A Non-Parametric Approach to Stochastic Inventory Planning with Lost Sales and Censored Demand

We study stochastic inventory planning systems with lost sales and censored demand under stationary and non-stationary settings. Contrary to classical inventory theory, we assume that no knowledge of demand is initially available, and lost sales in each period are unobservable. We take a non-parametric approach and propose adaptive inventory policies that generate a sequence of ordering decisions over time. The decision in each period depends only on historical sales data of the past. In the stationary demand setting, any excess inventory in each period is either scrapped (perishable) or carried over to the next period (non-perishable). We also consider non-stationary inventory systems with seasonal demand – allowing for a cyclic pattern of demand distributions – with product updates at the beginning of each season. To assess the quality of our inventory policies, we use as a benchmark the optimal expected cost that would have incurred if the true distribution were known. Our adaptive algorithms are easy to implement and converge to the optimal solution. Furthermore, for any T ≥ 1, the average cost during the first T periods under our inventory policies differs from the optimal cost by at most O ( 1/ √ T ) . Extensive computation shows that our adaptive policies perform well. ∗Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA. [email protected]. †School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA. [email protected].