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Optimal Inventory Policies when the Demand Distribution is not Known

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

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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Paper provided by The A. Gary Anderson Graduate School of Management. University of California Riverside in its series The A. Gary Anderson Graduate School of Management with number 92-12.

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Length: 34 pages
Date of creation: 1992
Date of revision:
Handle: RePEc:fth:caland:92-12
Contact details of provider: Postal: The A. Gary Anderson Graduate School of Management. University of California, Riverside. Riverside CA 92521
Web page: http://www.agsm.ucr.edu/
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  1. 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.
  2. S. Bikhchandani & S. Sharma, 1990. "Optimal Search with Learning," UCLA Economics Working Papers 580, UCLA Department of Economics.
  3. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
  4. William S. Lovejoy, 1990. "Myopic Policies for Some Inventory Models with Uncertain Demand Distributions," Management Science, INFORMS, vol. 36(6), pages 724-738, June.
  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. 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.
  7. 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..
  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. Donald L. Iglehart, 1964. "The Dynamic Inventory Problem with Unknown Demand Distribution," Management Science, INFORMS, vol. 10(3), pages 429-440, April.
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