Robust cyclic berth planning of container vessels

We consider a container terminal operator who faces the problem ofconstructing a cyclic berth plan. Such a plan defines the arrival anddeparture times of each cyclically calling vessel on a terminal, takinginto account the expected number of containers to be handled and thenecessary quay and crane capacity to do so. Conventional berth planningmethods ignore the fact that, in practice, container terminal operatorand shipping line agree upon an arrival window rather than an arrivaltime: if a vessel arrives within that window then a certain vesselproductivity and hence departure time is guaranteed.The contributions of this paper are twofold. We not only minimize thepeak loading of quay cranes in a port, but also explicitly take intoaccount the arrival window agreements between the terminal operator andshipping lines. We present a robust optimization model for cyclicberth planning. Computational results on a real-world scenario for acontainer terminal in Antwerp show that the robust planning model canreach a substantial reduction in the crane capacity that is necessary tomeet the window arrival agreements, as compared to a deterministicplanning approach.