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Optimal inventory control with path-dependent cost criteria

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  • Weerasinghe, Ananda
  • Zhu, Chao

Abstract

This paper deals with a stochastic control problem arising from inventory control, in which the cost structure depends on the current position as well as the running maximum of the state process. A control mechanism is introduced to control the growth of the running maximum which represents the required storage capacity. The infinite horizon discounted cost minimization problem is addressed and it is used to derive a complete solution to the long-run average cost minimization problem. An associated control cost minimization problem subject to a storage capacity constraint is also addressed. Finally, as an application of the above results, a related infinite-horizon discounted control problem with a regime-switching inventory model is also solved.

Suggested Citation

  • Weerasinghe, Ananda & Zhu, Chao, 2016. "Optimal inventory control with path-dependent cost criteria," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1585-1621.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:6:p:1585-1621
    DOI: 10.1016/j.spa.2015.11.014
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    References listed on IDEAS

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    1. J. Michael Harrison & Thomas M. Sellke & Allison J. Taylor, 1983. "Impulse Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 454-466, August.
    2. Alain Bensoussan & Lama Moussawi-Haidar & Metin Çakanyıldırım, 2010. "Inventory control with an order-time constraint: optimality, uniqueness and significance," Annals of Operations Research, Springer, vol. 181(1), pages 603-640, December.
    3. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2010. "Optimal Control of a Mean-Reverting Inventory," Operations Research, INFORMS, vol. 58(6), pages 1697-1710, December.
    4. Burdzy, Krzysztof & Kang, Weining & Ramanan, Kavita, 2009. "The Skorokhod problem in a time-dependent interval," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 428-452, February.
    5. Jennifer M. George & J. Michael Harrison, 2001. "Dynamic Control of a Queue with Adjustable Service Rate," Operations Research, INFORMS, vol. 49(5), pages 720-731, October.
    6. Fleischmann, Moritz & Kuik, Roelof, 2003. "On optimal inventory control with independent stochastic item returns," European Journal of Operational Research, Elsevier, vol. 151(1), pages 25-37, November.
    7. Agnès Sulem, 1986. "A Solvable One-Dimensional Model of a Diffusion Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 125-133, February.
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    Cited by:

    1. Lijun Bo & Huafu Liao & Xiang Yu, 2020. "Optimal Tracking Portfolio with A Ratcheting Capital Benchmark," Papers 2006.13661, arXiv.org, revised Apr 2021.
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    3. Lijun Bo & Yijie Huang & Xiang Yu, 2023. "Stochastic control problems with state-reflections arising from relaxed benchmark tracking," Papers 2302.08302, arXiv.org, revised Aug 2023.
    4. Amir Ahmadi-Javid & Mohsen Ebadi, 2021. "Economic design of memory-type control charts: The fallacy of the formula proposed by Lorenzen and Vance (1986)," Computational Statistics, Springer, vol. 36(1), pages 661-690, March.

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