Outpatient scheduling with unpunctual patients and no-shows

We assess appointment scheduling strategies for outpatient services. To this end, we consider a fixed-length consultation session in which K patients have to be scheduled at predefined appointment times, but who may not be punctual. Their effective arrival time deviates from their appointment time by a stochastic unpunctuality time. We assume general, possibly distinct distributions for the patients' consultation times as well as for their unpunctuality. The heterogeneity of the consultation times is motivated by patient classification: the schedule can be adapted to the patients' characteristics. Our evaluation approach is based on a modified Lindley recursion in a discrete-time framework and obtains accurate predictions for the moments of the patient waiting times as well as the doctor's idle times and overtime. This evaluation method is then included in a local search algorithm to provide general insights into appointment scheduling under unpunctual patients. Our results suggest that the proposed method obtains substantial cost reductions when patient classification is correctly exploited. Finally, it is shown that our analysis can also be used to determine optimal sequencing rules for patients who arrive out of turn.