Due to the increasing amount of goods transported by vessels and the resulting increased size of the vessels, waterway scheduling becomes a challenging task. Waterways can often only be expanded with enormous costs and environmental damage. Therefore, this paper investigates a scheduling problem on a restricted waterway. Wide vessels are only allowed to pass in a passing box and vessels with deep draught can only pass the waterway in a time window around high tide. We present a mixed-integer program (MIP) for the problem setting and develop techniques which allow us to fix variables and reduce the number of variables and constraints of the model. The resulting model formulations are evaluated in a comprehensive computational study on a real-world setting at the river Elbe next to Hamburg (Germany).