Tug scheduling for hinterland barge transport: A branch-and-price approach

In a hinterland barge transport system, barges are usually not self-propelled and need to be towed or pushed by tugs. This study investigates a tug-scheduling problem at a seaport that is located at a river mouth and that connects the hinterland ports along the river with the global maritime transportation network. A mixed-integer programming model is proposed to optimize the assignment of barges to tugs as well as the time when the tugs depart from the seaport and go to the hinterland ports. Some properties of the model are also investigated. Moreover, an exact solution method based on a branch-and-price approach is developed to solve the proposed model. Numerical experiments are also conducted to validate the effectiveness of the proposed model and the efficiency of the proposed solution method.