Outpatient appointment scheduling strongly affects patient waiting time, doctor utilization, and overall service quality. Many clinics, especially small and medium ones, cannot use complex simulation-based tools due to limited resources. There is a need for simple and practical methods that can improve scheduling without advanced software or heavy computation. This study aims to reduce total patient time in the system and minimize physician idle time using an easy-to-implement optimization approach. A deterministic scheduling model was developed and optimized using Particle Swarm Optimization (PSO), and its performance was compared to a Genetic Algorithm (GA) under equal computational conditions. PSO consistently produced better appointment schedules than GA, with lower total waiting time, reduced physician idle time, and better overall objective values. It also converged faster and showed more stable performance across multiple runs. Compared with standard booking rules, PSO reduced waiting time by 12-18% and idle time by 8-14% for typical daily loads of 20-40 patients. GA also improved scheduling outcomes but was slower and more variable. These results show that even a simple deterministic model can achieve meaningful improvements when paired with an effective optimization method. The findings demonstrate that clinics with limited computational capacity can still improve scheduling using simple optimization tools such as PSO. This work also provides a foundation for future extensions involving multi-stage, stochastic, or multi-objective scheduling problems.