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Risk pooling in a two‐period, two‐echelon inventory stocking and allocation problem

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  • Peter L. Jackson
  • John A. Muckstadt

Abstract

The object of this article is to investigate the risk‐pooling effect of depot stock in two‐echelon distribution system in which the depot serves n retailers in parallel, and to develop computationally tractable optimization procedures for such systems. The depot manager has complete information about stock levels and there are two opportunities to allocate stock to the retailers within each order cycle. We identify first‐ and second‐order aspects to the risk‐pooling effect. In particular, the second‐order effect is the property that the minimum stock available to any retailer after the second allocation converges in probability to a constant as the number of retailers in the system increases, assuming independence of the demands. This property is exploited in the development of efficient procedures to determine near‐optimal values of the policy parameters.

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  • Peter L. Jackson & John A. Muckstadt, 1989. "Risk pooling in a two‐period, two‐echelon inventory stocking and allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 1-26, February.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:1:p:1-26
    DOI: 10.1002/1520-6750(198902)36:13.0.CO;2-S
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    Cited by:

    1. Peter L. Jackson & John A. Muckstadt & Yuexing Li, 2019. "Multiperiod Stock Allocation via Robust Optimization," Management Science, INFORMS, vol. 65(2), pages 794-818, February.
    2. Huaxiao Shen & Tian Tian & Han Zhu, 2019. "A Two-Echelon Inventory System with a Minimum Order Quantity Requirement," Sustainability, MDPI, vol. 11(18), pages 1-22, September.
    3. Jérémie Gallien & Adam J. Mersereau & Andres Garro & Alberte Dapena Mora & Martín Nóvoa Vidal, 2015. "Initial Shipment Decisions for New Products at Zara," Operations Research, INFORMS, vol. 63(2), pages 269-286, April.
    4. De‐bi Cao & Edward A. Silver, 2005. "A dynamic allocation heuristic for centralized safety stock," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 513-526, September.
    5. Johan Marklund & Kaj Rosling, 2012. "Lower Bounds and Heuristics for Supply Chain Stock Allocation," Operations Research, INFORMS, vol. 60(1), pages 92-105, February.

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