Vessel passage scheduling through cascaded bridges using mixed-integer programming

This paper addresses the problem of guaranteeing efficient inland waterway transport in the presence of sequential movable bridges, which must be operated to grant vessel passage. The main contribution is the formulation of the vessel passage scheduling problem as a mixed-integer programming problem. The scheduling algorithm receives vessel widths and voyage plans, and determines feasible vessel passage through bridges that best matches vessel plans. Process optimization is carried out using a rolling horizon implementation to keep the problem computationally tractable in real-time applications. Finally, a realistic case study based on the Rhine-Alpine corridor is used to test the approach and demonstrate its effectiveness.