Scheduling Recurring Radiotherapy Appointments in an Ion Beam Facility: Considering Optional Activities and Time Window Constraints

Ion beam radiotherapy is a modern form of cancer treatment that is offered in specialized facilities. Treatment consists of multiple, almost daily irradiation appointments, followed by optional imaging and control assignments. The corresponding problem of scheduling these recurring radiotherapy treatment appointments can be classified as a complex job shop scheduling problem with custom constraints, such as recurring activities, optional activities, and special time window constraints. The objective is to minimize the operation time of the bottleneck resource, the particle beam, while simultaneously minimizing any penalties arising from violations of time window constraints. The authors model the problem mathematically and introduce various customized constraints. Three metaheuristic solution approaches—namely a genetic algorithm with tailor-made feasibility-preserving crossover operators, an iterated local search, and a combination of the two approaches—all perform well on both small and large problem instances. However, the simple combination of the two stand-alone algorithms leads to best results when applied to real-world inspired problem instances.