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An inventory with constant demand and Poisson restocking

Authors
Baxter, Laurence A.Lee, Eui Yong
Issue Date
Apr-1987
Publisher
Cambridge University Press
Citation
Probability in the Engineering and Informational Sciences, v.1, no.2, pp 203 - 210
Pages
8
Journal Title
Probability in the Engineering and Informational Sciences
Volume
1
Number
2
Start Page
203
End Page
210
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/159239
DOI
10.1017/S0269964800000401
ISSN
0269-9648
1469-8951
Abstract
An inventory whose stock decreases linearly with time is considered. The inventory may be replenished at the instants at which a deliveryman arrives provided that the level of the inventory does not exceed a certain threshold; deliveries are made according to a Poisson process. A partial differential equation for the distribution function of the level of the inventory is solved to yield a formula for the corresponding Laplace–Stieltjes transform. The evaluation of the transform is discussed and explicit results are obtained for the stationary case.
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