Inventory Control for Omnichannel Retailing Between One Warehouse and Multiple Stores

In this article, we research a multiperiod two-echelon inventory control problem for omnichannel retailing [i.e., online channel, offline channel, and buy-online-and-pick-up-in-store (BOPS) channel]. Especially, we jointly consider the limited storage capacity of the stores and the delivery lead time of the warehouse. For the out of stock, the unsatisfied demands for multiple purchasing channels have different processes (i.e., lost sales or backlog), based on the different characteristics of multiple channels. First, we divide the multiperiod inventory control problem for omnichannel retailing into two subproblems (the inventory control problem for the stores and the inventory control problem for the warehouse). Then, to reduce the scale of the first subproblem and the computation effort, we propose a method based on Lagrangian relaxation and value iteration to solve the inventory control problem of stores. Further, based on the results of the inventory control problem of stores, we construct a delay-aware Markov decision process (DAMDP) for the inventory control problem of the warehouse and employ the Q-learning technique based on the constructed DAMDP to solve the second subproblem. Besides, we also extend our analysis to the case of the low-level backlog in buying-online channels (i.e., online and BOPS channels). Finally, some numerical experiments are conducted to illustrate the performance of the inventory control policy for omnichannel retailing and reveal some managerial insights.