The Tactical Berth Allocation Problem (TBAP) with quay crane assignment and transshipment-related quadratic yard costs

International sea-freight container transport has grown dramatically over the last years and container terminals play nowadays a key-role in the global shipping network. Increasing competition and competitiveness among terminals require more and more efficiency in container handling operations, both in the quayside and the landside, in order to better utilize limited resources (such as cranes, trucks, berths, storage space, etc.) as well as minimize ship's turnaround time. Operations research methods are therefore worth being use for the optimization of terminal operations. We take into account two decision problems which are usually solved hierarchically by terminal planners: the Berth Allocation Problem (BAP), which consists of assigning and scheduling incoming ships to berthing positions, and the Quay Crane Assignment Problem (QCAP), which assigns to incoming ships a certain QC profile (i.e. number of quay cranes per working shift). These two problems are indeed strictly correlated: the QC profile assigned to the incoming ships affects their handling time and has thus an impact on the berth allocation. In this work, we aim to combine BAP with QCAP and analyze the resulting new integrated problem from the point of view of a transshipment terminal. We solve this problem at the tactical decision level, with the intent of supporting the terminal in its negotiation process with shipping lines, as the number of quay cranes is usually bounded by contracts which are discussed months in advance. Devised analytic tools and quantitative methods allow terminal managers to assign the right value to the QC profiles proposed to shipping lines, considering their impact on the terminal productivity. In addition to profile evaluation, the combined solution of these two problems optimizes the utilization of terminal resources. Alternative objectives are used for this purpose, such as the minimization of total distance covered to move containers, the minimization of ships turnaround time, etc. Starting from a collaboration with the transshipment terminal of Gioia Tauro in Italy, one of the busiest in Europe, we propose a new model for the Tactical Berth Allocation Problem (TBAP) with Quay Crane Assignment, which has been validated on real-world instances provided by the terminal, taking into account a time horizon up to one month. 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 caused by transshipment flows between ships. Preliminary results obtained through commercial software will be presented and further methodological approaches to the problem, such as decomposition techniques, will be outlined.