The Tactical Berth Allocation Problem with Quay Crane Assignment and Transshipment-related Quadratic Yard Costs

In this paper we integrate two decision problems arising in container terminals: the berth allocation problem, which consists of assigning and scheduling incoming ships to berthing positions, and the quay crane assignment problem, which assigns to incoming ships a certain QC profile (i.e. number of quay cranes per working shift). They are indeed strictly correlated, as the QC profile assigned to the ships affects the handling times and therefore it has impact on the berth allocation. We present two formulations for the integrated problem: a mixed integer quadratic program and a linearization which reduces to a mixed integer linear program. The objective function aims, on the one hand, to maximize the total value of chosen QC profiles and, on the other hand, to minimize the housekeeping costs generated by transshipment flows between ships. An economical analysis of the value of QC assignment profiles and of yard-related costs in a transshipment context is provided. Both models have been validated on instances based on real data; computational results are presented and discussed.