A Rolling-Horizon Approach for a Surgery Case Scheduling Problem with Sterilizing Constraints

In this paper, we study a real scheduling problem which consists in scheduling a set of elective surgical cases that arrive over the time taking into account the uncertainties on their duration, and the delay to sterilize surgical instruments. The objectives are to schedule as many surgeries as possible, and to minimize the overtime of the surgical block staff and the number of instruments processed in emergency in the sterilizing unit. This research was performed in collaboration with the University Hospital of Angers in France, which has also provided historical data for the experiments. We propose a rolling horizon approach based on the iterative resolution of a robust mixed integer linear programming model, in which the objective functions are taken into account in a lexicographic order. The experiments on real data show a reduction of more than 50% of overtime, and around 87% less stress situations in the sterilizing unit.