Informatics and Applications
2018, Volume 12, Issue 2, pp 83-89
SOLUTION TO THE PROBLEM OF OPTIMAL CONTROL OF A STOCHASTIC SEMI-MARKOV MODEL OF CONTINUOUS SUPPLY OF PRODUCT MANAGEMENT UNDER THE CONDITION OF CONSTANTLY HAPPENING CONSUMPTION
- P. V. Shnurkov
- A. Y. Egorov
Abstract
The solution of the optimal control problem in the semi-Markov model in question is theoretically justified. To achieve this goal, formal analytic transformations of the integral representations obtained by the authors earlier for the basic probabilistic characteristics of the model were carried out. These transformations made it possible to use the theorem on the analytical representation of the stationary value of the management effectiveness of a semi-Markov process in the form of a fractional-linear integral functional. In the sequel, the authors use the general theorem on the extremum of a fractional-linear integral functional, proved by P. V. Shnurkov. This theorem makes it possible to reduce the problem of optimal reserve management to the problem of investigating the global extremum of a given function from a finite number of real nonnegative variables that can be effectively solved in practice using the known numerical methods.
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[+] About this article
Title
SOLUTION TO THE PROBLEM OF OPTIMAL CONTROL OF A STOCHASTIC SEMI-MARKOV MODEL OF CONTINUOUS SUPPLY OF PRODUCT MANAGEMENT UNDER THE CONDITION OF CONSTANTLY HAPPENING CONSUMPTION
Journal
Informatics and Applications
2018, Volume 12, Issue 2, pp 83-89
Cover Date
2018-05-30
DOI
10.14357/19922264180212
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
inventory management; semi-Markov stochastic process; stationary value index; optimal control of stochastic systems; fractional-linear integral functional
Authors
P. V. Shnurkov  and A. Y. Egorov
Author Affiliations
National Research University Higher School of Economics, 34 Tallinskaya Str., Moscow 123458, Russian Federation
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