Planning for Overtime: The Value of Shift Extensions in Physician Scheduling

Scheduling physicians is a key success factor in hospitals. Heterogeneous demand and 24/7 service make the problem challenging. Approaches in the literature use flexible shift patterns to match demand with scarce resources. In these approaches, demand is usually assumed to be deterministic. However, surgery durations and emergency arrivals are both uncertain, leading to massive staff overtime. We introduce stochastic demand for physicians using a scenario-based approach. To incorporate this in scheduling, we allow variable shift extensions. If a variable shift extension is scheduled, the physician knows that with a given probability he or she may have to work a few periods longer. Thus, we ensure a matching of supply with demand, and at the same time we increase predictability of working hours. We propose a mixed-integer model and a column generation heuristic to solve our problem and provide experimental data from a German university hospital. Our approach reduces unplanned overtime by more than 80%, given a constant workforce. In cases of similar levels of unplanned overtime, the required workforce level can be decreased by 20%. Our approach aims at improving physicians' work-life balance and provides insights for hospitals' contract design processes.