Simultaneous operation of next-generation and traditional quay cranes at container terminals

Container terminal quay crane scheduling may enter a new era with the recently patented quay crane design. These next-generation cranes can induce noticeable improvements to the service time and quay side's capacity. Specifically, they can access containers from both sides of the vessel and can perform up to four container operations at a time. Port managers may find it useful to operate these cranes in conjunction with traditional cranes, whether in the transition phase or in following a strategic resource allocation. For that, in this work, we model the simultaneous scheduling of next-generation and traditional cranes. We introduce a mixed integer program and two solution methodologies to solve the problem. The first is a column generation approach, designed based on the main problem formulation. It shows improvement over solving the formulation in commercial solver but requires considerable computational time. For that, we introduce a re-visualized vessel structure that results in a reduction of possible feasible arrangements for column generation purposes. Thus, the second approach uses a (modified) column generation algorithm to solve a re-visualized vessel structure, where the new structure's workload is enumerated using a fast set-partitioning formulation. Through a computational study, we show that the proposed approach can solve real cases in a reasonable time. Finally, a case study sheds light on how the positioning of cranes affects the service time and motivates a modelling extension.