Calendar design for assignment of ongoing appointments: Modeling, analysis and application

Appointment booking (AB) is a widely used technique for managing elective services like hospital surgical units, law courtrooms, and other services with high demand and limited resources. AB typically assigns services to specific time slots using an appointment calendar. However, devising an effective AB policy is challenging due to varying service types, durations, and demand variability. In this study, we present a preplanned appointment calendar (PAC), designed using a two-stage stochastic programming model to tackle service scheduling challenges based on demand and historical data. The design of the PAC is generated offline, prior to the arrival of any customers requesting an appointment, and aims to minimize the time from the initial appointment request to service completion, namely, the patient’s sojourn time. Despite the substantial public expenses incurred when appointments are scheduled far in the future, encompassing both indirect costs (e.g., those related to the development of chronic diseases) and direct costs (e.g., those arising from employee absence), the sojourn-time measure has not received sufficient attention in the existing literature. Our method minimizes patients’ sojourn time while considering operational constraints and quality of service (QoS) considerations, resulting in a practical and user-friendly appointment booking system. Our approach is adjustable and easy to apply in real time. We introduce the chained-PAC (CPAC) mechanism, in which multiple, smaller PACs are joined together, and demonstrate the applicability of this approach by implementing it in a cardiac surgical operating room at a major hospital in Toronto, Canada. Results show the PAC approach reduces wait times and improves resource utilization in the surgical unit compared to the existing AB system. Our approach benefits healthcare providers and patients and can extend to other similar service systems.