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The manual scheduling of patients for radiation therapy is difficult and labor-intensive. With the increase in cancer patient numbers, efficient resource planning is an important tool to achieve short waiting times and equal right to care. This thesis studies an operations research approach to the radiation therapy scheduling problem. The four appended papers each provide incremental steps towards a clinical implementation of an automated scheduling algorithm. In Paper A, three models for the radiation therapy scheduling problem in a simplified clinical setup are proposed. It is shown that the two constraint programming models find feasible solutions more quickly, while the integer programming model proves optimality faster. However, none of the models can solve large problem instances in sufficient time. In Paper B a collaboration with a large cancer center with ten linear accelerators is initiated. The previous models are refined and adapted to a more realistic clinical setup. Moreover, a column generation approach is introduced. The models are compared using different objective function combinations designed to mimic the scheduling objectives at different cancer centers. The column generation approach outperforms the other methods on all problem instances, regardless of what objective is optimized. In Paper C the column generation approach is further developed to include additional medical and technical constraints. Different methods to ensure that there are available resources for high priority patients at arrival are compared. Finally, in Paper D the potential for clinical implementation of the column generation approach is evaluated. The schedules generated by the column generation model are clinically validated. Compared to manually constructed, historical schedules for a time period of one year, the automatically generated schedules are shown to decrease the average patient waiting time by 80%, improve the consistency in treatment times between appointments, Att för hand schemalägga patienter för strålterapi är svårt och tidskrävande. Antalet cancerfall ökar i världen, vilket har gjort effektiv resursplanering till ett viktigt verktyg för att uppnå korta väntetider och patienters lika rätt till vård. Denna avhandling studerar användandet av operationsanalys för schemaläggning av patienter för strålterapi. Var och en av de fyra bifogade artiklarna gör inkrementella steg mot en klinisk implementation av en automatiserad schemaläggningsalgoritm. Artikel A presenterar tre modeller för att schemalägga patienter för strålterapi. Resultaten visar att de två villkorsprogrammeringsmodellerna tidigare hittar tillåtna lösningar, medan heltalsprogrammeringsmodellen snabbare kan bevisa optimalitet. Ingen av modellerna kan dock lösa större problem inom en rimlig tidsram. I artikel B förbättras och utvecklas modellerna för att återspegla en mer realistisk cancerklinik. Utöver det introduceras en ny kolumngenereringsmetod. Olika målfunktioner utformas för att efterlikna målen med schemaläggningen på olika cancerkliniker, och de olika modellerna jämförs med hjälp av dessa målfunktioner. Resultaten visar att kolumngenereringsmetoden överträffar de andra modellerna på alla probleminstanser, oavsett vilken målfunktion som används. I artikel C utökas kolumngenereringsmodellen med fler bivillkor för ytterligare medicinska och tekniska krav på schemana inom ett kliniskt samarbete med en stor cancerklinik med tio linjäracceleratorer. Därtill jämförs olika sätt att säkerställa att det finns resurser för akuta patienter direkt vid ankomst. I artikel D utvärderas slutligen vilken potential kolumngenereringsalgoritmen har för klinisk implementation. Automatiskt genererade scheman valideras kliniskt och jämförs med ett kliniskt schema som lagts manuellt för en tidsperiod av ett år. Det automatiskt genererade schemat minskar den genomsnittliga väntetiden för behandlingsstart med 80%, förbättrar den genomsnittliga jämnheten i tidsbokningarna med 8, QC 20230427

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., QC 20230428

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., QC 20230428

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., QC 20230428