Attended home delivery in narrow time windows is the prevailing service model in internet grocery retailing. E-grocers typically serve their customers from one or more dedicated e-fulfillment centers. To simplify planning, each fulfillment center is often responsible for a fixed delivery region. In this contribution, we investigate the benefits of allowing flexibility in the assignment customers to fulfillment centers from a routing perspective. The underlying routing problem can be characterized by a multi-depot vehicle routing problem with time windows.

We analyze the advantages of a flexible assignment as compared to a decomposed planning per fulfillment center by using a new exact mixed-integer programming model and a state-of-the-art heuristic. In addition, we investigate the impact of different factors on this benefit and the associated solutions.