The implementor/adversary algorithm for the cyclic and robust scheduling problem 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, and 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. However, the demand typically varies from week to week: even if we know in advance the exact demand for each week, the weekly schedule cannot be adapted accordingly. 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 and show that it corresponds to the implementor/adversary 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.