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A Series System with Returns: Stationary Analysis

Author

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  • Gregory DeCroix

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Jing-Sheng Song

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Paul Zipkin

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

This paper analyzes a series inventory system with stationary costs and stochastic demand over an infinite horizon. A distinctive feature is that demand can be negative, representing returns from customers, as well as zero or positive. We observe that, as in a system with nonnegative demand, a stationary echelon base-stock policy is optimal here. However, the steady-state behavior of the system under such a policy is different from that in systems with nonnegative demands. We present an exact procedure and several approximations for computing the operating characteristics and system costs for any stationary echelon base-stock policy, and also describe an algorithm for computing a good policy. As an alternative to the echelon base-stock policy, we discuss a policy that uses only local information. Finally, we describe how to extend the analysis to the case where returns occur at multiple stages instead of just at the stage closest to demand, and the case where returns require a recovery lead time.

Suggested Citation

  • Gregory DeCroix & Jing-Sheng Song & Paul Zipkin, 2005. "A Series System with Returns: Stationary Analysis," Operations Research, INFORMS, vol. 53(2), pages 350-362, April.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:2:p:350-362
    DOI: 10.1287/opre.1040.0184
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    References listed on IDEAS

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    Cited by:

    1. Tomoaki Yamazaki & Keisuke Shida & Takashi Kanazawa, 2016. "An approach to establishing a method for calculating inventory," International Journal of Production Research, Taylor & Francis Journals, vol. 54(8), pages 2320-2331, April.
    2. Feng, Yan & Viswanathan, S., 2014. "Heuristics with guaranteed performance bounds for a manufacturing system with product recovery," European Journal of Operational Research, Elsevier, vol. 232(2), pages 322-329.
    3. Xuanming Su, 2009. "Consumer Returns Policies and Supply Chain Performance," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 595-612, March.
    4. Alexandar Angelus, 2011. "A Multiechelon Inventory Problem with Secondary Market Sales," Management Science, INFORMS, vol. 57(12), pages 2145-2162, December.
    5. Peter Berling & Victor Martínez‐de‐Albéniz, 2016. "A characterization of optimal base‐stock levels for a multistage serial supply chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(1), pages 32-46, February.
    6. Gregory A. DeCroix & Jing-Sheng Song & Paul H. Zipkin, 2009. "Managing an Assemble-to-Order System with Returns," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 144-159, October.
    7. Wei Huang & Vidyadhar Kulkarni & Jayashankar M. Swaminathan, 2008. "Managing the Inventory of an Item with a Replacement Warranty," Management Science, INFORMS, vol. 54(8), pages 1441-1452, August.
    8. Gregory A. DeCroix, 2006. "Optimal Policy for a Multiechelon Inventory System with Remanufacturing," Operations Research, INFORMS, vol. 54(3), pages 532-543, June.
    9. Gad Allon & Jan A. Van Mieghem, 2010. "Global Dual Sourcing: Tailored Base-Surge Allocation to Near- and Offshore Production," Management Science, INFORMS, vol. 56(1), pages 110-124, January.
    10. Linwei Xin & David A. Goldberg, 2018. "Asymptotic Optimality of Tailored Base-Surge Policies in Dual-Sourcing Inventory Systems," Management Science, INFORMS, vol. 64(1), pages 437-452, January.
    11. Lin, Yizhong & Leung, Janny M.Y. & Zhang, Lianmin & Gu, Jia-Wen, 2020. "Single-item repairable inventory system with stochastic new and warranty demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    12. Gregory A. DeCroix & Paul H. Zipkin, 2005. "Inventory Management for an Assembly System with Product or Component Returns," Management Science, INFORMS, vol. 51(8), pages 1250-1265, August.
    13. Wei, Cansheng & Li, Yongjian & Cai, Xiaoqiang, 2011. "Robust optimal policies of production and inventory with uncertain returns and demand," International Journal of Production Economics, Elsevier, vol. 134(2), pages 357-367, December.
    14. V. Daniel R. Guide & Luk N. Van Wassenhove, 2009. "OR FORUM---The Evolution of Closed-Loop Supply Chain Research," Operations Research, INFORMS, vol. 57(1), pages 10-18, February.
    15. Zerhouni, Hichem & Gayon, Jean-Philippe & Frein, Yannick, 2013. "Influence of dependency between demands and returns in a reverse logistics system," International Journal of Production Economics, Elsevier, vol. 143(1), pages 62-71.
    16. Jing-Sheng Song & Paul Zipkin, 2013. "Supply Streams," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 444-457, July.
    17. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.

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