Stochastic radiotherapy appointment scheduling

When scheduling the starting times for treatment appointments of patients in hospitals or outpatient clinics such as radiotherapy centers, minimizing patient waiting time and simultaneously maximizing resource usage is crucial. Significant uncertainty in the treatment durations makes scheduling those activities particularly challenging. In addition to the treatments themselves, also preparation times and exiting times have to be considered, which are uncertain as well. To address and analyze this type of problems, the current study develops a model for planning appointment times under uncertain activity durations for a medical unit with a single “core resource” (in our application case a radiotherapy beam device), several treatment rooms, and required preparation and exiting phases for each patient. We employ a novel buffer concept based on quantiles of duration distributions and introduce a reactive procedure that adapts a pre-determined baseline schedule to the actual patient flow. For heuristically solving the resulting stochastic optimization model, a combination of a Genetic Algorithm and Monte Carlo simulation is proposed. A case study uses real-world data on activity durations gathered from an ion beam therapy facility in Austria. Experimental results comparing different variants of the method are carried out. In particular, comparisons of the stochastic optimization approach to a simpler deterministic approach are given.