Comparing Optimization Methods for Radiation Therapy Patient Scheduling Using Different Objectives

Radiation therapy (RT) is a medical treatment to kill cancer cells or shrink tumors. To manually schedule patients for RT is a time-consuming and challenging task. By the use of optimization, patient schedules for RT can be created automatically. This paper presents a study of different optimization methods for modeling and solving the RT patient scheduling problem, which can be used as decision support when implementing an automatic scheduling algorithm in practice. We introduce an Integer Programming (IP) model, a column generation IP model (CG-IP), and a Constraint Programming model. Patients are scheduled on multiple machine types considering their priority for treatment, session duration and allowed machines. Expected future arrivals of urgent patients are included in the models as placeholder patients. Since different cancer centers can have different scheduling objectives, the models are compared using multiple objective functions, including minimizing waiting times, and maximizing the fulfillment of patients’ preferences for treatment times. The test data is generated from historical data from Iridium Netwerk, Belgium’s largest cancer center with 10 linear accelerators. The results demonstrate that the CG-IP model can solve all the different problem instances to a mean optimality gap of less than 1% within one hour. The proposed methodology provides a tool for automated scheduling of RT treatments and can be generally applied to RT centers.