جرثقیل زیردریایی تعاونی را با مشاغل ساحلی و ساحلی برنامه ریزی می کند

We consider the problem of scheduling two identical rail mounted gantry cranes (twin cranes) working within a single storage area (block) at a seaport. The cranes, referred to as seaside crane and landside crane, cannot pass each other. Our focus is on peak times, where the minimization of dwell times of vessels at the berth is typically the major objective of port authorities. We allow the seaside crane to drop inbound containers at intermediate positions where the landside crane takes over and delivers the containers to their target slots. Earlier studies have shown that allowing the cranes to cooperate in this manner is beneficial, at least when there are no containers that are already stored in the block at the beginning of the planning horizon and that have to be delivered to the landside handover point by the landside crane within given time windows. In this paper, we analyze if the positive effect of letting the cranes cooperate persists when these latter jobs are present. This might have a critical impact, because these tasks are performed close to the landside whereas supporting the seaside crane is performed rather close to the seaside. We present complexity results and some general problem insights. Furthermore, we introduce lower bounds and develop heuristic procedures that apply these bounds. The performance of the algorithms is evaluated in computational tests.