A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

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 ).