Appointment overbooking with different time slot structures

Unattended appointments result in underperformance of a healthcare service provider. Such uncertainty in the appointment process not only lowers healthcare utilization and productivity but also hinders patients from having timely access to healthcare services and extends waiting time for receiving medical examinations or treatments. In this study, we formulate this stochastic optimization problem for appointment scheduling as its two-stage deterministic equivalent to simultaneously optimize overbooking and scheduling decisions to compensate patient no-shows with different time slot structures. We examine the impacts of three types of time slot structures, which are of fixed-length slot intervals, dome-pattern slot intervals and flexible appointment start times, on the efficiency of the system. With the optimal solutions found, we investigate the interaction between the time slot structure and the optimal overbooking solution. We found that the flexibility in appointment start times result in a “dome-dome-dome pattern with alternate long and short time slots” and could achieve a better patient experience (regarding the patient waiting time) while maintaining the same service provider efficiency (regarding the resource overtime and idle time), compared with the pre-defined time intervals. While there has been a large body of literature on appointment scheduling, to the best of our knowledge, this “dome-dome-dome” pattern has not been reported in the existing literature. Sensitivity analysis further shows that the flexible slot scheme is more effective when the number of overbooked patients is relatively low and the service duration is relatively long.