This paper investigates the current patient transportation between services in a large hospital and provides a simulation-optimization solution to reduce completion times of demands. Historical data of the service calls is available and an in-depth analysis is conducted to identify popular routes and current assignment of demands to patient transport employees. We present a mixed-integer model to determine the best distribution of the employees throughout the most popular routes of the hospital to minimize demand completion time. Experiments are conducted on real data from CHU de Québec-Université Laval, Hôpital de l'Enfant Jésus, in the province of Québec, Canada.