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On the (S – 1, S) Stock Model for Renewal Demand Processes: Poisson's poison

Published online by Cambridge University Press:  27 July 2009

Marcel A. J. Smith  and
Rommert Dekker
Marcel A. J. Smith
Affiliation:
Erasmus University Rotterdam, P.O. Box 1738, 300O DR Rotterdam, The Netherlands
Rommert Dekker
Affiliation:
Erasmus University Rotterdam, P.O. Box 1738, 300O DR Rotterdam, The Netherlands
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Abstract

In the standard (S – 1, S) stock model, demand follows a Poisson process. It has appeared to many stock analysts that this model causes an abundance of stock in reality. In case demand is caused by failure or is derived from another process, demand typically does not follow a Poisson process. In this paper, we discuss the (S – 1, S) stock model where demand follows a renewal process and the lead time is deterministic. Moreover, we will extend this to compound renewal demand and multi-echelon inventory systems. Our goal is to show the severe influence of taking the Poisson process for granted.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 3 , July 1997 , pp. 375 - 386
Copyright
Copyright © Cambridge University Press 1997

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