Appointment scheduling under uncertainty encounters a fundamental trade-off between capacity utilization and waiting times. In contrast to traditional approaches, we maximize capacity utilization while limiting waiting times. We derive a robust mixed-integer linear model, prove NP-hardness for the general problem, and optimality of well-known scheduling rules for special cases. Using real patient data, we show that our approach is a win-win solution to this fundamental trade-off.

Using distributionally robust optimization (DRO) that accounts for service times’ correlation, we study a two-sequential-server appointment scheduling problem. We observe that the optimal schedule can lead to imbalanced waiting times in the two servers, concentrating on the downstream server. To rebalance the waiting times without rescheduling patients, we adopt an idea in the queueing literature to strategically idle (SI) the upstream server. A DRO model is used to find the optimal SI policy.

We present a personalized and probabilistic framework to model the risk of hospital admissions for patients (with and without COVID-19) that attended an Emergency Department (ED) during the pandemic. As predictors, we use patient demographics, measures of ED crowdedness, and the triage information, and investigate if population-level data (such as human mobility, number of COVID-19 cases, vaccination status etc.) could help improve the prediction accuracy of admission risk at the patient level.