### 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 language | English |
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Title of host publication | Operations, Logistics and Supply Chain Management |

Editors | Henk Zijm, Matthias Klumpp, Alberto Regattieri, Sunderesh Heragu |

Place of Publication | Cham |

Publisher | Springer |

Chapter | 20 |

Pages | 441-467 |

ISBN (Electronic) | 978-3-319-92447-2 |

ISBN (Print) | 978-3-319-92446-5 |

DOIs | |

Publication status | Published - 2019 |

### Publication series

Name | Lecture 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