Two mathematical formulations for the containers drayage problem with time windows

The containers drayage problem studied here arise in ISO container distribution and collecting processes, in regions which are oriented to container sea ports or inland terminals. Containers of different sizes, but mostly 20ft, and 40ft empty and/or loaded should be delivered to, or collected from the customers. Therefore, the problem studied here is closely related to the vehicle routing problem with the time windows that finds an optimal set of or routes visiting deliveries and pickups customers. The specificity of the container drayage problem analyzed here lies in the fact that a truck may simultaneously carry one 40ft, or two 20ft containers, using an appropriate trailer type. This means that in one route two, three or four nodes can be visited, which is equivalent to the problem of matching nodes in single routes which provide a total travel distance shorter than in the case when nodes are visited separately. The paper presents two optimal MIP mathematical formulations for the case when pickup and delivery nodes could be visited only in specific time interals - time windows. Proposed approaches are tested on numerical examples.