Yu. I. Dorofieiev, L. M. Lyubchyk


Context. The urgent task of the decentralized inventory control synthesis of material resources in supply chains with uncertainty of
external demand and availability of operational constraints has been solved. Objective is a development of the method of optimal stabilization of local supply chain nodes using a linear dynamic feedback from deviation between available and safety levels of resource stocks in the chain nodes, providing suppression of «bullwhip effect» and the development of the stability analysis method of the decentralized inventory control system in supply chains.
Method. An approach based on the invariant ellipsoids method, which provides a complete and timely response of the «unknown, but
bounded» external demand for resources, the stabilization of the closed local subsystems under predefined constraints on the values of local
states and control actions, as well as the suppression of «bullwhip effect» in the supply chains has been invited. The stability conditions for
decentralized inventory control system in supply chains using the vector Lyapunov functions method and the comparison method has been
Results. The problem of control synthesis using the technique of linear matrix inequalities was reduced to a sequence of semidefinite
programming problems, which are solved numerically in real time.
Conclusions. The method of suboptimal structural and parametric synthesis of the decentralized constrained inventory control in supply
chains was further developed through the development of the invariant ellipsoids method, thus the costs associated with transportation and
storage of material resources were reduced due to suppression of «bullwhip effect»; the degree of suppression of mentioned above effect for different levels of the supply chains is determined by the choice of weighting matrices of local quality criteria. The developed models and
algorithms of the decentralized inventory control under uncertainty of demand and availability of operational constraints were introduced at
the industrial enterprises and organizations which deal with the production, storage and distribution of material resources, such as the
«Kharkivvodokanal» – one of the largest enterprises in Ukraine providing water services and the Ltd. Company «SV» (Kharkiv) – the leading manufacturer of household chemical goods in Ukraine.


inventory control; bullwhip effect; decentralized control; invariant ellipsoids method; linear matrix inequality.


Disney S. M. The effect of vendor managed inventory dynamics on the bullwhip effect in supply chains / S. M. Disney, D. R. Towill // Int. J. Prod. Econ. – 2003. – Vol. 85. – P. 199– 215. 2. Лотоцкий В. А. Модели и методы управления запасами / В. А. Лотоцкий, А. С. Мандель. – М. : Наука, 1991. – 188 c. 3. Поляк Б. Т. Управление линейными системами при внешних возмущениях: техника линейных матричных неравенств / Б. Т. Поляк, М. В. Хлебников, П. С. Щербаков. – М. : ЛЕНАНД, 2014. – 560 с. 4. Чурилов А. Н. Исследование линейных матричных неравенств. Путеводитель по программным пакетам / А. Н. Чурилов, А. В. Гессен. – СПб. : Изд-во С.-Петерб. ун-та, 2004. – 148 с. 5. Wang X. The bullwhip effect: progress, trends and directions / X. Wang, S. M. Disney // Eur. J. Operat. Res. – 2016. – Vol. 250. – P. 691–701. 6. Вохмянина А. В. Анализ влияния «эффекта хлыста» на уровень обслуживания в логистической цепи поставок / А. В. Вохмянина, М. А. Журавская, Qiao Cong // Транспорт: наука, техника, управление. – 2015. – № 9. – С. 38–45. 7. Fu D. Decentralized and centralized model predictive control to reduce the bullwhip effect in supply chain management / D. Fu, C. M. Ionescu, El-H. Aghezzaf, R. De Keyser // Comput. Ind. Eng. – 2014. – Vol. 73. – P. 21–31. 8. Blanchini F. Feedback control of production-distribution systems with unknown demand and delays / F. Blanchini, R. Pesenti, F. Rinaldi, W. Ukovich // IEEE Transactions on Robotics and Automation. – 2000. – Vol. 16, No. 3. – P. 313–317. 9. Дорофеев Ю. И. Робастное управление запасами в сетях поставок в условиях неопределенности спроса и транспортных за- паздываний : дис. ... доктора техн. наук : 05.13.07 / Дорофеев Юрий Иванович. – Харьков, 2016. – 284 с. 10. Grant M. CVX: MATLAB software for disciplined convex programming, version 2.1 / M. Grant, S. Boyd // [Electronic resource]. – Access mode: http://cvxr.com/cvx.

GOST Style Citations

DOI: http://dx.doi.org/10.15588/1607-3274-2017-1-18

Copyright (c) 2017 Yu. I. Dorofieiev, L. M. Lyubchyk

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

Address of the journal editorial office:
Editorial office of the journal «Radio Electronics, Computer Science, Control»,
Zaporizhzhya National Technical University, 
Zhukovskiy street, 64, Zaporizhzhya, 69063, Ukraine. 
Telephone: +38-061-769-82-96 – the Editing and Publishing Department.
E-mail: rvv@zntu.edu.ua

The reference to the journal is obligatory in the cases of complete or partial use of its materials.