A patient scheduling method for non-emergency medical cases on short and medium term is proposed in this paper. It aims to establish a balanced workload of medical personnel and resources considering their availability during a future specified time periods and possible fluctuations of number of medical emergencies due to epidemic periods. Another main objective is the minimization of the waiting time of patients programed for appointments at multiple medical specialties. A stochastic Petri nets based model, using statistic registered data is used to determine the workload, then transposed in a number of daily available appointments for non-emergency cases. Finally, a genetic algorithm was applied to minimize the waiting time of patients programmed for specialized medical examinations. The method was implemented and tested proving its efficiency. The stochastic PN based model is easy to be updated taking into account different changes, leading to the workloads modifications and the obtained response time of the implemented genetic algorithm corresponds to the necessities of a real application.