Dynamic allocation of same-day requests in multi-physician primary care practices in the presence of prescheduled appointments

Appointments in primary care are of two types: 1) prescheduled appointments, which are booked in advance of a given workday; and 2) same-day appointments, which are booked as calls come during the workday. The challenge for practices is to provide preferred time slots for prescheduled appointments and yet see as many same-day patients as possible during regular work hours. It is also important, to the extent possible, to match same-day patients with their own providers (so as to maximize continuity of care). In this paper, we present a mathematical framework (a stochastic dynamic program) for same-day patient allocation in multi-physician practices in which calls for same-day appointments come in dynamically over a workday. Allocation decisions have to be made in the presence of prescheduled appointments and without complete demand information. The objective is to maximize a weighted measure that includes the number of same-day patients seen during regular work hours as well as the continuity provided to these patients. Our experimental design is motivated by empirical data we collected at a 3-provider family medicine practice in Massachusetts. Our results show that the location of prescheduled appointments – i.e. where in the day these appointments are booked – has a significant impact on the number of same-day patients a practice can see during regular work hours, as well as the continuity the practice is able to provide. We find that a 2-Blocks policy which books prescheduled appointments in two clusters – early morning and early afternoon – works very well. We also provide a simple, easily implementable policy for schedulers to assign incoming same-day requests to appointment slots. Our results show that this policy provides near-optimal same-day assignments in a variety of settings.