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Ergodicity of age-dependent inventory control systems

Olsson, Fredrik LU and Turova, Tatyana S. LU (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.

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Please use this url to cite or link to this publication:
author
organization
publishing date
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
  • scopus:84991677509
  • wos:000386349900004
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
2017-02-27 07:00:16
@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},
  keyword      = {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},
  volume       = {53},
  year         = {2016},
}