Informatics and Applications
2018, Volume 12, Issue 1, pp 109-117
DEVELOPMENT AND PRELIMINARY STUDY OF A STOCHASTIC SEMI-MARKOV MODEL OF CONTINUOUS SUPPLY OF PRODUCT MANAGEMENT UNDER THE CONDITION OF CONSTANT CONSUMPTION
- P. V. Shnurkov
- A. Y. Egorov
Abstract
The paper deals with a discrete semi-Markov stochastic model describing the operation of a control system of continuous supply of product with constant consumption. The model is a couple of random processes (x(t), Z(t)) where the main process x(t) describes the amount of stock in the system at time t and the accompanying random process is a semi-Markov process with a finite set of states. The optimal control problem is put in relation to the stationary indicators related to the accompanying process. This indicator is the average of the specific nature of the profits earned in the evolution of the initial inventory control system. An explicit analytical representation for the probability characteristics of semi-Markov models is obtained. In the future, the results will allow to find an explicit representation of the Quality Score and solving the problem of optimal control.
[+] References (10)
- Shnurkov, P. V., and A. Y. Egorov. 2017. Prilozhe- nie k stat'e "Razrabotka i predvaritel'noe issledovanie stokhasticheskoy polumarkovskoy modeli upravleniya zapasom nepreryvnogo produkta pri postoyanno prois- khodyashchem potreblenii" [Appendix to article "Development and preliminary study of stochastic semi- Markov model of continuous supply of product management at constantly happening consumption"]. 49 p. Available at: http://www.ipiran.ru/publications/ ripk^o>KeHMe_upd.pdf (accessed December 22, 2017).
- Korolyuk, V. S., and A. F. Turbin. 1976. Polumarkovskie protsessy i ikh prilozheniya [Semi-Markov processes and their applications]. Kiev: Naukova Dumka. 184 p.
- Janssen, J., and R. Manca. 2006. Applied semi-Markov process. New York, NY: Springer. 309 p.
- Jewell, W S. 1963. Markov-renewal programming. Oper. Res. 11:938-971.
- Mine, H., and S. Osaki. 1970. Markovian decision processes. New York, NY: Elsevier. 142 p.
- Shnurkov, P. V., and A. V. Ivanov. 2015. Analysis of a discrete semi-Markov model of continuous inventory control with periodic interruptions of consumption. Discrete Math. Appl. 25(1):59-67.
- Shnurkov, P. V. 1990. Stokhasticheskaya model' planovogo tekhnicheskogo obsluzhivaniya [Stochastic model of scheduled maintenance]. Stokhasticheskie sistemy i ikh prilozheniya [Stochastic systems and their applications]. Kiev: Institute of Mathematics of the Ukrainian Academy of Sciences. 98-105.
- Luque-Vasquez, F, and O. Herndndez-Lerma. 1999. Semi-Markov control models with average costs. Appl. Math. 26(3):315-331.
- Shnurkov, P. V. 2016. Solution of the unconditional extremum problem for a linear-fractional integral functional on a set of probability measures. Doklady Mathematics 94(2):550-554.
- Shnurkov, P. V., A. K. Gorshenin, and V.V. Belousov 2016. Analiticheskoe reshenie zadachi optimal'nogo upravleniya polumarkovskim protsessom s konechnym mnozhestvom sostoyaniy [An analytic solution of the optimal control problem for a semi-Markov process with a finite set of states]. Informatika i ee Primeneniya - Inform. Appl. 10(4):72-88.
[+] About this article
Title
DEVELOPMENT AND PRELIMINARY STUDY OF A STOCHASTIC SEMI-MARKOV MODEL OF CONTINUOUS SUPPLY OF PRODUCT MANAGEMENT UNDER THE CONDITION OF CONSTANT CONSUMPTION
Journal
Informatics and Applications
2018, Volume 12, Issue 1, pp 109-117
Cover Date
2018-03-30
DOI
10.14357/19922264180114
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 functional; optimal control of stochastic systems
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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