The strategic allocation of cyclically calling vessels for multi-terminal container operators

We consider a terminal operator, who provides his logistics services of container handling at multiple terminals within the same port. In this setting, the well-known berth allocation problem can no longer be considered per terminal for two main reasons: i) vessel calls should be spread over the various terminals to avoid peaks and troughs in quay crane utilizations, ii) an allocation of two connecting vessels to different terminals will generate inter-terminal container transport, whose costs should be taken into account. In this paper, we address the problem of spreading a set of cyclically calling vessel lines over the different terminals and allocating a berthing and departure time to each of them. The objectives are to i) balance the quay crane workload over the terminals and over time, and ii) minimize the amount of inter-terminal container transport. A two-step solution approach is developed, which enables us to solve real-life instances within satisfactory time. Additionally, a case study is performed for the terminal operator PSA HNN, who operates multiple terminals in the port of Antwerp, Belgium. Results suggest that with relatively small modifications to the currently applied allocation in Antwerp, significant reductions in required crane capacities and inter-terminal transport can be achieved.