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Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales


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  • Martin A. Lariviere

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Evan L. Porteus

    (Stanford Business School, Stanford University, Stanford, California 94305)

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    Retailers are frequently uncertain about the underlying demand distribution of a new product. When taking the empirical Bayesian approach of Scarf (1959), they simultaneously stock the product over time and learn about the distribution. Assuming that unmet demand is lost and unobserved, this learning must be based on observing sales rather than demand, which differs from sales in the event of a stockout. Using the framework and results of Braden and Freimer (1991), the cumulative learning about the underlying demand distribution is captured by two parameters, a scale parameter that reflects the predicted size of the underlying market, and a shape parameter that indicates both the size of the market and the precision with which the underlying distribution is known. An important simplification result of Scarf (1960) and Azoury (1985), which allows the scale parameter to be removed from the optimization, is shown to extend to this setting. We present examples that reveal two interesting phenomena: (1) A retailer may hope that, compared to stocking out, realized demand will be strictly less than the stock level, even though stocking out would signal a stochastically larger demand distribution, and (2) it can be optimal to drop a product after a period of successful sales. We also present specific conditions under which the following results hold: (1) Investment in excess stocks to enhance learning will occur in every dynamic problem, and (2) a product is never dropped after a period of poor sales. The model is extended to multiple independent markets whose distributions depend proportionately on a single unknown parameter. We argue that smaller markets should be given better service as an effective means of acquiring information.

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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 45 (1999)
    Issue (Month): 3 (March)
    Pages: 346-363

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    Handle: RePEc:inm:ormnsc:v:45:y:1999:i:3:p:346-363

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    Related research

    Keywords: Bayesian inventory management; unobserved lost sales; information acquisition; dropping products; Bayesian dynamic programming; newsvendor distributions; dimensionality reduction; product profitability; multiple markets; favoring small markets;


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    Cited by:
    1. Nils Rudi & David Drake, 2009. "Observation bias: The impact of demand censoring on newsvendor level and adjustment behavior," Harvard Business School Working Papers 12-042, Harvard Business School, revised Dec 2011.
    2. Alexandre X. Carvalho & Martin L. Puterman, 2005. "Dynamic Optimization and Learning: How Should a Manager set Prices when the Demand Function is Unknown ?," Discussion Papers 1117, Instituto de Pesquisa Econômica Aplicada - IPEA.
    3. Lu, Jye-Chyi & Tsao, Yu-Chung & Charoensiriwath, Chayakrit & Dong, Ming, 2012. "Dynamic decision-making in a two-stage supply chain with repeated transactions," International Journal of Production Economics, Elsevier, vol. 137(2), pages 211-225.
    4. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, vol. 38(3-4), pages 218-227, June.
    5. 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).
    6. 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.
    7. Erhan Bayraktar & Mike Ludkovski, 2012. "Inventory Management with Partially Observed Nonstationary Demand," Papers 1206.6283,
    8. Wanke, Peter F., 2008. "The uniform distribution as a first practical approach to new product inventory management," International Journal of Production Economics, Elsevier, vol. 114(2), pages 811-819, August.


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