Optimal aggregation of production systems with parametric connections

Authors

DOI:

https://doi.org/10.15587/1729-4061.2014.26306

Keywords:

modeling, production function, development function, algebraization, binary operator, optimal aggregation

Abstract

Today, all conditions for effective functioning and development of production systems, with the exception of effective mathematical models for the new production management problems are provided. Based on the analysis of the state of theory and practice, requirements to models of production systems: absence of restrictions on the type of production functions, except for non-strict monotony and non-strict positivity; eliminating the dimensionality problem for optimization problems; isomorphic mapping of the structure of the production system in the decomposition structure of the optimization problem were formulated. To solve the problem of optimal control, methodology of optimal aggregation of production systems was used. The key point of this methodology is the decomposition of multidimensional nonlinear programming problem in the system of one-dimensional optimization problems. The structure of this system corresponds to the structure of the resource connections in the production system. Solutions for optimal aggregation of typical structures of production systems with parametric connections: “production – development”, “production – warehouse”, “production with recycling” that satisfy the set requirements were first obtained. The properties of this class of models for production systems are insufficiently investigated. Concrete results of modeling for these tasks were presented in the paper. Models are open for modifications and customization to specific segments of the production.

Author Biography

Таиса Николаевна Боровская, Vinnitsa National Technical University Khmelnytske shosse 95, Vinnitsa, Ukraine, 21021

Assistant Professor, Cand. Sc. (Eng.)

Department of Computer Control Systems

References

  1. Borovska, Т. М., Kolesnik, I. C., Severilov, V. A. (2009). Optimal aggregation method in optimization problems. Vinnitsa, Ukraine: UNIVERSUM Vinnitsa, 229.
  2. Borovska Т. М., Badera, S. P., Severilov, V. A., Severilov, P. V. (2009). Modeling and optimization processes of production systems with the use of external resources and the effects of development: Vinnitsa, Ukraine: VNTU, 255.
  3. Bellman, R. E., Kalaba, R. E. (1969). Dynamic programming and modern control theory. Moscow, USSR: Science, 131.
  4. Forrester, J. W. (1971). Basics of Cybernetics enterprises (Industrial Dynamics). Moscow, USSR: Progress, 340.
  5. Eklund, I. (1983). Elements of Mathematical Economics. Moscow, USSR: World, 248.
  6. Fagin, R., Kumar, R., Sivakumar, D. (2003). Efficient similarity search and classification via rank aggregation. Proceedings of the 2003 ACM SIGMOD international conference on on Management of data – SIGMOD 03 (p. 301). Association for Computing Machinery (ACM). doi:10.1145/872794.872795
  7. Mesarovich, M., Takahara, I. (1978). General systems theory: the mathematical foundations of. Moscow, USSR: World, 312.
  8. Opoitsev, V. I. (1977). Equilibrium and stability in models of collective behavior. Moscow, USSR: World, 346.
  9. Kohonen, T. (2001). Self-Organizing Maps. New York, 501.
  10. Borovska Т. М., Severilov, V. A., Badera, S. P., Kolesnik, I. C. (2009). Modeling and optimization of management. Vinnitsa, Ukraine: UNIVERSUM Vinnitsa, 145.

Downloads

Published

2014-07-24

How to Cite

Боровская, Т. Н. (2014). Optimal aggregation of production systems with parametric connections. Eastern-European Journal of Enterprise Technologies, 4(11(70), 9–19. https://doi.org/10.15587/1729-4061.2014.26306

Issue

Vol. 4 No. 11(70) (2014): Mathematical and information support of computer-integrated control systems

Section

Mathematical and information support of computer-integrated control systems

License

Copyright (c) 2014 Таиса Николаевна Боровская

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.