This paper proposes a new scheduling problem for patient visits with two objectives: minimizing patient waiting time and travel time. It also presents a novel encoding method for Genetic Algorithms (GA) that is well-suited for this problem. Experiments demonstrate that the proposed encoding method reduces optimization iterations by 17% compared to conventional methods, and the GA can decrease waiting time by up to 58.2% and travel time by up to 89.3% for specific examples. The novel scheduling problem and the encoding method are two main contributions of this work.