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Near-Optimal Echelon-Stock (R, nQ) Policies in Multistage Serial Systems

Author

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  • Fangruo Chen

    (Columbia University, New York, New York)

  • Yu-Sheng Zheng

    (University of Pennsylvania, Philadelphia, Pennsylvania)

Abstract

We study echelon-stock ( R , nQ ) policies in a multistage, serial inventory system with compound Poisson demand. We provide a simple method for determining near-optimal control parameters. This is achieved in two steps. First, we establish lower and upper bounds on the cost function by over- and under-charging a penalty cost to each upstream stage for holding inadequate stock. Second, we minimize the bounds, which are simple, separable functions of the control parameters, to obtain heuristic solutions. We also provide an algorithm that guarantees an optimal solution at the expense of additional computational effort. A numerical study suggests that the heuristic solutions are easy to compute (even for systems with many stages) and are close to optimal. It also suggests that a traditional approach for determining the order quantities can be seriously suboptimal. All the results can be easily extended to the discrete-time case with independent, identically distributed demands.

Suggested Citation

  • Fangruo Chen & Yu-Sheng Zheng, 1998. "Near-Optimal Echelon-Stock (R, nQ) Policies in Multistage Serial Systems," Operations Research, INFORMS, vol. 46(4), pages 592-602, August.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:4:p:592-602
    DOI: 10.1287/opre.46.4.592
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    References listed on IDEAS

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    1. Ralph D. Badinelli, 1992. "A Model for Continuous-Review Pull Policies in Serial Inventory Systems," Operations Research, INFORMS, vol. 40(1), pages 142-156, February.
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    Cited by:

    1. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    2. Kevin H. Shang & Sean X. Zhou, 2010. "Optimal and Heuristic Echelon ( r, nQ, T ) Policies in Serial Inventory Systems with Fixed Costs," Operations Research, INFORMS, vol. 58(2), pages 414-427, April.
    3. Kevin H. Shang, 2008. "Note: A Simple Heuristic for Serial Inventory Systems with Fixed Order Costs," Operations Research, INFORMS, vol. 56(4), pages 1039-1043, August.
    4. Agrawal, Narendra & Smith, Stephen A., 2019. "Optimal inventory management using retail prepacks," European Journal of Operational Research, Elsevier, vol. 274(2), pages 531-544.
    5. Kevin H. Shang & Jing-Sheng Song & Paul H. Zipkin, 2009. "Coordination Mechanisms in Decentralized Serial Inventory Systems with Batch Ordering," Management Science, INFORMS, vol. 55(4), pages 685-695, April.
    6. Xiuli Chao & Sean X. Zhou, 2009. "Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals," Operations Research, INFORMS, vol. 57(2), pages 377-390, April.
    7. Kevin H. Shang & Zhijie Tao & Sean X. Zhou, 2015. "Optimizing Reorder Intervals for Two-Echelon Distribution Systems with Stochastic Demand," Operations Research, INFORMS, vol. 63(2), pages 458-475, April.
    8. Jinfeng Yue & Bintong Chen & Min-Chiang Wang, 2006. "Expected Value of Distribution Information for the Newsvendor Problem," Operations Research, INFORMS, vol. 54(6), pages 1128-1136, December.
    9. Fernando Bernstein & Yang Li & Kevin Shang, 2016. "A Simple Heuristic for Joint Inventory and Pricing Models with Lead Time and Backorders," Management Science, INFORMS, vol. 62(8), pages 2358-2373, August.
    10. Amir Hosein Afshar Sedigh & Rasoul Haji & Seyed Mehdi Sajadifar, 2023. "The Cost Function of a Two-Level Inventory System with identical retailers benefitting from Information Sharing," Papers 2312.03898, arXiv.org.
    11. Kevin H. Shang & Jing-Sheng Song, 2007. "Serial Supply Chains with Economies of Scale: Bounds and Approximations," Operations Research, INFORMS, vol. 55(5), pages 843-853, October.
    12. Zhao, Qiu-Hong & Chen, Shuang & Zang, Cun-Xun, 2008. "Model and algorithm for inventory/routing decision in a three-echelon logistics system," European Journal of Operational Research, Elsevier, vol. 191(3), pages 623-635, December.
    13. Fangruo Chen, 1998. "Echelon Reorder Points, Installation Reorder Points, and the Value of Centralized Demand Information," Management Science, INFORMS, vol. 44(12-Part-2), pages 221-234, December.
    14. Ming Hu & Yi Yang, 2014. "Modified Echelon ( r, Q ) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems," Operations Research, INFORMS, vol. 62(4), pages 812-828, August.
    15. Fangruo Chen, 2000. "Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering," Operations Research, INFORMS, vol. 48(3), pages 376-389, June.

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