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94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand

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  • Fangruo Chen

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

A two-stage inventory system is considered where Poisson demand occurs at Stage 1, and Stage 1 replenishes its inventory from Stage 2, which in turn orders from an outside supplier with unlimited stock. Each shipment, either to Stage 2 or to Stage 1, incurs a fixed setup cost. Under the assumption that the supply leadtime at Stage 2 is zero, we characterize a simple heuristic policy whose long-run average cost is guaranteed to be within 6% of optimality, i.e., a 94%-effective policy. The paper also provides heuristic policies for more general inventory systems and reports computational results.

Suggested Citation

  • Fangruo Chen, 1999. "94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand," Management Science, INFORMS, vol. 45(12), pages 1679-1696, December.
    • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:12:p:1679-1696
    DOI: 10.1287/mnsc.45.12.1679
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    References listed on IDEAS

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    1. Stephen C. Graves, 1985. "A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment," Management Science, INFORMS, vol. 31(10), pages 1247-1256, October.
    2. Marc A. De Bodt & Stephen C. Graves, 1985. "Continuous-Review Policies for a Multi-Echelon Inventory Problem with Stochastic Demand," Management Science, INFORMS, vol. 31(10), pages 1286-1299, October.
    3. Fangruo Chen, 1998. "Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging," Operations Research, INFORMS, vol. 46(3-supplem), pages 26-34, June.
    4. A. Federgruen & M. Queyranne & Yu-Sheng Zheng, 1992. "Simple Power-of-Two Policies are Close to Optimal in a General Class of Production/Distribution Networks with General Joint Setup Costs," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 951-963, November.
    5. Joseph S. B. Mitchell, 1987. "98%-Effective Lot-Sizing for One-Warehouse, Multi-Retailer Inventory Systems with Backlogging," Operations Research, INFORMS, vol. 35(3), pages 399-404, June.
    6. Awi Federgruen & Zvi Schechner, 1983. "Technical Note—Cost Formulas for Continuous Review Inventory Models with Fixed Delivery Lags," Operations Research, INFORMS, vol. 31(5), pages 957-965, October.
    7. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    8. Kamran Moinzadeh & Hau L. Lee, 1986. "Batch Size and Stocking Levels in Multi-Echelon Repairable Systems," Management Science, INFORMS, vol. 32(12), pages 1567-1581, December.
    9. Peter L. Jackson, 1988. "Stock Allocation in a Two-Echelon Distribution System Or "What to Do Until Your Ship Comes In"," Management Science, INFORMS, vol. 34(7), pages 880-895, July.
    10. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    11. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    12. Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    13. Derek Atkins & Daning Sun, 1995. "98%-Effective Lot Sizing for Series Inventory Systems with Backlogging," Operations Research, INFORMS, vol. 43(2), pages 335-345, April.
    14. 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.
    15. Paul Zipkin, 1986. "Inventory Service-Level Measures: Convexity and Approximation," Management Science, INFORMS, vol. 32(8), pages 975-981, August.
    16. Craig C. Sherbrooke, 1968. "Metric: A Multi-Echelon Technique for Recoverable Item Control," Operations Research, INFORMS, vol. 16(1), pages 122-141, February.
    17. Antony Svoronos & Paul Zipkin, 1991. "Evaluation of One-for-One Replenishment Policies for Multiechelon Inventory Systems," Management Science, INFORMS, vol. 37(1), pages 68-83, January.
    18. Fangruo Chen & Yu-Sheng Zheng, 1994. "Evaluating Echelon Stock (R, nQ) Policies in Serial Production/Inventory Systems with Stochastic Demand," Management Science, INFORMS, vol. 40(10), pages 1262-1275, October.
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