An exact robust approach for the integrated berth allocation and quay crane scheduling problem under uncertain arrival times

We consider an integrated berth allocation and quay crane assignment and scheduling problem where the arrival times of the vessels may be affected by uncertainty. The problem is modelled as a two-stage robust mixed integer program where the berth allocation decisions are taken before the exact arrival times are known, and the crane assignment and scheduling operations are adjusted to the arrival times. To solve the robust two-stage model, we follow a decomposition algorithm that decomposes the problem into a master problem and a separation problem. A new scenario reduction procedure for solving the separation problem is proposed as well as a warm start technique for reducing the number of iterations performed by the decomposition algorithm. To scale the proposed decomposition algorithm for large size instances, it is combined with a rolling horizon heuristic.The efficiency and effectiveness of the proposed algorithms are demonstrated through extensive computational experiments carried out on randomly generated instances with both homogeneous and heterogeneous cranes as well as on instances from the literature.publishe