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A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853
huh{at}ieor.columbia.edu, http://www.columbia.edu/th2113/
paatrus{at}cornell.edu, http://legacy.orie.cornell.edu/paatrus/

We study stochastic inventory planning with lost sales and instantaneous replenishment where, contrary to the classical inventory theory, knowledge of the demand distribution is not available. Furthermore, we observe only the sales quantity in each period and lost sales are unobservable, that is, demand data are censored. The manager must make an ordering decision in each period based only on historical sales data. Excess inventory is either perishable or carried over to the next period. In this setting, we propose nonparametric adaptive policies that generate ordering decisions over time. We show that the T-period average expected cost of our policy differs from the benchmark newsvendor cost—the minimum expected cost that would have incurred if the manager had known the underlying demand distribution—by at most O(1/T^0.5).

Key Words: newsvendor problem; nonparametric demand; censored demand; online optimization
History: Received: April 16, 2007; revision received: June 26, 2008;

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