Patient punctuality significantly impacts resource utilization and patient waiting times, among other quality indicators, within psychiatry clinics. In pursuit of service improvement, this study endeavors to develop effective appointment scheduling systems that optimally distribute patients' needs during clinical sessions, thereby enhancing resource utilization and patient satisfaction. In developing these scheduling rules, three patient-related uncertainties are considered: preference, availability, and punctuality. Various scheduling rules are evaluated based on their average total cost under different scenarios. The HSBGDM rules have emerged as a balanced approach for clinic operations, effectively managing physician time but occasionally leading to overtime variations. Increased patient delays often exacerbate physician idle times, particularly under IBVST and VBVST rules. Hybrid rules, such as the HSBGDM series, adapt well, improving patient wait times and managing unscheduled patients. However, scheduling systems like REPDM may prolong waits, potentially impacting patient satisfaction. Systems prioritizing new appointments can increase physician idle times due to unpredictability. While accommodating unscheduled patients enhances service quality, it may also cause disruptions. This study provides valuable insights into scheduling dynamics, assisting administrators in balancing efficiency, cost, and patient satisfaction.