We consider a terminal operator who provides container handling services at multiple terminals within the same port. In this setting, the well-known berth allocation problem can no longer be considered for each terminal in isolation since vessel calls should be spread over the various terminals to avoid peaks and troughs in quay crane utilization, and an allocation of two connecting vessels to different terminals will generate inter-terminal container transport. In this paper, we address the problem of spreading a set of cyclically calling vessels over the various terminals and allocating a berthing and departure time to each of them. The objectives are (1) to balance the quay crane workload over the terminals and over time and (2) to minimize the amount of inter-terminal container transport. We develop a solution approach based on mixed-integer programming that allows to solve real-life instances of the problem within satisfactory time. Additionally, a practical case study is presented based on data from the terminal operator PSA Antwerp who operates multiple terminals in the port of Antwerp, Belgium. The computational results show the cost of the currently agreed schedules, and that relatively small modifications can significantly reduce the required crane capacities and inter-terminal transport.
We consider a container terminal operator who faces the problem of constructing a cyclic berth plan. Such a plan defines the arrival and departure times of each cyclically calling vessel on a terminal, taking into account the expected number of containers to be handled and the necessary quay and crane capacity to do so. Conventional berth planning methods ignore the fact that, in practice, container terminal operator and shipping line agree upon an arrival window rather than an arrival time: if a vessel arrives within that window then a certain vessel productivity and hence departure time is guaranteed. The contributions of this paper are twofold. We not only minimize the peak loading of quay cranes in a port, but also explicitly take into account the arrival window agreements between the terminal operator and shipping lines. We present a robust optimization model for cyclic berth planning. Computational results on a real-world scenario for a container terminal in Antwerp show that the robust planning model can reach a substantial reduction in the crane capacity that is necessary to meet the window arrival agreements, as compared to a deterministic planning approach.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.