Stochastic Inventory Models

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Abstract

We discuss inventory systems in an independent demand setting, where demand over time is modeled as a stationary stochastic process. We begin with some basic notions and definitions on inventory management, followed by a discussion of well-known (and applied) control systems. Under periodic review and a linear cost structure, it is known that the optimal control policy has a critical level structure, hence we analyze such critical level policies in detail. After that, in an advanced section, we turn to multi-echelon or multi-stage systems. We present a complete analysis of the decomposition result proven initially by Clark and Scarf, and its analogue in distribution systems, i.e., systems with an arborescent instead of a linear structure (state-of-the-art). Computational aspects are briefly discussed after which we close with some guidelines for further reading.
Original languageEnglish
Title of host publicationOperations, Logistics and Supply Chain Management
EditorsHenk Zijm, Matthias Klumpp, Alberto Regattieri, Sunderesh Heragu
Place of PublicationCham
PublisherSpringer
Chapter20
Pages441-467
ISBN (Electronic)978-3-319-92447-2
ISBN (Print)978-3-319-92446-5
DOIs
Publication statusPublished - 2019

Publication series

NameLecture notes in logistics

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  • Cite this

    Zijm, H. (2019). Stochastic Inventory Models. In H. Zijm, M. Klumpp, A. Regattieri, & S. Heragu (Eds.), Operations, Logistics and Supply Chain Management (pp. 441-467). (Lecture notes in logistics). Cham: Springer. https://doi.org/10.1007/978-3-319-92447-2_20