In this study, a two-step method for the daily priority-based surgical case scheduling of elective patient of non-identical Operating Rooms (OR) is presented. In the first step, we present a mixed integer programming model to select patients from the waiting list and to assign the selected patients to the operating room. The objectives are to minimize the makespan, undertime and overtime costs simultaneously and maximize the weighted sum priority of selected surgeries. After assigning the patients to the ORs, in the second phase, the sequence of selected surgeries in the operating room assigned them has been determined by discrete event simulation by two dispatching rules including the Shortest Surgery Time based on priority (SST), and the Longest Surgery Time based on priority (LST).  Also, the schedules obtained by these two dispatching rules are compared with the head surgeon schedule. This research has been performed in one of the surgical departments of a public hospital located in Iran.