The implementor/adversarial algorithm for cyclic and robust scheduling problems in health-care

A general problem in health-care consists in allocating some scarce medical resource, such as operating rooms or medical staff, to medical specialties in order to keep the queue of patients as short as possible. A major difficulty stems from the fact that such an allocation must be established several months in advance, whereas the exact number of patients for each specialty is an uncertain parameter. Another problem arises for cyclic schedules, where the allocation is defined over a short period, e.g. a week, and then repeated during the time horizon. Even if the demand is perfectly known in advance, the number of patients may vary from week to week. We model both the uncertain and the cyclic allocation problem as adjustable robust scheduling problems. We develop a row and column generation algorithm to solve this problem: this turns out to be the implementor/adversarial algorithm for robust optimization recently introduced by Bienstock for portfolio selection. We apply our general model to compute master surgery schedules for a real-life instance from a large hospital in Oslo.