Stochastic Inventory Models

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.