Task assignments with rotations and flexible shift starts to improve demand coverage and staff satisfaction in healthcare

In recent years, the importance of achieving staffing flexibility to balance supply and demand in unpredictable environments, such as hospitals, has grown. This study focuses on shift design with task rotations for a multi-skilled workforce, specifically in service contexts characterized by pronounced demand variability. We introduce a mathematical programming model designed to identify optimal shift start times with task assignments for both full-time and part-time employees, where workers can rotate between multiple tasks during their shifts. We develop a column generation approach that allows us to solve realistically-sized problem instances. Our analysis, derived from staffing data of a university hospital’s radiation oncology department, reveals the model's robust applicability across varying demand landscapes. We demonstrate that incorporating task rotations in the shift design can improve workload balancing when task demands fluctuate considerably. Remarkably, our column generation technique produces optimal integer solutions for realistic problem instances, outperforming the compact mixed-integer formulation which struggles to achieve feasible results. We find that the success of embedding task rotations in shift design decisions is directly influenced by the demand profile, which in turn affects the necessary qualification mix of the workforce.