Graph dynamical modeling of organizational systems structures
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Keywords

graph
hierarchical graph
graph dynamical systems
function of subordination
graph dynamical modeling

How to Cite

Kovalenko , I., Shved, A., & Davydenko, Y. (2020). Graph dynamical modeling of organizational systems structures. Computer Science and Engineering, 1(1), 1-19. https://doi.org/10.26693/cse2020.01.001

Abstract

The article considers the main principles of graph dynamical systems, as well as a number of examples of the use of graph dynamical operations for simulation modeling of the organizational system structure and composition management problems. The basic concepts and definitions of the graph dynamical systems theory are given. Using the subordination function as an example, a graph is constructed with numbered vertices, each component of which is a tree. Considered the situation when initial graph is time variant and there is a sequence of graphs such that every graph of sequence is either a tree or a forest. At the ”development” of the sequence in time the unilaterally connected graph can be multiply connected graph, i.e. new roots and ”growing” trees may form. The vertex resubordination may occur inside of the tree. Each graph of this sequence corresponds to a well-defined function of subordination. As result, the sequence of alternately graphs, i.e. a graph path represented as a sequence of functions of subordination. Transition of each of the subordination functions of the path into other subordination function is carried out by performing three types of operations: unary, binary and r-ary operations. Graph dynamical modeling of organizational structure transformation with its preliminary destructuring are described. As an example of such modeling considered the task of the functioning organization restructuring, the structure of which is represented by 4-level hierarchy. Also in the paper are examples of graph and dynamic modelling of organizational structure’s members reducing.

https://doi.org/10.26693/cse2020.01.001
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References

V. N. Burkov, N. A. Korgin, D. A. Novikov, Introduction to organizational systems management theory, Librocom, Moscow, 2009, p. 264, (in Russian) [cited 3 Mar 2020]. url: http://www.mtas.ru/upload/vtuos.pdf.

Y. N. Kuznetsov, I. B. Muchnik, Structural methods of analysis of organizational systems, Autom. Remote Control 5 1983. 5-27, (in Russian) [cited 3 Mar 2020]. url: http://www.mathnet.ru/links/b96ad5dc801107aaaae462ee1a769117/at5116.pdf.

D. A. Novikov, Organizational systems management theory, 2nd Edition, Fizmatlit, Moscow, 2007, p. 584, (in Russian) [cited 3 Mar 2020]. url: http://www.mtas.ru/start/tyos2005.pdf.

R. L. Sheinin, Quantitative analysis of the functioning of organizational systems, in: B. Z. Milner, R. L. Sheinin (Eds.), Problems of analysis of the functioning of organizational systems, Vol. 11, (in Russian), VNIISI, Moscow, 1986, pp. 3-21.

A. R. Leibkind, Issues of formation of organizational structures for managing production and economic complexes, Izv. ANUSSR. Economic Series 1 1985. 25-36, (in Russian).

B. Z. Milner, L. I. Evenko, V. S. Rapoport, Systematic approach to management organization, Economy, Moscow, 1983, p. 224, (in Russian).

V. N. Burkov, A. Y. Zalozhnev, D. A. Novikov, Graph theory in organizational systems management, Sinteg, Moscow, 2001, p. 124, (in Russian) [cited 4 Mar 2020]. url: https://www.researchgate.net/publication/274390436_Teoria_grafov_v_upravlenii_organizacionnymi_sistemami.

A. R. Leibkind, B. L. Rudnik, A. I. Chukhnov, Models of the formation of organizational structures, Economics and Mathematical Methods 16 (1) 1980. 39-59, (in Russian).

M. A. Aizerman, S. V. Gusev, S. V. Petrov, I. M. Smirnova, A dynamic approach to the analysis of structures described by graphs (basics of graphodynamics) i, Autom. Remote Control 38 (7) 1977. 135-151, (in Russian) [cited 4 Mar 2020]. url: http://www.mathnet.ru/links/1f781ca5be04d0c4a752558186583f1d/at7406.pdf.

M. A. Aizerman, S. V. Gusev, S. V. Petrov, I. M. Smirnova, A dynamic approach to the analysis of structures described by graphs (basics of graphodynamics) ii, Autom. Remote Control 38 (9) 1977. 123-136, (in Russian) [cited 4 Mar 2020]. url: http://www.mathnet.ru/links/19ee879ae3cdbaddef3ab5367595b875/at7454.pdf.

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