Rethinking cyclic structures in liner shipping networks

Liner shipping networks are a central feature of modern supply chains that consist of cyclical, periodic services operated by container vessels. This specialized, cyclical structure eases planning for both shipper and carrier, but the combination of cyclical planning with the available time windows at ports can lead to inefficient operations. We propose to relax the cyclical assumption and allow vessels to move between services to avoid inefficient connections without interruption to container flows. From the view of a shipper, the cyclical and periodic properties of the services still hold, and the liner carrier can offer a more efficient overall network. The ensuing optimization problem consists of a combined vessel routing problem and cargo allocation problem, resulting in large and challenging instances. We model the problem using mixed-integer linear programming and use an expanding horizon heuristic to find starting solutions for our model. We use real-world data to show that giving flexibility to a liner network can result in a significant cost reduction over standard cyclical schedules.