Inventory replenishment control under supply uncertainty

Taesu Cheong () and Chelsea White ()

Annals of Operations Research, 2013, vol. 208, issue 1, 592 pages

Abstract: We consider a discrete state, discrete decision epoch inventory replenishment control problem under supply uncertainty. We assume that there is no backlogging, the single period demand d is deterministic, and once an item is placed in inventory, it will not perish. If a units of the product are ordered, then α units are placed into inventory with probability P(α|a), where $\sum_{\alpha=0}^{a}P(\alpha|a)=1$ . Let z=d−x, where x is the current inventory level. For the infinite horizon, total discounted cost criterion, we present conditions that guarantee that an optimal replenishment policy δ ∗ is such that δ ∗ (z)=0 for z≤0, δ ∗ (z)≥z≥0, and δ ∗ (z)−z is monotonically non-decreasing for z≥0. Such a “staircase” structure has a simple parametric description, which can help to accelerate value iteration and policy iteration. Copyright Springer Science+Business Media, LLC 2013

Keywords: Inventory systems; Periodic review; Supply uncertainty; Random yields; Markov decision processes (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10479-011-0929-9

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