We consider the optimization of the cross-docking operations at three INtermodal LOgistics Plat-forms (INOLPs) of a large European car manufacturer (ECM). The planning horizon is a weekand the time bucket is a day. An inbound flow of products is gradually received over the week bytruck from inland suppliers, and has to be loaded into containers which are then shipped to offshoreproduction plants. The full content of a container must be available at the INOLP to enable itsloading operations to start, hence temporary storage is needed. The objective is to minimize aninventory penalty, computed as the largest daily volume of temporary product storage observedover the planning horizon. The current practice at ECM is to first optimize the content of theinbound trucks and of the outbound containers independently, and then determine the loading dayof each container to be shipped based on these fixed contents. We propose to integrate, within thesame optimization framework, the decisions on both truck and container contents, which involvecomplex loading constraints related to the dimensions and weights of the products, with those onthe scheduling of container loading. We model the resulting problem as a mixed integer linearprogram, 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 showthat a combination of these two matheuristics is able to generate solutions that reduce the averageinventory penalty by 40%.