Robust Multi-Class Multi-Period Scheduling of MRI Services with Wait Time Targets

Abstract

In recent years, long wait times for healthcare services have become a challenge in most healthcare delivery systems in Canada. This issue becomes even more important when there are priorities in patients' treatment which means some of the patients need emergency treatment, while others can wait longer. One example of excessively long wait times in Canada is the MRI scans. These wait times are partially due to limited capacity and increased demand, but also due to sub-optimal scheduling policies. Patients are typically prioritized by the referring physician based on their health condition, and there is a wait time target for each priority level. The difficulty of scheduling increases due to uncertainty in patients' arrivals and service times. In this thesis, we develop a multi-priority robust optimization (RO) method to schedule patients for MRI services over a multi-period finite horizon. First, we present a deterministic mixed integer programming model which considers patient priorities, MRI capacity, and wait time targets for each priority level. We then investigate robust counterparts of the model by considering uncertainty in patients' arrivals and employing the notion of the budget of uncertainty. Finally, we apply the proposed robust model to a set of numerical examples and compare the results with those of the non-robust method. Moreover, sensitivity analysis is performed over capacity, penalty cost, service level, and budget of uncertainty. Our results demonstrate that the proposed robust approach provides solutions with higher service levels for each priority, and lower patients' wait time in realistic problem instances. The analysis also provides some insights on expanding capacity and choosing the budget of uncertainty as a trade-off between performance and conservatism.