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Optimal Inventory Policies When the Demand Distribution is Not Known

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  • Erik W. Larson
  • Sunil Sharma
  • 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.

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Bibliographic Info

Paper provided by International Monetary Fund in its series IMF Working Papers with number 00/183.

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Length: 24
Date of creation: 01 Nov 2000
Date of revision:
Handle: RePEc:imf:imfwpa:00/183

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Keywords: Economic models; inventory; probability; statistics; equation; probabilities; inventory control; bayesian analysis; operations research; mathematical statistics; optimization; stochastic inventory control; algebra; mathematical methods; probability distributions; statistical decisions; random variables; consistent estimator; sample size; survey; sampling; binomial distributions; random sample; markov chain; probability distribution;

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  1. Donald L. Iglehart, 1964. "The Dynamic Inventory Problem with Unknown Demand Distribution," Management Science, INFORMS, INFORMS, vol. 10(3), pages 429-440, April.
  2. William S. Lovejoy, 1990. "Myopic Policies for Some Inventory Models with Uncertain Demand Distributions," Management Science, INFORMS, INFORMS, vol. 36(6), pages 724-738, June.
  3. Michael Rothschild, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown: A Summary," NBER Chapters, National Bureau of Economic Research, Inc, in: Annals of Economic and Social Measurement, Volume 3, number 1, pages 293-294 National Bureau of Economic Research, Inc.
  4. Katy S. Azoury & Bruce L. Miller, 1984. "A Comparison of the Optimal Ordering Levels of Bayesian and Non-Bayesian Inventory Models," Management Science, INFORMS, INFORMS, vol. 30(8), pages 993-1003, August.
  5. Rothschild, Michael, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 82(4), pages 689-711, July/Aug..
  6. Katy S. Azoury, 1985. "Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution," Management Science, INFORMS, INFORMS, vol. 31(9), pages 1150-1160, September.
  7. S. Bikhchandani & S. Sharma, 1990. "Optimal Search with Learning," UCLA Economics Working Papers, UCLA Department of Economics 580, UCLA Department of Economics.
  8. Dutta, Prajit K. & Majumdar, Mukul K. & Sundaram, Rangarajan K., 1994. "Parametric continuity in dynamic programming problems," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 18(6), pages 1069-1092, November.
  9. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, INFORMS, vol. 6(3), pages 231-258, April.
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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, Tilburg University, Center for Economic Research 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, Elsevier, vol. 118(1), pages 34-42, March.

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