E-commerce shipping through a third-party supply chain

We consider an e-commerce retailer who must ship orders from a warehouse to a set of customers with delivery deadlines. As is often the case, the retailer uses a third-party service provider to ensure its distribution. The retailer can enter the supply chain of the service provider at various levels. Entering it at a higher level entails lower sorting costs for the retailer, but higher delivery costs, and longer delivery times. The customer orders arrive at various moments over a rolling planning horizon. This means that the retailer must also make consolidation decisions. We model and solve the static and dynamic cases of this problem. The static case is modeled as an integer linear program and solved by CPLEX. We develop and compare four shipping policies for the dynamic case. Extensive computational results based on real location data from California and Texas are reported.