Appointment-scheduling systems traditionally schedule patient appointments at fixed intervals, without taking into account several complexity factors of health-care system. This schedule can make the server idle at certain times of the day and can produce long queues of patients at other times. In this context, the objective of this study is to propose a new scheduling policy for a clinic specialized in bariatric surgery in Rio de Janeiro, considering the following factors of this system: stochastic service times, patient unpunctuality, delays and interruptions of the provider and presences of no-shows. This study analyzed several scenarios with overbooking, and tested the main policies with a simulation model, proposing the most appropriate for the clinic. The 18 scheduling policies applied were found through an extensive systematic review of the literature. With the use of the OFFSET scheduling policy, it was possible to increase the number of appointments by 30 percent to the scheduling of the main clinic provider, maintaining the level of service provided. In addition, a new scheduling policy, called DOME CYCLE, was proposed, which has outperformed the other policies in the average of the tests performed.