Inbound and outbound flow integration for cross-docking operations

We consider the optimization of the cross-docking operations at three INtermodal LOgistics Platforms (INLOPs) of a large European car manufacturer (ECM). The planning horizon is a week and the time bucket is a day. An inbound flow of products is gradually received over the week by truck from inland suppliers, and has to be loaded into containers which are then shipped to offshore production plants. The full content of a container must be available at the INLOP to enable its loading operations to start, hence temporary storage is needed. The objective is to minimize an inventory penalty, computed as the largest daily volume of temporary product storage observed over the planning horizon. The current practice at ECM is to first optimize the content of the inbound trucks and of the outbound containers independently, and then determine the loading day of each container to be shipped based on these fixed contents. We propose to integrate, within the same optimization framework, the decisions on both truck and container contents, which involve complex loading constraints related to the dimensions and weights of the products, with those on the scheduling of container loading. We model the resulting problem as a mixed integer linear program, and we develop a decomposition scheme for it, as well as a fix-and-optimize matheuristic. We perform extensive computational experiments on real instances provided by ECM. Results show that a combination of these two matheuristics is able to generate solutions that reduce the average inventory penalty by 40%.