Ergodicity of age-dependent inventory control systems
(2016) In Journal of Applied Probability 53(3). p.688-699- Abstract
We consider continuous review inventory systems with general doubly stochastic Poisson demand. In this specific case the demand rate, experienced by the system, varies as a function of the age of the oldest unit in the system. It is known that the stationary distributions of the ages in such models often have a strikingly simple form. In particular, they exhibit a typical feature of a Poisson process: given the age of the oldest unit the remaining ages are uniform. The model we treat here generalizes some known inventory models dealing with partial backorders, perishable items, and emergency replenishment. We derive the limiting joint density of the ages of the units in the system by solving partial differential equations. We also... (More)
We consider continuous review inventory systems with general doubly stochastic Poisson demand. In this specific case the demand rate, experienced by the system, varies as a function of the age of the oldest unit in the system. It is known that the stationary distributions of the ages in such models often have a strikingly simple form. In particular, they exhibit a typical feature of a Poisson process: given the age of the oldest unit the remaining ages are uniform. The model we treat here generalizes some known inventory models dealing with partial backorders, perishable items, and emergency replenishment. We derive the limiting joint density of the ages of the units in the system by solving partial differential equations. We also answer the question of the uniqueness of the stationary distributions which was not addressed in the related literature.
(Less)
- author
- Olsson, Fredrik LU and Turova, Tatyana S. LU
- organization
- publishing date
- 2016-09-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Base-stock policy, Doubly stochastic Poisson process, Ergodicity, Inventory
- in
- Journal of Applied Probability
- volume
- 53
- issue
- 3
- pages
- 12 pages
- publisher
- Applied Probability Trust
- external identifiers
-
- wos:000386349900004
- scopus:84991677509
- ISSN
- 0021-9002
- DOI
- 10.1017/jpr.2016.34
- language
- English
- LU publication?
- yes
- id
- 0c48f33a-fe6e-435d-9c1d-3bac7920ede9
- date added to LUP
- 2016-12-12 15:00:22
- date last changed
- 2024-01-04 18:55:19
@article{0c48f33a-fe6e-435d-9c1d-3bac7920ede9,
abstract = {{<p>We consider continuous review inventory systems with general doubly stochastic Poisson demand. In this specific case the demand rate, experienced by the system, varies as a function of the age of the oldest unit in the system. It is known that the stationary distributions of the ages in such models often have a strikingly simple form. In particular, they exhibit a typical feature of a Poisson process: given the age of the oldest unit the remaining ages are uniform. The model we treat here generalizes some known inventory models dealing with partial backorders, perishable items, and emergency replenishment. We derive the limiting joint density of the ages of the units in the system by solving partial differential equations. We also answer the question of the uniqueness of the stationary distributions which was not addressed in the related literature.</p>}},
author = {{Olsson, Fredrik and Turova, Tatyana S.}},
issn = {{0021-9002}},
keywords = {{Base-stock policy; Doubly stochastic Poisson process; Ergodicity; Inventory}},
language = {{eng}},
month = {{09}},
number = {{3}},
pages = {{688--699}},
publisher = {{Applied Probability Trust}},
series = {{Journal of Applied Probability}},
title = {{Ergodicity of age-dependent inventory control systems}},
url = {{http://dx.doi.org/10.1017/jpr.2016.34}},
doi = {{10.1017/jpr.2016.34}},
volume = {{53}},
year = {{2016}},
}