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Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution

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  • Katy S. Azoury

    (School of Business Administration and Economics, California State University, Northridge, California 91330)

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    Abstract

    This paper considers the periodic review inventory problem for which one or more parameters of the demand distribution are unknown with a known prior distribution chosen from the natural conjugate family. The Bayesian formulation of this problem results in a dynamic program with a multi-dimensional state space. Two models are analysed: the depletive inventory model of consumable items and the nondepletive model of reparable items. For both models and for some specific demand distributions, it is shown that the solution of the Bayesian model can be reduced to that of solving another dynamic program with a one-dimensional state space. Moreover, an explicit form for the optimal Bayesian ordering policy is given in each case.

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    File URL: http://dx.doi.org/10.1287/mnsc.31.9.1150
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 31 (1985)
    Issue (Month): 9 (September)
    Pages: 1150-1160

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    Handle: RePEc:inm:ormnsc:v:31:y:1985:i:9:p:1150-1160

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    Related research

    Keywords: inventory control; unknown demand; dynamic programming;

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    Cited by:
    1. Graves, Stephen C., 1997. "A single-item inventory model for a non-stationary demand process," Working papers WP 3944-97., Massachusetts Institute of Technology (MIT), Sloan School of 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. Larson, C.E. & Olson, L.J. & Sharma, S., 1992. "Optimal Inventory Policies when the Demand Distribution is not Known," The A. Gary Anderson Graduate School of Management 92-12, The A. Gary Anderson Graduate School of Management. University of California Riverside.
    4. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand," MPRA Paper 39650, University Library of Munich, Germany.
    5. Janssen, E. & Strijbosch, L.W.G. & Brekelmans, R.C.M., 2006. "Assessing the Effects of using Demand Parameters Estimates in Inventory Control," Discussion Paper 2006-90, Tilburg University, Center for Economic Research.
    6. Bitran, Gabriel R. & Wadhwa, Hitendra K. S. (Hitendra Kumar Singh), 1996. "A methodology for demand learning with an application to the optimal pricing of seasonal products," Working papers 3898-96., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    8. Marbán Sebastián & Rutten Cyriel & Vredeveld Tjark, 2010. "Tight performance in Bayesian Scheduling," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Glenn, David & Bisi, Arnab & Puterman, Martin L., 2004. "The Bayesian Newsvendors in Supply Chains with Unobserved Lost Sales," Working Papers 04-0110, University of Illinois at Urbana-Champaign, College of Business.
    10. Erhan Bayraktar & Mike Ludkovski, 2012. "Inventory Management with Partially Observed Nonstationary Demand," Papers 1206.6283, arXiv.org.
    11. Choi, Tsan-Ming, 2007. "Pre-season stocking and pricing decisions for fashion retailers with multiple information updating," International Journal of Production Economics, Elsevier, vol. 106(1), pages 146-170, March.
    12. Tan, Tarkan & Gullu, Refik & Erkip, Nesim, 2007. "Modelling imperfect advance demand information and analysis of optimal inventory policies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 897-923, March.
    13. Choi, Tsan-Ming & Chow, Pui-Sze, 2008. "Mean-variance analysis of Quick Response Program," International Journal of Production Economics, Elsevier, vol. 114(2), pages 456-475, August.
    14. Agrawal, Narendra & Smith, Stephen A., 2013. "Optimal inventory management for a retail chain with diverse store demands," European Journal of Operational Research, Elsevier, vol. 225(3), pages 393-403.

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