Abstract
This paper studies inventory replenishment planning problems for retailers with online channels. Such retailer is able to obtain advance demand information (ADI) in an environment of time-varying demands. We incorporate ADI into dynamic lot-sizing models to formulate the replenishment planning problems for retailers in three scenarios: (1) companies act as pure-play online retailers with customers homogeneous in demand lead time, (2) online customers are heterogeneous in demand lead time with priorities, and (3) retailers operate in a bricks and clicks structure, in which demands come from online and offline channels, with either independent or interactive channels. We formulate the problem in the general scenario of interactive demand channels as a mixed-integer linear programming model, and then develop a unified model through reformulation. Based on the optimality properties, we design a dynamic programming algorithm with polynomial running time to solve the unified model. The numerical experiments for several online retailers find that the method can significantly reduce the total inventory cost.