Scheduling medical appointments plays a fundamental role in managing patient flow and ensuring high-quality care. However, no-shows can significantly disrupt this process and affect patient care. To address this challenge, healthcare facilities can adopt different strategies, including overbooking in medical consultations. While this reduces the risk of unused slots, it can generate associated costs and affect the perception of service quality. In this article, we propose an integer linear optimization model that maximizes the expected utility of a medical center, considering the risk of no-shows and overbooking. For this purpose, machine learning is used to estimate the propensity of each patient to attend their medical appointment, using real data from three medical specialties of a hospital. The results of the application demonstrate the model's ability to assign appointments and perform overbooking efficiently and in an organized manner, implying an improvement in the utility of a medical center and a positive impact on the perception of the quality of care.