An Adaptive Algorithm for Finding the Optimal Base-Stock Policy in Lost Sales Inventory Systems with Censored Demand

We consider a periodic-review single-location single-product inventory system with lost sales and positive replenishment lead times. It is well known that the optimal policy does not possess a simple structure. Motivated by recent results showing that base-stock policies perform well in these systems, we study the problem of finding the best base-stock policy in such a system. In contrast to the classical inventory literature, we assume that the manager does not know the demand distribution a priori, but must make the replenishment decision in each period based only on the past sales (censored demand) data. We develop a nonparametric adaptive algorithm that generates a sequence of order-up-to levels whose T -period running average of the inventory holding and lost sales penalty cost converges to the cost of the optimal base-stock policy at the rate of O(1/T ). Our analysis is based on recent advances in stochastic online convex optimization and on the uniform ergodicity of Markov chains associated with bases-stock policies. ∗Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA. E-mail: [email protected]. †IOMS-OM Group, Stern School of Business, New York University, 44 W. 4th Street, Room 8-71, New York, NY 10012-1126. E-mail: [email protected] ‡School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA. E-mail: [email protected] §School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA. E-mail: [email protected]