In this paper, we study a real scheduling problem which consists in scheduling a set of elective surgical cases which require surgical instruments and tools to several operating rooms. The main objective is to minimize the operating costs while taking into account the uncertainties in surgery duration and the activities of the sterilizing unit. This research was performed in collaboration with the University Hospital of Angers in France (UHA Angers), which has also provided historical data for the experiments. We propose two robust MILP formulations to deal with the uncertainties and a Relax and Fix method to solve the first formulation. The solutions obtained are competitive in terms of number of operating rooms, and significantly improve those operationally implemented at the UHA in terms of overtime and emergencies at the sterilizing unit.