Efficient optimization of the dual-index policy using Markov chains

J.J. Arts, M. Vuuren, van, G.P. Kiesmüller

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Abstract

3We consider the inventory control of a single product in one location with two supply sources facing stochastic demand. A premium is paid for each product ordered from the faster `emergency' supply source. Unsatistfied emand is backordered and ordering decisions are made periodically. The optimal control policy for this system is known to be complex. For this reason we study a type of base-stock policy known as the dual-index policy (DIP) as control mechanism for this inventory system. Under this policy ordering decisions are based on a regular and an emergency inventory position and their corresponding order-up-to-levels. Previous work on this policy assumes deterministic lead times and uses simulation to and their optimal order-up-to levels. We provide an alternate proof for the result that separates the optimization of the DIP in two one-dimensional problems. An insight from this proof allows us to generalize the model to accommodate stochastic regular lead times and provide an approximate evaluation method based on limiting results so that optimization can be done without simulation. An extensive numerical study shows that this approach yields excellent results for deterministic lead times and good results for stochastic lead times.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages28
ISBN (Print)978-90-386-2079-4
Publication statusPublished - 2009

Publication series

NameBETA publicatie : working papers
Volume291
ISSN (Print)1386-9213

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