOI 10.17580/cisisr.2021.01.17
ArticleAuthor N. V. Kireeva, E. S. Zambrzhitskaia, S. S. Voinov

Ural Social and Economical Institute, branch of Educational Institution of Trade Unions of Higher Education “Academy of Labor and Social Relations” (Chelyabinsk, Russia):
N. V. Kireeva, Dr. Econ., Prof., Head of Dept. of Economics, e-mail:


Nosov Magnitogorsk State Technical University (Magnitogorsk, Russia);
E. S. Zambrzhitskaia, Cand. Econ., Associate Prof., Dept. of Economics, e-mail:


Magnitogorsk Factory of Precision Products (Magnitogorsk, Russia):
S. S. Voinov, Director, e-mail:


Development of information systems and technologies makes it possible to use complex models for information support of management decisions. The most particular interest shows the theory of graphs and matrix calculus in order to assess the production capacity of an industrial enterprise. The study of the authors is devoted to development of methodological approaches to assessing of production capacity based on graph-matrix models. The essence of these models lies in the fact that a manufacturing enterprise is depersonalized by perceiving it as a kind of production system, consisting of production links that add up to a production chain and form a kind of production network, which is represented as a model of the production cycle. In order to perform the appropriate calculations, the specified graph model is linked to the matrix model, which takes into account the main parameters of the production system: technological connections; assortment structure of products; direct consumption coefficients; production capacity of the links. Suggested approach determines the flexibility and broad analytical capabilities of the proposed models for calculating of production capacities. The basis for theoretical and methodological researches became the methods of analysis and synthesis, principles of consistency and complexity, graph theory and matrix calculus. The approbation of the proposed graph-matrix models of production systems was carried out using the examples of a metal working enterprise. The theoretical and practical significance of the study lies in the fact that the proposed graph-matrix model makes it possible to ensure effective management of production facilities by taking into account the mobility of the product assortment structure and complex technological links.

keywords Metal working enterprise, production capacity, production system, production link, throughput, assortment structure, “limiting” link, graph-matrix model, matrix, production network

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