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Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales, Management Science


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 and a shape parameter. An important simplification which allows the scale parameter to be removed form the optimization is shown to extend to this setting. Examples are presented that reveal: 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. 2. It can be optimal to drop a product after a period of successful sales.




Martin Lariviere, Evan L. Porteus

Date Published



Lariviere, Martin, and Evan L. Porteus. 1999. Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales. Management Science.(3): 346-363.


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