Inland waterways form a natural network infrastructure with the capacity for waterborne transport of people and goods for moving freight from seaports to the hinterland. Recently, Inland Waterway Transport (IWT) has been promoted more extensively by the European Union and various governments as it plays a crucial role in reducing road congestion and CO2 emissions from transport. However, the advantages of IWT are not fully exploited due to inefficiencies in the logistics system, such as long waiting times at locks and sub-optimal navigation on waterways. Currently, no scheduling at infrastructures or routing optimisation of the overall waterway network is happening. The scheduling of vessels through a lock is usually performed on a First In First Out basis, providing an opportunity for improvement. Hence, this thesis aims to design a scheduling strategy for generating an optimal plan for sending inland vessels through a waterway network with minimal delays, yielding a significant positive impact on the modal shift towards IWT.  A promising approach to scheduling problems is by using Switching Max-Plus-Linear (SMPL) systems. SMPL systems have proven to be effective in various Discrete-Event Systems and transportation networks. Using SMPL models is convenient since non-linear scheduling problems can be described linearly using Max-Plus operators without compromising on the system dynamics. Moreover, as the SMPL systems can be transformed into Mixed-Integer-Linear-Programming (MILP) problems, it is also possible to use fast optimisers for solving the scheduling problems. This thesis will show how one can describe IWT systems, consisting of; waterways, vessels and locks, as SMPL systems. The optimal schedule for the inland vessels is determined based on multiple input parameters, including waterway network lay-out, the sailing speeds of vessels and arrival deadlines of the vessels. The scheduler will return the individual vessel routing and overall vessel order in the waterway network. This routing and order selection is defined using binary control variables, turning the IWT scheduling problem into a MILP problem, which will allow finding the solution to large scale IWT scheduling problems in a reasonable computation time. Furthermore, this thesis will show how the goal of minimising the cumulative arrival times of all vessels in a network can be achieved. This is done for different types of waterway network cases, for which the results are shown and analysed.