IDEAS home Printed from
   My bibliography  Save this article

The Dynamic Inventory Problem with Unknown Demand Distribution


  • Donald L. Iglehart

    (Cornell University)


In this paper we consider the dynamic inventory problem in which the demand distribution possesses a density belonging to either the exponential or range family of densities and having an unknown parameter. An a priori density is chosen for the unknown parameter. Using a Bayesian estimation scheme, inequalities are obtained for the optimal purchase policies as the amount of demand information varies. In addition, asymptotic expansions for the optimal policies are found as the number of observations of the demand becomes large. This paper extends the results of Scarf, [8].

Suggested Citation

  • Donald L. Iglehart, 1964. "The Dynamic Inventory Problem with Unknown Demand Distribution," Management Science, INFORMS, vol. 10(3), pages 429-440, April.
  • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:3:p:429-440

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. M. E. Salveson, 1956. "A Problem in Optimal Machine Loading," Management Science, INFORMS, vol. 2(3), pages 232-260, April.
    2. M. Beckman & R. Muth, 1956. "An Inventory Policy for a Case of Lagged Delivery," Management Science, INFORMS, vol. 2(2), pages 145-155, January.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Berk, Emre & Gurler, Ulku & Levine, Richard A., 2007. "Bayesian demand updating in the lost sales newsvendor problem: A two-moment approximation," European Journal of Operational Research, Elsevier, vol. 182(1), pages 256-281, October.
    2. Larson, C. Erik & Olson, Lars J. & Sharma, Sunil, 2001. "Optimal Inventory Policies when the Demand Distribution Is Not Known," Journal of Economic Theory, Elsevier, vol. 101(1), pages 281-300, November.
    3. Prak, Dennis & Teunter, Ruud & Syntetos, Aris, 2017. "On the calculation of safety stocks when demand is forecasted," European Journal of Operational Research, Elsevier, vol. 256(2), pages 454-461.
    4. Ghate, Archis, 2015. "Optimal minimum bids and inventory scrapping in sequential, single-unit, Vickrey auctions with demand learning," European Journal of Operational Research, Elsevier, vol. 245(2), pages 555-570.
    5. 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.
    6. Bulinskaya, E. V., 2004. "Stochastic orders and inventory problems," International Journal of Production Economics, Elsevier, vol. 88(2), pages 125-135, March.
    7. Srinagesh Gavirneni & Roman Kapuscinski & Sridhar Tayur, 1999. "Value of Information in Capacitated Supply Chains," Management Science, INFORMS, vol. 45(1), pages 16-24, January.
    8. Sen, Alper & Zhang, Alex X., 2009. "Style goods pricing with demand learning," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1058-1075, August.
    9. Katy S. Azoury & Julia Miyaoka, 2009. "Optimal Policies and Approximations for a Bayesian Linear Regression Inventory Model," Management Science, INFORMS, vol. 55(5), pages 813-826, May.
    10. Joseph M. Milner & Panos Kouvelis, 2002. "On the Complementary Value of Accurate Demand Information and Production and Supplier Flexibility," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 99-113, December.
    11. Zhang, Jian & Zhang, Juliang & Hua, Guowei, 2016. "Multi-period inventory games with information update," International Journal of Production Economics, Elsevier, vol. 174(C), pages 119-127.
    12. Srinagesh Gavirneni & Sridhar Tayur, 1999. "Managing a Customer Following a Target Reverting Policy," Manufacturing & Service Operations Management, INFORMS, vol. 1(2), pages 157-173.
    13. 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.
    14. Joseph M. Milner & Panos Kouvelis, 2005. "Order Quantity and Timing Flexibility in Supply Chains: The Role of Demand Characteristics," Management Science, INFORMS, vol. 51(6), pages 970-985, June.
    15. 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.
    16. Yossi Aviv, 2001. "The Effect of Collaborative Forecasting on Supply Chain Performance," Management Science, INFORMS, vol. 47(10), pages 1326-1343, October.
    17. Ananth V. Iyer & Vinayak Deshpande & Zhengping Wu, 2003. "A Postponement Model for Demand Management," Management Science, INFORMS, vol. 49(8), pages 983-1002, August.
    18. Alp Akcay & Bahar Biller & Sridhar Tayur, 2011. "Improved Inventory Targets in the Presence of Limited Historical Demand Data," Manufacturing & Service Operations Management, INFORMS, vol. 13(3), pages 297-309, July.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:10:y:1964:i:3:p:429-440. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.