A multi-mode resource-constrained project scheduling reformulation for the waterway ship scheduling problem

In this paper, we address the waterway ship scheduling problem (WSSP), which finds applications in the management of ship arrivals and departures at maritime ports near channels and waterways. It incorporates practically relevant conflicts which stem from tidal changes, curfews, ship properties or traffic. We propose a reformulation of the WSSP as a variant of the multi-mode resource-constrained project scheduling problem, which incorporates time-dependent resource capacities besides earliest and latest start times for the tasks. This problem is solved through integer programming, using a compact mathematical formulation. Our approach outperforms previous methods by solving all the existing literature instances to optimality. Most of them are solved at the root node within less than 2 s.