An integrated approach to the vehicle routing and container loading problems

Real-world distribution problems raise some practical considerations that usually are not considered in a realistic way in more theoretical studies. One of these considerations is related to the vehicle capacity, not only in terms of cubic meters or weight capacity but also in terms of the cargo physical arrangements. In a distribution scene, two combinatorial optimization problems, the vehicle routing problem with time windows and the container loading problem, are inherently related to each other. This work presents a framework to integrate these two problems using two different resolution methods. The first one treats the problem in a sequential approach, while the second uses a hierarchical approach. To test the quality and efficiency of the proposed approaches, some test problems were created based on the well-known Solomon, Bischoff and Ratcliff test problems. The results of the integrated approaches are presented and compared with results of the vehicle routing problem with time windows and the container loading problem applied separately.