In the service industry, scheduling medical procedures causes difficulties for both patients and management. Factors such as fluctuations in customer demand and service time affect the appointment scheduling systems’ performance in terms of, for example, patients’ waiting time, idle time of resources, and total cost/profits. This research implements four appointment scheduling policies, i.e., constant arrival, mixed patient arrival, three-section pattern arrival, and irregular arrival, in an ultrasound department of a hospital in Taiwan. By simulating the four implemented policies’ optimization procedures, optimal or near-optimal solutions can be obtained for patients per arrival, patients’ inter-arrival time, and the number of the time slots for arrived patients. Furthermore, three objective functions are tested, and the results are discussed. The managerial implications and discussions are summarized to demonstrate how outcomes can be useful for hospital managers seeking to allocate their healthcare service capacities.