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Optimal Inventory Policies when the Demand Distribution is not Known

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  • Larson, C.E.
  • Olson, L.J.
  • Sharma, S.

Abstract

This paper analyzes the stochastic inventory control problem when the demand distribution is not known. In contrast to previous Bayesian inventory models, this paper adopts a non-parametric Bayesian approach in which the firm’s prior information is characterized by a Dirichlet process prior. This provides considerable freedom in the specification of prior information about demand and it permits the accommodation of fixed order costs. As information on the demand distribution accumulates, optimal history-dependent (s,S) rules are shown to converge to an (s,S) rule that is optimal when the underlying demand distribution is known.
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  • Larson, C.E. & Olson, L.J. & Sharma, S., 1992. "Optimal Inventory Policies when the Demand Distribution is not Known," The A. Gary Anderson Graduate School of Management 92-12, The A. Gary Anderson Graduate School of Management. University of California Riverside.
    • Handle: RePEc:fth:caland:92-12
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    References listed on IDEAS

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    1. Rothschild, Michael, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 689-711, July/Aug..
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    5. Bikhchandani, Sushil & Sharma, Sunil, 1996. "Optimal search with learning," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 333-359.
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    7. Katy S. Azoury & Bruce L. Miller, 1984. "A Comparison of the Optimal Ordering Levels of Bayesian and Non-Bayesian Inventory Models," Management Science, INFORMS, vol. 30(8), pages 993-1003, August.
    8. Michael Rothschild, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown: A Summary," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 1, pages 293-294, National Bureau of Economic Research, Inc.
    9. Donald L. Iglehart, 1964. "The Dynamic Inventory Problem with Unknown Demand Distribution," Management Science, INFORMS, vol. 10(3), pages 429-440, April.
    10. William S. Lovejoy, 1993. "Suboptimal Policies, with Bounds, for Parameter Adaptive Decision Processes," Operations Research, INFORMS, vol. 41(3), pages 583-599, June.
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    Cited by:

    1. Janssen, E. & Strijbosch, L.W.G. & Brekelmans, R.C.M., 2006. "Assessing the Effects of using Demand Parameters Estimates in Inventory Control," Discussion Paper 2006-90, Tilburg University, Center for Economic Research.
    2. Janssen, Elleke & Strijbosch, Leo & Brekelmans, Ruud, 2009. "Assessing the effects of using demand parameters estimates in inventory control and improving the performance using a correction function," International Journal of Production Economics, Elsevier, vol. 118(1), pages 34-42, March.
    3. Mor Armony & Erica L. Plambeck, 2005. "The Impact of Duplicate Orders on Demand Estimation and Capacity Investment," Management Science, INFORMS, vol. 51(10), pages 1505-1518, October.
    4. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.

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