Appointment scheduling in tandem-type service systems

• A computational approach to appointment scheduling for a two-node tandem.
• A general approach to evaluate the steady-state distribution of sojourn times.
• Deriving optimal schedules for a two-node tandem (transient and in steady-state).
• An assessment of various effects in a multi-node appointment scheduling model.

Appointment-based service systems arise in a broad variety of healthcare settings (for example an outpatient clinic or a dentist). Where most existing algorithms specifically consider the situation of the patient undergoing a single service, in many practical situations multiple services have to be sequentially performed. Modeling the service system as a tandem queue, the main objective of this paper is to generate schedules that soundly balance the interests of patients (i.e., low waiting times) and staff (i.e., low idle times). Importantly, following up on prior work for the single-node queue, we advocate a phase-type based technique that can deal with any service-time distribution (which may, in addition, vary across patients). Relying on a novel recursive scheme to evaluate the sojourn-time distribution of clients in such tandem systems, we show how optimal schedules can be computed. Our technique is illustrated by extensive numerical experimentation, also leading to practical guidelines that apply to a broad range of parameter settings.