Inventory Control and Learning for One-Warehouse Multi-Store System with Censored Demand

Motivated by our collaboration with one of the largest fast-fashion retailers in Europe, we study a two-echelon inventory control problem called the One-Warehouse Multi-Store (OWMS) problem when the demand distribution is unknown. This system has a central warehouse that receives an initial replenishment and distributes its inventory to multiple stores in each time period during a finite horizon. The goal is to minimize the total expected cost which consists of shipment costs, holding costs, lost-sales costs, and end-of-horizon disposal costs. The OWMS system is ubiquitous in supply chain management, yet its optimal policy is notoriously difficult to calculate even under complete demand distribution case. In this work, we consider the OWMS problem when the demand distribution is unknown a priori. By observing the censored demand, the firm has to jointly learn the demand and make inventory control decisions on the fly. We first develop a learning algorithm based on empirical demand distribution and prove an upper bound on its theoretical performance when the demand information is uncensored. Then, in the censored demand case, we propose a more sophisticated algorithm based on a primal-dual learning and optimization approach. Results show that both algorithms have great theoretical and empirical performances