Multi-objective optimisation for constructing cyclic appointment schedules for elective and urgent patients

In this paper, we study the construction of a cyclic appointment schedule in an outpatient department. In particular, we determine the capacity distribution between elective and urgent patients and the scheduling of the time slots reserved for these patients such that the operational waiting times of elective and urgent patients are minimised. The proposed solution methodology devises a Pareto set of cyclic appointment schedules based on these waiting times with different capacity allocations for urgent patients. An approximation of the Pareto set of non-dominated schedules is obtained using a multi-objective archived simulated annealing heuristic. To accurately validate the cyclic appointment schedules, we incorporate operational decision-making via scheduling individual patients. To this end, we simulate operational variability, i.e., patient arrivals, no-show behaviour, punctuality and scan durations, based on real-life input data. The patients are assigned one-by-one using an online scheduling rule. Computational experiments are conducted with a real-life case study. We compare different appointment scheduling rules and discuss the impact of the capacity distribution between elective and urgent patients and the timing of urgent slots in the cyclic appointment schedules. The results show that the distribution of capacity between patient types, the timing of urgent slots and appointment rules all have significant impacts on patient waiting times. Appointment waiting times improve when urgent slots are spread equally over and throughout the days considered and when the Bailey–Welch rule is used to schedule patients. Trade-offs between elective and urgent waiting times resulting from different capacity distributions or slot timing are exemplified via a Pareto front. The proposed method outperforms relevant single-pass methodologies, and we demonstrate that its performance is strengthened thanks to the integrated optimisation of strategic, tactical and operational decisions.