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Optimal Inventory Policies when the Demand Distribution Is Not Known

  • Larson, C. Erik
  • Olson, Lars J.
  • Sharma, Sunil

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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File URL: http://www.sciencedirect.com/science/article/B6WJ3-457D4K0-V/2/10a10c6f12f632293a4c8a6345ce8db8
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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 101 (2001)
Issue (Month): 1 (November)
Pages: 281-300

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Handle: RePEc:eee:jetheo:v:101:y:2001:i:1:p:281-300
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Donald L. Iglehart, 1964. "The Dynamic Inventory Problem with Unknown Demand Distribution," Management Science, INFORMS, vol. 10(3), pages 429-440, April.
  2. 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..
  3. S. Bikhchandani & S. Sharma, 1990. "Optimal Search with Learning," UCLA Economics Working Papers 580, UCLA Department of Economics.
  4. Katy S. Azoury, 1985. "Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution," Management Science, INFORMS, vol. 31(9), pages 1150-1160, September.
  5. 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.
  6. William S. Lovejoy, 1990. "Myopic Policies for Some Inventory Models with Uncertain Demand Distributions," Management Science, INFORMS, vol. 36(6), pages 724-738, June.
  7. 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.
  8. 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.
  9. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
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