Planning hinterland container transportation in congested deep-sea terminals

The size of container ships and the number of containers being transshipped at container terminals have steadily increased over the years. Consequently, it is important to make efficient use of the hinterland capacity. A concept that is used to do this is synchromodal transportation, in which at the very last moment the mode of transportation for a container is decided. Unfortunately, some deep-sea terminals are rather congested and it is unknown by the time the transportation plan is made how many containers can be loaded to and unloaded from a barge. Motivated by this, we study an operational planning problem with uncertainty that is faced by an inland terminal in the port of Amsterdam as a two-stage stochastic problem with recourse. We solve this problem using sample average approximation (SAA) and a fast heuristic using constraints based on stochastic programming (SP). The SAA method gives near-optimal solutions for small instances. For larger instances, the SP-based method is shown to be a good alternative because it is much faster than the SAA method and produces solutions that are less than 1% from the SAA solutions.