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One of the current challenges faced by health centers is to reduce the number of patients who do not attend their appointments. The existence of these patients causes the underutilization of the center's services, which reduces their income and extends patient's access time. In order to reduce these negative effects, several appointment scheduling systems have been developed. With the recent availability of electronic health records, patient scheduling systems that incorporate the patient's no-show prediction are being developed. However, the benefits of including a personalized individual variable time slot for each patient in those probabilistic systems have not been yet analyzed. In this article, we propose a scheduling system based on patients' no-show probabilities with variable time slots and a dynamic priority allocation scheme. The system is based on the solution of a mixed-integer programming model that aims at maximizing the expected profits of the clinic, accounting for first and follow-up visits. We validate our findings by performing an extensive simulation study based on real data and specific scheduling requirements provided by a Spanish hospital. The results suggest potential benefits with the implementation of the proposed allocation system with variable slot times. In particular, the proposed model increases the annual cumulated profit in more than 50% while decreasing the waiting list and waiting times by 30% and 50%, respectively, with respect to the actual appointment scheduling system.