Coordinated scheduling for in-clinic and virtual medicine patients in a multi-station network

In this article, we study a coordinated scheduling problem with both Virtual Medicine patients (VM patients) and In-Clinic patients (IC patients) in a multi-disciplinary setting. The problem was motivated by appointment scheduling requirements in a multi-disciplinary clinic called an Integrated Practice Unit (IPU), which incorporates differing priorities, heterogeneous service time distributions, distinct cost structures and unique care paths in a multi-station network. We establish priority for IC patients and introduce time windows for VM patients to create flexibility. Recursion expressions are derived for a performance measure of interest, which balances revenue against clinic overtime and patient waiting time costs. We develop an approach where IC patients are scheduled first. To do so, we establish discrete convexity for a special tree-type directed network structure and generate near-optimal IC patient schedules for a more general acyclic directed network. Conditioned on IC patients’ schedule, we show that the VM patient scheduling problem has a discrete convexity property even in the presence of non-linear costs. Through numerical examples based on IPUs being implemented by the Dell Medical School at the University of Texas at Austin, we find that the introduction of VM patients can substantially improve system performance and patient access without adding resources.