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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.

Suggested Citation

  • 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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    References listed on IDEAS

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    1. Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
    2. Awi Federgruen & Paul Zipkin, 1984. "Approximations of Dynamic, Multilocation Production and Inventory Problems," Management Science, INFORMS, vol. 30(1), pages 69-84, January.
    3. William L. Maxwell & John A. Muckstadt, 1985. "Establishing Consistent and Realistic Reorder Intervals in Production-Distribution Systems," Operations Research, INFORMS, vol. 33(6), pages 1316-1341, December.
    4. Dieter Hochstaedter, 1970. "An Approximation of the Cost Function for Multi-Echelon Inventory Model," Management Science, INFORMS, vol. 16(11), pages 716-727, July.
    5. Stephen C. Allen, 1958. "Redistribution of total stock over several user locations," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 5(4), pages 337-345, December.
    6. S. G. Allen, 1962. "Computation for the Redistribution Model with Set-Up Charge," Management Science, INFORMS, vol. 8(4), pages 482-489, July.
    7. G. Hadley & T. M. Whitin, 1961. "A model for procurement, allocation, and redistribution for low demand items," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 8(4), pages 395-414, December.
    8. Bruce L. Miller, 1974. "Dispatching from Depot Repair in a Recoverable Item Inventory System: On the Optimality of a Heuristic Rule," Management Science, INFORMS, vol. 21(3), pages 316-325, November.
    9. Yoichiro Fukuda, 1961. "Optimal disposal policies," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 8(3), pages 221-227, September.
    10. Gregory P. Prastacos, 1981. "Allocation of a Perishable Product Inventory," Operations Research, INFORMS, vol. 29(1), pages 95-107, February.
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    Cited by:

    1. 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.
    2. Johan Marklund & Kaj Rosling, 2012. "Lower Bounds and Heuristics for Supply Chain Stock Allocation," Operations Research, INFORMS, vol. 60(1), pages 92-105, February.
    3. 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.
    4. 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.
    5. 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.

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