Matrix production systems offer the flexibility to meet an increasingly individualized and volatile customer demand. However, production supply processes within these systems have rarely been investigated in detail despite playing an integral role in their performance. Contributing to closing this research gap, this work utilizes reinforcement learning for routing in the production supply of matrix production systems. In particular, it focuses on dispatching orders to the vehicles and scheduling the orders within a route. Various constraints are considered to simulate a realistic setting, including order time windows, vehicle battery limitations, and a vehicle capacity allowing to transport multiple items at once. A reinforcement learning framework is conceptualized and implemented, assigning orders to vehicles based on various route construction heuristics. Its observation space contains abstract information about current orders of the matrix production supply environment and specific data on the vehicles for the reinforcement learning agent to select both a vehicle and a heuristic. The action and observation spaces are complemented by a multi-criteria reward function, prompting the agent to learn not to violate any constraints of the environment while simultaneously choosing actions that lead to the most cost-effective routes after route optimization. The reinforcement learning route constructor approach is trained and deployed on a discrete-event simulation of a matrix production system, which is connected to the reinforcement learning framework via a socket interface. The approach has proven to be successful by outperforming two non-reinforcement learning heuristics for route construction.