Mitigating Delays and Unfairness in Appointment Systems

We consider an appointment system where heterogeneous participants are sequenced and scheduled for service. Because service times are uncertain, the aims are to mitigate the unpleasantness experienced by the participants in the system when their waiting times or delays exceed acceptable thresholds and to address fairness in the balancing of service levels among participants. To evaluate uncertain delays, we propose the Delay Unpleasantness Measure, which takes into account the frequency and intensity of delays above a threshold, and introduce the concept of lexicographic min-max fairness to design appointment systems from the perspective of the worst-off participants. We focus our study in the healthcare industry in balancing physicians’ overtime and patients’ waiting times in which patients are distinguished by their service time characterizations. The model can be adapted in the robust setting when the underlying probability distribution is not fully available. To capture the correlation between uncertain service times, we suggest using the mean absolute deviations as the descriptive statistics in the distributional uncertainty set to preserve the linearity of the model. The optimal sequencing and scheduling decisions can be derived by solving a sequence of mixed-integer programming problems, and we report the insights from our computational studies. This paper was accepted by Yinyu Ye, optimization.