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In this paper we formulate a stochastic overbooking model and develop an appointment scheduling policy for outpatient clinics. This schedule is constructed for a single service period partitioned into time slots of equal length. A clinic scheduler must provide each calling patient with an appointment time before the patient's call terminates. Once an appointment is added to the schedule, it cannot be changed. Each callling patient has a no-show probability, and overbooking is used to compensate for patient no-shows. The scheduling objective captures patient waiting time, staff overtime, and patient revenue.