Construction of a State Vector Observer for a Discrete Inventory Management System

Authors

  • A. V. Savranska National University Zaporizhzhia Polytechnic
  • M. V. Shevchuk National University Zaporizhzhia Polytechnic

DOI:

https://doi.org/10.31649/1997-9266-2024-175-4-122-128

Keywords:

discrete control systems, state vector observers, inventory control, differential equations

Abstract

All control objects are uncertain to one degree or another. Uncertainties significantly affect the performance of the control system and can lead to its loss. Therefore, for high-quality management of any object, it is necessary to know its state vector. This enables to organize management, which ensures the efficient operation of the system. This problem is solved by estimating the state vector of the system, which leads to the construction of observers.

Inventory management tasks are focused on maintaining a balance between avoiding product shortages and overall reduction of balances through their effective distribution between individual groups of goods or between enterprise divisions.

In this article, a discrete system for managing the company's product balances is built, which consists of the difference equation of the system state vector, the equation for estimating this state, and the control vector, which consists of costs aimed at replenishing the product balances. A sales forecast matrix is built in advance based on the company's historical data for several previous years

The objective of this study is to create a regulator for the balance management system, which takes into account the real state of the system for any period of time. For this purpose, a full-order state vector observer is built, which, monitoring the observed output of the system, correlates the vector of control influences and the value of the system state vector. The control vector is a vector of expenses necessary to form the number of balances by product groups at a level that allows you to reach the forecast sales volume.

The scientific novelty of the study consists in the creation of a control system with a state vector observer of full order, which allows to perform monitoring of the real state of the system and correcting the vector of control influences.

The results of this study were tested at a small wholesale enterprise, which allowed the manager to improve the efficiency of procurement planning.

Author Biographies

A. V. Savranska, National University Zaporizhzhia Polytechnic

 Cand. Sc. (Phys.-Math.), Associate Professor with the Chair of System Analysis and Computational Mathematics

M. V. Shevchuk, National University Zaporizhzhia Polytechnic

Post-Graduate Student with the Chair of System Analysis and Computational Mathematics

References

Y. Wangand, and Xu Li. “Dynamics and Control on a Discrete Multi-Inventory System,” Journal of Control Science and Engineering, vol. 2019, 2019. https://doi.org/10.1155/2019/6926342 .

S. Antic, L. D., Milutinovic, and A. Lisec, “Dynamic Discrete Inventory Control Model with Deterministic and Stochastic Demand,” in Pharmaceutical Distribution. Applied Sciences, № 12, 2022. https://doi.org/10.3390/app12031536 .

М. Є. Юрченко, «Дискретна модель оптимального управління запасами підприємства,» Ефективна економіка, 2019. https://doi.org/ 10.32702/2307-2105-2019.3.32 .

Ogata Katsuhiko, “Discrete-time Control Systems,” A Simon & Schuster Company Englewood Cliff, New Jersey, 1995, 732 p.

P. E. Moraal, and J. W. Grizzle, “Observerd esignfornon linear systems with discrete-time measurement,” IEEE Transactionson Automatic Control, vol. 40(3), pp. 395-404, 1995. https://doi.org/10.1109/9.376051 .

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Published

2024-08-30

How to Cite

[1]
A. V. Savranska and M. V. Shevchuk, “Construction of a State Vector Observer for a Discrete Inventory Management System”, Вісник ВПІ, no. 4, pp. 122–128, Aug. 2024.

Issue

No. 4 (2024)

Section

Information technologies and computer sciences

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