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Inventory Management with Partially Observed Nonstationary Demand

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  • Erhan Bayraktar
  • Mike Ludkovski

Abstract

We consider a continuous-time model for inventory management with Markov modulated non-stationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are completely met. We first derive the explicit filtering equations and pass to an equivalent fully observed impulse control problem in terms of the sufficient statistics, the a posteriori probability process and the current inventory level. We then solve this equivalent formulation and directly characterize an optimal inventory policy. We also describe a computational procedure to calculate the value function and the optimal policy and present two numerical illustrations.

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File URL: http://arxiv.org/pdf/1206.6283
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Paper provided by arXiv.org in its series Papers with number 1206.6283.

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Date of creation: Jun 2012
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Publication status: Published in Annals of Operations Research, 2010, 176 (1), 7-39
Handle: RePEc:arx:papers:1206.6283

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Web page: http://arxiv.org/

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  1. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
  2. Yossi Aviv & Amit Pazgal, 2005. "A Partially Observed Markov Decision Process for Dynamic Pricing," Management Science, INFORMS, vol. 51(9), pages 1400-1416, September.
  3. James T. Treharne & Charles R. Sox, 2002. "Adaptive Inventory Control for Nonstationary Demand and Partial Information," Management Science, INFORMS, vol. 48(5), pages 607-624, May.
  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, 1985. "Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution," Management Science, INFORMS, vol. 31(9), pages 1150-1160, September.
  6. Arjas, Elja & Haara, Pentti & Norros, Ikka, 1992. "Filtering the histories of a partially observed marked point process," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 225-250, March.
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