Joint scheduling of barges and tugboats for river–sea intermodal transport

In this paper, we study a barge and tugboat joint scheduling problem arising from a river–sea intermodal transport system, where non-self-propelled barges travel with the help of tugboats between an inland river bulk port and sea transshipment platforms to transport cargo. Due to limited channels and the sequential scheduling among ships, transit inefficiency and resource under-utilization often occur, thus it is essential to design barge timetables and tugboat paths. This paper jointly schedules barges and tugboats in a river–sea transshipment port with a tidally influenced channel, and focuses on barge round trips with multiple legs. We construct a state-space–time network from the perspective of tugboats, in which the state implies whether a barge is served by a tugboat. The problem is formulated as an integer programming model based on the network to minimize time taken for bulk cargo transshipment. A tailored variable neighborhood search algorithm is designed and its efficiency, effectiveness, and stability are demonstrated by numerical experiments, which are based on real data from the Boffa port. It is demonstrated that, by joint scheduling barges and tugboats, transfer efficiency can be significantly improved under limited tugboat resources and shorter tidal windows. The results also provide managerial insights on schedule and valuable conclusions about the resource allocation in the port.