A Column Generation Approach for Radiation Therapy Patient Scheduling with Planned Machine Unavailability and Uncertain Future Arrivals

Abstract

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.

Automated Radiation Therapy Patient Scheduling: A Case Study at a Belgian Hospital

“…The potential for clinical implementation of the mathematical model for RT patient scheduling presented by Frimodig et al [25] is evaluated using clinical input from different stakeholders. The input from medical physicists, booking administrators and radiation oncologists is used for data acquisition, defining quality metrics, and schedule validation.…”

“…The mathematical model developed in [25] is based on a column generation approach. It generates a schedule where each treatment session is assigned to a machine, day and time window, and the patient is assigned a specific start time within the time window in a post-processing step.…”

“…However, literature shows that the majority of patients find it reasonable to receive a notification of their start date three days in advance [11]. In [25] a compromise is used; for priority B and C patients, the notification period is one week and priority A patients are notified immediately. Iridium Netwerk communicates all fractions at once, so the same approach is applied to the automatic algorithm.…”

“…In a previous paper, we presented a mathematical model for the RT scheduling problem [25]. Daily batch scheduling collects new patients during one day, and schedules their fractions on a machine, day and time for a planning horizon of three months.…”

“…The main contribution in this paper is the evaluation of an OR method for automatic RT patient scheduling from a clinical point of view. The potential for clinical implementation of the previously developed method [25] is investigated using a clinical dataset from a one-year period. The automatically generated schedules were validated by the clinical staff to ensure compliance with the medical and technical constraints posed at the clinic.…”