Informatics and Applications
2019, Volume 13, Issue 2, pp 54-61
RESEARCH OF THE OPTIMAL CONTROL PROBLEM OF INVENTORY OF A DISCRETE PRODUCT IN THE STOCHASTIC REGENERATION MODEL WITH CONTINUOUSLY OCCURING CONSUMPTION AND RANDOM DELIVERY DELAY
- P. V. Shnurkov
- N. A. Vakhtanov
Abstract
The paper considers the optimal control problem of inventory of a discrete product in a regeneration scheme with a Poisson flow of customer requirements. In the system, deferred demand is allowed, the volume of which is limited by a given value. The control parameter is the level of the stock, at which achievement it is necessary to make an order for replenishment. The indicator of management effectiveness is the average specific profit received in one regeneration period. The optimal control problem is solved on the basis of the statement about the extremum of a fractional-linear integral functional on the set of discrete probability distributions.
[+] References (13)
- Shnurkov, P. V., and R. V Mel'nikov. 2006. Optimal'noe upravlenie zapasom nepreryvnogo produkta v modeli re- generatsii [Optimal control of a continuous product inventory in the regeneration model]. Obozrenieprikladnoy i promyshlennoy matematiki [Review of Applied and Industrial Mathematics] 13(3):434-452.
- Shnurkov, P.V., and R. V. Mel'nikov. 2008. Analysis of the problem of continuous-product inventory control under deterministic lead time. Automat. Rem. Contr. 69(10):1734-1751.
- Shnurkov, P. V., and E. Yu. Pimenova. 2017. Optimal'noe upravlenie zapasom nepreryvnogo produkta v skheme re- generatsii s determinirovannoy zaderzhkoy postavki i peri- odom real'nogo popolneniya [Optimal inventory control of continuous product in regeneration theory with determinate delay of the delivery and the period of real replenishment]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 27(4):80-94.
- Porteus, E. L. 2002. Foundations of stochastic inventory theory. Stanford, CA: Stanford Business Book. 299 p.
- Simchi-Levi, D., X. Chen, and J. Bramel. 2014. The logic of logistics: Theory, algorithms, and applications for logistics management. New York, NY: Springer-Verlag. 447 p.
- Rykov, V.V., and D.V. Kozyrev. 2016. Osnovy teorii massovogo obsluzhivania [Fundamentals of queuing theory]. Moscow: Infra-M. 224 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.
- Klimov, G.P. 2011. Teoriya massovogo obsluzhivaniya [Queuing theory]. Moscow: MSU Publs. 312 p.
- Borovkov, A. A. 2009. Teoriya veroyatnostey [Probability theory]. Moscow: Librokom. 656 p.
- Shnurkov, P.V. 2016. Solution of the unconditional extremum problem for a linear-fractional integral functional on a set of probability measures. Dokl. Math. 94(2):550- 554.
- Shnurkov, P.V., and N.A. Vakhtanov. 2019. Prilozhe- nie k stat'e "Issledovanie problemy optimal'nogo up- ravleniya zapasom diskretnogo produkta v stokhastiche- skoy modeli regeneratsii s nepreryvno proiskhodyashchim potrebleniem i sluchaynoy zaderzhkoy postavki" [Appendix to article "Research of the optimal control problem of inventory of a discrete product in stochastic regeneration model with continuously occurring con-sumption and random delivery delay"]. 16 p. Available at: http://www.ipiran.ru/publications/npk^cweHMe.pdf (accessed May 6, 2019).
- Shnourkoff, P. V., and D.A. Novikov. 2018. Analysis of the problem of intervention control in the economy on the basis of solving the problem of tuning. arxiv.org. arXiv:1811.10993 [q-fin.GN]. 15p.
[+] About this article
Title
RESEARCH OF THE OPTIMAL CONTROL PROBLEM OF INVENTORY OF A DISCRETE PRODUCT IN THE STOCHASTIC REGENERATION MODEL WITH CONTINUOUSLY OCCURING CONSUMPTION AND RANDOM DELIVERY DELAY
Journal
Informatics and Applications
2019, Volume 13, Issue 2, pp 54-61
Cover Date
2019-06-30
DOI
10.14357/19922264190208
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
inventory management of a discrete product; controlled regenerative process; extremal problem for a fractional-linear integral functional
Authors
P. V. Shnurkov  and N. A. Vakhtanov
Author Affiliations
National Research University Higher School of Economics, 34 Tallinskaya Str., Moscow 123458, Russian Federation
|