Abstract:
Planning and scheduling of resources is a crucial process within healthcare organisations. Careful planning allows limited resources, such as staff and operating rooms, to be used efficiently. However this is often a difficult and time consuming process, and not all elements are known with certainty. Mathematical modelling can be applied to assist in rostering and scheduling. Further, historical data collected by the healthcare organisations enables modelling of the uncertainty in the planning processes. This thesis considers two planning processes: rostering physicians; and scheduling surgeries; and develops mathematical models for both situations. A model for rostering physicians is proposed which incorporates the admission and discharge of patients, and uses patient pathways to connect multiple rosters. In addition an objective function for scheduling surgeries is formed that utilises a risk measure applied to the due dates of operations, and new methods for estimating the probability that surgical sessions run overtime are developed. Further, both models are applied to case studies in a practical setting. The rostering model has been used to create a roster that was implemented in a hospital department, while efforts are ongoing to promote the adoption of the surgery scheduling methods in several surgical services. Both uncertainty and risk are investigated in the two models. In the rostering model the uncertainty considered is in the number of patients the physicians are caring for, whereas in the surgery scheduling model the uncertainty lies in the duration of the operations performed. In the rostering model risk directly relating to the uncertainty modelled, which is in the admissions and discharges of patients, is avoided. On the other hand, in the surgery scheduling model the risk of operations being performed much after they are due is avoided, rather than risk associated with the durations of operations. This research demonstrates the incorporation of historical data and the related uncertainty into rostering and scheduling approaches in order to improve the quality of the rosters and schedules produced.