Optimal scheduling of autonomous vessel trains in a hub-and-spoke network

An autonomous vessel train features several autonomous vessels sailing together, piloted by a conventional, manned leader vessel. It is a promising transitional solution at the present technological level before full autonomy is realized. We develop mixed-integer programming models for jointly optimizing the autonomous vessel assignment to vessel trains and vessel train routes and schedules in a hub-and-spoke network. Solutions to these models capture the optimal tradeoff between vessel trains' added detour and delay costs and the lower sailing cost of autonomous ships. Numerical case studies are carried out for a real-world short-sea shipping network around the Bohai Bay of China. Results reveal sizeable cost savings of vessel train operations compared to the case where only conventional ships are used. Sensitivity analyses are performed to unveil how the benefit of vessel trains is affected by key operating factors, e.g., the fleet composition, the vessel train size limit, and the network topology. The results inform practitioners of suitable and profitable scenarios for implementing the vessel train strategy. This study can be viewed as the first step toward real implementation of the economically competitive and environmentally friendly autonomous freight ships via vessel trains.