In Europe, around half of all patients diagnosed with cancer are treated with radiation therapy. To reduce waiting times, optimizing the use of linear accelerators for treatment is crucial. This paper introduces an Integer Programming (IP) and two Constraint Programming (CP) models for the non-block radiotherapy patient scheduling problem. Patients are scheduled considering priority, pattern, duration, and start day of their treatment. The models include expected future patient arrivals. Treatment time of the day is included in the models as time windows which enable more realistic objectives and constraints. The models are thoroughly evaluated for multiple different scenarios, altering: planning day, machine availability, arrival rates, patient backlog, and the number of time windows in a day. The results demonstrate that the CP models find feasible solutions earlier, while the IP model reaches optimality considerably faster.

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 patient arrivals 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.

The number of cancer cases per year is rapidly increasing worldwide. In radiation therapy (RT), radiation from linear accelerators is used to kill malignant tumor cells. Scheduling patients for RT is difficult both due to the numerous medical and technical constraints, and because of the stochastic inflow of patients with different urgency levels. In this paper, a Column Generation (CG) approach is proposed for the RT patient scheduling problem. The model includes all the constraints necessary for the generated schedules to work in practice, including for example different machine compatibilities, individualized patient protocols, and multiple hospital sites. The model is the first to include planned interruptions in treatments due to maintenance on machines, which is an important aspect when scheduling patients in practice, as it can create bottlenecks in the patient flow. Different methods to ensure that there are available resources for high priority patients at arrival are compared, including static and dynamic time reservation. Data from Iridium Netwerk, the largest cancer center in Belgium, is used to evaluate the CG approach. The results show that the dynamic time reservation method outperforms the other methods used to handle uncertainty in future urgent patients. A sensitivity analysis also shows that the dynamic time reservation method is robust to fluctuations in arrival rates. The CG approach produces schedules that fulfill all the medical and technical constraints posed at Iridium Netwerk with acceptable computation times.

The predicted increase in the number of patients receiving radiation therapy (RT) to treat cancer calls for an optimized use of resources. To manually schedule patients on the linear accelerators delivering RT is a time-consuming and challenging task. Operations research (OR), a discipline in applied mathematics, uses a variety of analytical methods to improve decision-making. In this paper, we study the implementation of an OR method that automatically generates RT patient schedules at an RT center with ten linear accelerators. The OR method is designed to produce schedules that mimic the objectives used in the clinical scheduling while following the medical and technical constraints. The resulting schedules are clinically validated and compared to manually constructed, historical schedules for a time period of one year. It is shown that the use of OR to generate schedules decreases the average patient waiting time by 80%, improves the consistency in treatment times between appointments by 80%, and increases the number of treatments scheduled the machine best suited for the treatment by more than 90% compared to the manually constructed clinical schedules, without loss of performance in other quality metrics. Furthermore, automatically creating patient schedules can save the clinic many hours of administrative work every week.