A Robust Optimization Model for Managing Elective Admission in a Public Hospital

The admission of emergency patients in a hospital is unscheduled, urgent, and takes priority over elective patients, who are usually scheduled several days in advance. Hospital beds are a critical resource, and the management of elective admissions by enforcing quotas could reduce incidents of shortfall. We propose a distributionally robust optimization approach for managing elective admissions to determine these quotas. Based on an ambiguous set of probability distributions, we propose an optimized budget of variation approach that maximizes the level of uncertainty the admission system can withstand without violating the expected bed shortfall constraint. We solve the robust optimization model by deriving a second order conic problem (SOCP) equivalent of the model. The proposed model is tested in simulations based on real hospital admission data, and we report favorable results for adopting the robust optimization models.