Medical appointment overbooking and optimal scheduling: tradeoffs between schedule efficiency and accessibility to service

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Appointment overbooking has been commonly adopted for the mitigation of the adverse consequences of patient no-shows, such as reduced resource utilization and revenue. However, if there are more patients showing up than expected, the resource overtime and patient waiting time can increase. Due to the theoretical interest and the practical importance of the problem, there has been much research on the design of appointment schedules for the optimization of various performance measures. The adoption of appointment overbooking can also enhance the accessibility to medical service, by reducing the time between the date of calling for an appointment and the appointment date. Compared with the within-the-session schedule efficiency, the appointment lead time has drawn relatively little attention from researchers. In this research, we propose a framework that utilizes a stochastic mixed-integer linear program, which determines an optimal appointment schedule, for a simulation model for guiding the scheduling decisions. With this framework, we conduct a comprehensive analysis of the tradeoffs between schedule efficiency and accessibility to service. We first derive theoretical properties of our stochastic programming model. Then, we conduct computational experiments to examine the convergence of the stochastic mixed-integer linear programming model, the benefits of optimal appointment scheduling, the effects of two-dimensional uncertainty on the performance of appointment schedules, and the tradeoffs between schedule efficiency and accessibility to service. Our computational experiments suggest that a session capacity approximate to the request rate can balance the multiple conflicting objectives more effectively. We also examine the effects of a dynamic overbooking policy and a non-homogeneous appointment request rate. The computational results suggest that a fixed capacity policy can be as effective as a dynamic overbooking policy under the setting of a constant request rate; but the dynamic overbooking policy leads to a slightly better performance under the setting of a non-homogeneous appointment request rate.