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A Censored-Data Multiperiod Inventory Problem with Newsvendor Demand Distributions

Author

Listed:
  • Arnab Bisi

    (Krannert School of Management, Purdue University, West Lafayette, Indiana 47907)

  • Maqbool Dada

    (Johns Hopkins Carey Business School, Baltimore, Maryland 21202)

  • Surya Tokdar

    (Department of Statistical Science, Duke University, Durham, North Carolina 27708)

Abstract

We study the stochastic multiperiod inventory problem in which demand in excess of available inventory is lost and unobserved so that demand data are censored. A Bayesian scheme is employed to dynamically update the demand distribution for the problem with storable or perishable inventory and with exogenous or endogenous price. We show that the Weibull is the only newsvendor distribution for which the optimal solution can be expressed in scalable form. Moreover, for Weibull demand the cost function is not convex in general. Nevertheless, in all but the storable case, sufficient structure can be discerned so that the optimal solution can be easily computed. Specifically, for the perishable inventory case, the optimal policy can be found by solving simple recursions, whereas the perishable case with pricing requires solutions to more complex one-step look-ahead recursions. Interestingly, for the special case of exponential demand the cost function is convex, so that for the storable inventory case, the optimal policy can be found using simple one-step look-ahead recursions whereas for the perishable case the optimal policy can be expressed by exact closed-form formulas.

Suggested Citation

  • Arnab Bisi & Maqbool Dada & Surya Tokdar, 2011. "A Censored-Data Multiperiod Inventory Problem with Newsvendor Demand Distributions," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 525-533, October.
    • Handle: RePEc:inm:ormsom:v:13:y:2011:i:4:p:525-533
    DOI: 10.1287/msom.1110.0340
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    References listed on IDEAS

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    Cited by:

    1. Wen Chen & Ying He, 2022. "Dynamic pricing and inventory control with delivery flexibility," Annals of Operations Research, Springer, vol. 317(2), pages 481-508, October.
    2. Tianhu Deng & Zuo-Jun Max Shen & J. George Shanthikumar, 2014. "Statistical Learning of Service-Dependent Demand in a Multiperiod Newsvendor Setting," Operations Research, INFORMS, vol. 62(5), pages 1064-1076, October.
    3. Adam J. Mersereau, 2015. "Demand Estimation from Censored Observations with Inventory Record Inaccuracy," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 335-349, July.
    4. Zhang, Jian & Zhang, Juliang & Hua, Guowei, 2016. "Multi-period inventory games with information update," International Journal of Production Economics, Elsevier, vol. 174(C), pages 119-127.
    5. Aditya Jain & Nils Rudi & Tong Wang, 2015. "Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is (Almost) All You Need," Operations Research, INFORMS, vol. 63(1), pages 134-150, February.
    6. Li Chen & Adam J.Mersereau & Zhe (Frank) Wang, 2017. "Optimal Merchandise Testing with Limited Inventory," Operations Research, INFORMS, vol. 65(4), pages 968-991, August.
    7. Bharadwaj Kadiyala & Özalp Özer & Alain Bensoussan, 2020. "A Mechanism Design Approach to Vendor Managed Inventory," Management Science, INFORMS, vol. 66(6), pages 2628-2652, June.
    8. Deligiannis, Michalis & Liberopoulos, George & Pandelis, Dimitrios G., 2023. "Managing supply chain risks with dual sourcing: Bayesian learning of censored supply capacity," International Journal of Production Economics, Elsevier, vol. 265(C).
    9. Zhang, Guoqing & Shi, Jianmai & Chaudhry, Sohail S. & Li, Xindan, 2019. "Multi-period multi-product acquisition planning with uncertain demands and supplier quantity discounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 117-140.
    10. Jiri Chod & Mihalis G. Markakis & Nikolaos Trichakis, 2021. "On the Learning Benefits of Resource Flexibility," Management Science, INFORMS, vol. 67(10), pages 6513-6528, October.
    11. Bansal, Vishal & Bisi, Arnab & Roy, Debjit & Venkateshan, Prahalad, 2024. "Integrated inventory replenishment and online demand allocation decisions for an omnichannel retailer with ship-from-store strategy," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1085-1100.
    12. Rong Li & Jing‐Sheng Jeannette Song & Shuxiao Sun & Xiaona Zheng, 2022. "Fight inventory shrinkage: Simultaneous learning of inventory level and shrinkage rate," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2477-2491, June.
    13. 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.

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