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Optimal Inventory Policies when the Demand Distribution is not Known

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  • Erik W. Larson
  • Mr. Sunil Sharma
  • Mr. Lars J. Olson

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.

Suggested Citation

  • Erik W. Larson & Mr. Sunil Sharma & Mr. Lars J. Olson, 2000. "Optimal Inventory Policies when the Demand Distribution is not Known," IMF Working Papers 2000/183, International Monetary Fund.
    • Handle: RePEc:imf:imfwpa:2000/183
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    References listed on IDEAS

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    1. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
    2. Dutta, Prajit K. & Majumdar, Mukul K. & Sundaram, Rangarajan K., 1994. "Parametric continuity in dynamic programming problems," Journal of Economic Dynamics and Control, Elsevier, vol. 18(6), pages 1069-1092, November.
    3. 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.
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    5. William S. Lovejoy, 1993. "Suboptimal Policies, with Bounds, for Parameter Adaptive Decision Processes," Operations Research, INFORMS, vol. 41(3), pages 583-599, June.
    6. 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..
    7. William S. Lovejoy, 1990. "Myopic Policies for Some Inventory Models with Uncertain Demand Distributions," Management Science, INFORMS, vol. 36(6), pages 724-738, June.
    8. Katy S. Azoury, 1985. "Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution," Management Science, INFORMS, vol. 31(9), pages 1150-1160, September.
    9. Bikhchandani, Sushil & Sharma, Sunil, 1996. "Optimal search with learning," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 333-359.
    10. 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.
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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," Other publications TiSEM e61834bf-8202-4a25-9311-f, Tilburg University, School of Economics and Management.
    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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