Appointment Scheduling of Outpatient Clinical Services Under Uncertain Patient Flows

We study the problem of appointment scheduling for outpatient clinical services, where patient arrivals, appointment cancellations, and attendance are inherently random, leading to high variability in patient flow. Analyzing dynamic scheduling decisions is particularly challenging due to the need to track confirmed appointments within the scheduling window. For planning with a long horizon, we show that a probabilistic allocation policy can be efficiently computed by optimizing a closed-form function. This policy ensures that the system’s long-term profit asymptotically approaches the optimal profit in scalable settings. For a limited planning horizon, we propose a sequential assignment process implemented with a predetermined scheduling diagram. We characterize the conditions under which this scheduling diagram policy achieves optimality. Notably, an improved scheduling diagram policy emerges as a refinement of either a probabilistic allocation policy or a same-day scheduling policy, and we prove that it is optimal for two-day scheduling windows. The computation of the scheduling diagrams is straightforward, as it involves ranking the margins (i.e., first-order differences) of scalar profit functions, one for each day in the scheduling window. Extensive simulation analyses suggest that system efficiency can be achieved through a hybrid strategy, where a two-day policy is applied to a short scheduling window and an improved probabilistic policy is used for a long scheduling window.

Funding: This research was supported by the Major Program of the National Social Science Fund of China [Grant 21&ZD128].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results are available at https://doi.org/10.1287/opre.2022.0353.