This paper considers the inland waterborne transport (IWT) problem, and presents a scheduling approach for inland vessels and locks to generate optimal vessel and lock timetables. The scheduling strategy is designed in the switching max-plus-linear (SMPL) systems framework, as these are characterized by a number of features that make them well suited to represent the IWT problem. In particular, the resulting model is linear in the max-plus algebra, and SMPL systems can switch between modes, an interesting feature due to the presence of vessel routing and ordering constraints in the model. Moreover, SMPL systems can be transformed into mixed-integer linear programming (MILP) problems, for which efficient solvers are available. Finally, a realistic case study is used to test the approach and assess its effectiveness.