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Optimal and Near-Optimal (s,S) Inventory Policies for Levy Demand Processes

Published online by Cambridge University Press:  15 August 2002

Robin O. Roundy  and
Gennady Samorodnitsky
Robin O. Roundy
Affiliation:
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, U.S.A.
Gennady Samorodnitsky
Affiliation:
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, U.S.A.
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Abstract

A Levy jump process is a continuous-time, real-valued stochasticprocess which has independent and stationary increments, with no Browniancomponent. We study some of the fundamental properties of Levy jumpprocesses and develop (s,S) inventory models for them. Of particularinterest to us is the gamma-distributed Levy process, in which the demandthat occurs in a fixed period of time has a gamma distribution.We study the relevant properties of these processes, and we develop aquadratically convergent algorithm for finding optimal (s,S) policies. Wedevelop a simpler heuristic policy and derive a bound on its relative cost. For the gamma-distributed Levy process this bound is 7.9% ifbackordering unfilled demand is at least twice as expensive as holdinginventory.Most easily-computed (s,S) inventory policies assume theinventory position to be uniform and assume that there is no overshoot. Ourtests indicate that these assumptions are dangerous when the coefficient ofvariation of the demand that occurs in the reorder interval is less than one. This is often the case for low-demand parts that experience sporadic orspiky demand. As long as the coefficient of variation of the demand thatoccurs in one reorder interval is at least one, and the service level isreasonably high, all of the polices we tested work very well. However evenin this region it is often the case that the standard Hadley–Whitin costfunction fails to have a local minimum.

Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 1 , January 2001 , pp. 37 - 70
Copyright
© EDP Sciences, 2001

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