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Some remarks on bayes solutions to the inventory problem

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  • Herbert E. Scarf

Abstract

A functional equation is described for the inventory problem in which the demand distribution contains an unknown parameter with a known a priori distribution. If the demand distribution is a member of the exponential family, then the minimum cost is a function of two variables: current stock and past mean demand. Some properties of the optimum policies are described, and some conditions are given which imply that the functional equation can be reduced to one involving functions of one variable only. Under these conditions, the computation of optimal policies becomes no more difficult than the corresponding computation with a known demand distribution.

Suggested Citation

  • Herbert E. Scarf, 1960. "Some remarks on bayes solutions to the inventory problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 7(4), pages 591-596, December.
    • Handle: RePEc:wly:navlog:v:7:y:1960:i:4:p:591-596
    DOI: 10.1002/nav.3800070428
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    Cited by:

    1. Arnab Bisi & Maqbool Dada, 2007. "Dynamic learning, pricing, and ordering by a censored newsvendor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 448-461, June.
    2. Yong Zhang & Vladimir Vovk & Weiguo Zhang, 2014. "Probability-free solutions to the non-stationary newsvendor problem," Annals of Operations Research, Springer, vol. 223(1), pages 433-449, December.
    3. Yun Fong Lim & Chen Wang, 2017. "Inventory Management Based on Target-Oriented Robust Optimization," Management Science, INFORMS, vol. 63(12), pages 4409-4427, December.
    4. Kaijie Zhu & Ulrich W. Thonemann, 2004. "An adaptive forecasting algorithm and inventory policy for products with short life cycles," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(5), pages 633-653, August.
    5. Xin, Linwei & Goldberg, David A., 2021. "Time (in)consistency of multistage distributionally robust inventory models with moment constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1127-1141.
    6. Nicholas C. Petruzzi & Maqbool Dada, 2002. "Dynamic pricing and inventory control with learning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 303-325, April.
    7. Harun Avci & Kagan Gokbayrak & Emre Nadar, 2020. "Structural Results for Average‐Cost Inventory Models with Markov‐Modulated Demand and Partial Information," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 156-173, January.
    8. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
    9. Mila Nambiar & David Simchi‐Levi & He Wang, 2021. "Dynamic Inventory Allocation with Demand Learning for Seasonal Goods," Production and Operations Management, Production and Operations Management Society, vol. 30(3), pages 750-765, March.
    10. 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.
    11. 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.
    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. Li, Tianyun & Fang, Weiguo & Baykal-Gürsoy, Melike, 2021. "Two-stage inventory management with financing under demand updates," International Journal of Production Economics, Elsevier, vol. 232(C).

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