We assess appointment scheduling for outpatients in a hospital. A physician sees K patients during a fixed-length session. Each patient has been given an appointment time during the session in advance. Our evaluation approach aims at obtaining accurate predictions at a very low computational cost for the waiting times of the patients and the idle time of the physician. To this end, we investigate a modified Lindley recursion in a discrete-time framework. We assume general, possibly distinct, distributions for the patient's consultation times as well as for the patient unpunctuality, which allows for accounting for multiple treatment types, for patient unpunctuality as well as for patient no-shows. The moments of waiting and idle times are obtained and the computational complexity of the algorithm is discussed.
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