This study examined patient unpunctuality’s effect on patient appointment scheduling in the ultrasound department of a hospital. The study created a simulation system incorporating the formulated F3 distribution to describe patient unpunctuality. After the simulation model passed verification and validation processes, what-if scenarios were conducted under two policies: The preempt policy and the wait policy. A comparison of the total cost of each policy showed that the preempt policy performed better than the wait policy in the presence of unpunctuality. The study used sensitivity analyses to identify the different effects of patient unpunctuality on the system. The weights of the cost coefficient of both radiological technician’s idle time and patient waiting time must be equal in order to achieve a lower cost. The patient’s inter-arrival time must be close to the average total time in the system to achieve lower costs. Moreover, utilization decreases as the patient’s inter-arrival increases. Therefore, the patient’s inter-arrival time should be higher than, but close to, the service time to ensure less radiological technician’s idle time and patient waiting time.