Supervisor synthesis enables the design of supervisory controllers for large cyber-physical systems, with high guarantees for functionality and safety. The complexity of the synthesis problem, however, increases exponentially with the number of system components in the cyber-physical system and the number of models of this system, often resulting in lengthy or even unsolvable synthesis procedures. In this paper, a new method is proposed for reducing the model of the system before synthesis to decrease the required computational time and effort. The method consists of three steps for model reduction, that are mainly based on symmetry in dependency graphs of the system. Dependency graphs visualize the components in the system and the relations between these components. The proposed method is applied in a case study on the design of a supervisory controller for a road tunnel. In this case study, the model reduction steps are described, and results are shown on the effectiveness of model reduction in terms of model size and synthesis time.