Document Type
Journal article
Source Publication
Naval Research Logistics (NRL)
Publication Date
2-1-2012
Volume
59
Issue
1
First Page
18
Last Page
25
Keywords
assemble-to-order, diophantine equations, irreducibility, necessary and sufficient condition, order-based backorders, unit-skeleton condition
Abstract
In a typical assemble-to-order system, a customer order may request multiple items, and the order may not be filled if any of the requested items are out of stock. A key customer service measure when unfilled orders are backordered is the order-based backorder level. To evaluate this crucial performance measure, a fundamental question is whether the stationary joint inventory positions follow an independent and uniform distribution. In this context, this is equivalent to the irreducibility of the Markov chain formed by the joint inventory positions. This article presents a necessary and sufficient condition for the irreducibility of such a Markov chain through a set of simultaneous Diophantine equations. This result also leads to sufficient conditions that are more general than those in the published reports.
DOI
10.1002/nav.20486
Print ISSN
0894069X
E-ISSN
15206750
Publisher Statement
Copyright © 2011 Wiley Periodicals, Inc
Access to external full text or publisher's version may require subscription.
Full-text Version
Pre-print
Language
English
Recommended Citation
Feng, J., Liu, L., & Wan, Y.-w. (2012). Irreducibility of joint inventory positions in an assemble-to-order system under (r, nQ) policies. Naval Research Logistics, 59(1), 18-25. doi: 10.1002/nav.20486