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On the Optimal Policy Structure in Serial Inventory Systems with Lost Sales

Author

Listed:
  • Woonghee Tim Huh

    (Industrial Engineering and Operations Research Department, Columbia University, New York, New York 10027)

  • Ganesh Janakiraman

    (Stern School of Business, New York University, New York, New York 10012)

Abstract

We study a periodically reviewed, serial inventory system in which excess demand from external customers is lost. We derive elementary properties of the vector of optimal order quantities in this system. In particular, we derive bounds on the sensitivity (or, more mathematically, the derivative) of the optimal order quantity at each stage to the vector of the current inventory levels. Our analysis uses the concept of L -natural-convexity, which was studied in discrete convex analysis and recently used in the study of single-stage inventory systems with lost sales. We also remark on how our analysis extends to models with capacity constraints and/or backordering.

Suggested Citation

  • Woonghee Tim Huh & Ganesh Janakiraman, 2010. "On the Optimal Policy Structure in Serial Inventory Systems with Lost Sales," Operations Research, INFORMS, vol. 58(2), pages 486-491, April.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:2:p:486-491
    DOI: 10.1287/opre.1090.0716
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    References listed on IDEAS

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    1. Ganesh Janakiraman & John A. Muckstadt, 2009. "A Decomposition Approach for a Class of Capacitated Serial Systems," Operations Research, INFORMS, vol. 57(6), pages 1384-1393, December.
    2. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    3. Yingdong Lu & Jing-Sheng Song, 2005. "Order-Based Cost Optimization in Assemble-to-Order Systems," Operations Research, INFORMS, vol. 53(1), pages 151-169, February.
    4. Paul Zipkin, 2008. "On the Structure of Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 56(4), pages 937-944, August.
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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. Anyan Qi & Hyun-Soo Ahn & Amitabh Sinha, 2017. "Capacity Investment with Demand Learning," Operations Research, INFORMS, vol. 65(1), pages 145-164, February.
    3. Ang, Marcus & Song, Jing-Sheng & Wang, Mingzheng & Zhang, Hanqin, 2013. "On properties of discrete (r, q) and (s, T) inventory systems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 95-105.
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    8. Xiting Gong & Xiuli Chao, 2013. "Technical Note---Optimal Control Policy for Capacitated Inventory Systems with Remanufacturing," Operations Research, INFORMS, vol. 61(3), pages 603-611, June.
    9. Xin Chen & Zhan Pang & Limeng Pan, 2014. "Coordinating Inventory Control and Pricing Strategies for Perishable Products," Operations Research, INFORMS, vol. 62(2), pages 284-300, April.
    10. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    11. Yi Yang & Youhua (Frank) Chen & Yun Zhou, 2014. "Coordinating Inventory Control and Pricing Strategies Under Batch Ordering," Operations Research, INFORMS, vol. 62(1), pages 25-37, February.
    12. Zhan Pang & Frank Y. Chen & Youyi Feng, 2012. "Technical Note---A Note on the Structure of Joint Inventory-Pricing Control with Leadtimes," Operations Research, INFORMS, vol. 60(3), pages 581-587, June.
    13. Xin Chen & Menglong Li, 2021. "Discrete Convex Analysis and Its Applications in Operations: A Survey," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1904-1926, June.
    14. Zhuang, Weifen & Li, Michael Z.F., 2012. "Monotone optimal control for a class of Markov decision processes," European Journal of Operational Research, Elsevier, vol. 217(2), pages 342-350.
    15. Qing Li & Peiwen Yu, 2014. "Multimodularity and Its Applications in Three Stochastic Dynamic Inventory Problems," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 455-463, July.
    16. Goko, Hiromichi & Igarashi, Ayumi & Kawase, Yasushi & Makino, Kazuhisa & Sumita, Hanna & Tamura, Akihisa & Yokoi, Yu & Yokoo, Makoto, 2024. "A fair and truthful mechanism with limited subsidy," Games and Economic Behavior, Elsevier, vol. 144(C), pages 49-70.
    17. Tong Wang & Xiting Gong & Sean X. Zhou, 2017. "Dynamic Inventory Management with Total Minimum Order Commitments and Two Supply Options," Operations Research, INFORMS, vol. 65(5), pages 1285-1302, October.
    18. Mohammadreza Bolandnazar & Woonghee Tim Huh & S. Thomas McCormick & Kazuo Murota, 2019. "Technical Note—Error Noted in “Order-Based Cost Optimization in Assemble-to-Order Systems” by Lu and Song (2005)," Operations Research, INFORMS, vol. 67(1), pages 163-166, January.
    19. Anyan Qi & Hyun-Soo Ahn & Amitabh Sinha, 2017. "Capacity Investment with Demand Learning," Operations Research, INFORMS, vol. 65(1), pages 145-164, February.
    20. David A. Goldberg & Dmitriy A. Katz-Rogozhnikov & Yingdong Lu & Mayank Sharma & Mark S. Squillante, 2016. "Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 898-913, August.
    21. Liping Zhou & Na Geng & Zhibin Jiang & Shan Jiang, 2022. "Integrated Multiresource Capacity Planning and Multitype Patient Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 129-149, January.
    22. 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.
    23. Saif Benjaafar & David Chen & Rowan Wang, 2017. "Managing Production-Inventory Systems with Scarce Resources," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 216-229, May.
    24. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    25. Acar, Müge & Kaya, Onur, 2023. "Dynamic inventory decisions for humanitarian aid materials considering budget limitations," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).

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