Surgical case scheduling with sterilising activity constraints

In this paper, we study a real scheduling problem which consists in scheduling a set of elective surgical cases requiring surgical instruments and tools in several operating rooms. The objectives are to minimise the overtime of the surgical unit staff, the number of operating rooms used and the number of instruments processed in emergency in the sterilising unit while respecting the current level of service represented by the total number of patients operated per month at the orthopaedic surgery unit. This research was performed in collaboration with the University Hospital of Angers in France (CHU Angers), which has also provided historical data for the experiments. We propose a mixed integer linear programming model for the problem which is solved in a lexicographic fashion. We also propose a robust formulation to deal with the uncertain surgery durations. Both the deterministic and robust formulations are then compared over a set of instances provided by the CHU. The solutions obtained are competitive in terms of number of operating rooms and significantly improve those implemented operationally at the CHU in terms of overtime and emergencies at the sterilising unit.