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Inventory replenishment control under supply uncertainty

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  • Taesu Cheong
  • Chelsea White

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

Suggested Citation

  • Taesu Cheong & Chelsea White, 2013. "Inventory replenishment control under supply uncertainty," Annals of Operations Research, Springer, vol. 208(1), pages 581-592, September.
  • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:581-592:10.1007/s10479-011-0929-9
    DOI: 10.1007/s10479-011-0929-9
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    References listed on IDEAS

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    1. Eric Brodheim & Cyrus Derman & Gregory Prastacos, 1975. "On the Evaluation of a Class of Inventory Policies for Perishable Products Such as Blood," Management Science, INFORMS, vol. 21(11), pages 1320-1325, July.
    2. Abraham Grosfeld-Nir & Yigal Gerchak, 2004. "Multiple Lotsizing in Production to Order with Random Yields: Review of Recent Advances," Annals of Operations Research, Springer, vol. 126(1), pages 43-69, February.
    3. Woonghee Tim Huh & Mahesh Nagarajan, 2010. "Technical note ---Linear Inflation Rules for the Random Yield Problem: Analysis and Computations," Operations Research, INFORMS, vol. 58(1), pages 244-251, February.
    4. Mordechai Henig & Yigal Gerchak, 1990. "The Structure of Periodic Review Policies in the Presence of Random Yield," Operations Research, INFORMS, vol. 38(4), pages 634-643, August.
    5. Evan L. Porteus, 1971. "On the Optimality of Generalized (s, S) Policies," Management Science, INFORMS, vol. 17(7), pages 411-426, March.
    6. Candace Arai Yano & Hau L. Lee, 1995. "Lot Sizing with Random Yields: A Review," Operations Research, INFORMS, vol. 43(2), pages 311-334, April.
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