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We present a methodology to design appointment systems for outpatient clinics and diagnostic facilities that offer both walk-in and scheduled service. The developed blueprint for the appointment schedule prescribes the number of appointments to plan per day and the moment on the day to schedule the appointments. The method consists of two models; one for the day process that governs scheduled and unscheduled arrivals on the day and one for the access process of scheduled arrivals. Appointment schedules that balance the waiting time at the facility for unscheduled patients and the access time for scheduled patients are calculated iteratively using the outcomes of the two models. Two methods to calculate appointment schedules, complete enumeration and a heuristic procedure, are compared in various numerical experiments. Furthermore, an appointment schedule for the CT-scan facility at the Academic …