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Inventory Problems with Partially Observed Demands and Lost Sales

Author

Listed:
  • A. Bensoussan

    (University of Texas at Dallas)

  • M. Çakanyıldırım

    (University of Texas at Dallas)

  • J. A. Minjárez-Sosa

    (University of Texas at Dallas)

  • A. Royal

    (University of Texas at Dallas)

  • S. P. Sethi

    (University of Texas at Dallas)

Abstract

This paper considers the case of partially observed demand in the context of a multi-period inventory problem with lost sales. Demand in a period is observed if it is less than the inventory level in that period and the leftover inventory is carried over to the next period. Otherwise, only the event that it is larger than or equal to the inventory level is observed. These observations are used to update the demand distributions over time. The state of the resulting dynamic program consists of the current inventory level and the current demand distribution, which is infinite dimensional. The state evolution equation for the demand distribution becomes linear with the use of unnormalized probabilities. We study two demand cases. First, the demands evolve according to a Markov chain. Second, the demand distribution has an unknown parameter which is updated in the Bayesian manner. In both cases, we prove the existence of an optimal feedback ordering policy.

Suggested Citation

  • A. Bensoussan & M. Çakanyıldırım & J. A. Minjárez-Sosa & A. Royal & S. P. Sethi, 2008. "Inventory Problems with Partially Observed Demands and Lost Sales," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 321-340, March.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:3:d:10.1007_s10957-007-9311-0
    DOI: 10.1007/s10957-007-9311-0
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    References listed on IDEAS

    as
    1. Alain Bensoussan & Metin Çakanyıldırım & Suresh P. Sethi, 2007. "A Multiperiod Newsvendor Problem with Partially Observed Demand," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 322-344, May.
    2. Xiaomei Ding & Martin L. Puterman & Arnab Bisi, 2002. "The Censored Newsvendor and the Optimal Acquisition of Information," Operations Research, INFORMS, vol. 50(3), pages 517-527, June.
    3. Xiangwen Lu & Jing-Sheng Song & Kaijie Zhu, 2005. "On “The Censored Newsvendor and the Optimal Acquisition of Information”," Operations Research, INFORMS, vol. 53(6), pages 1024-1026, December.
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    Cited by:

    1. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2023. "Inventory control with modulated demand and a partially observed modulation process," Annals of Operations Research, Springer, vol. 321(1), pages 343-369, February.
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    3. Alain Bensoussan & Pengfei Guo, 2015. "Technical Note—Managing Nonperishable Inventories with Learning About Demand Arrival Rate Through Stockout Times," Operations Research, INFORMS, vol. 63(3), pages 602-609, June.
    4. 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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