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.
When scheduling the starting times for treatment appointments of patients in hospitals or outpatient clinics such as radiotherapy centers, minimizing patient waiting time and simultaneously maximizing resource usage is crucial. Significant uncertainty in the treatment durations makes scheduling those activities particularly challenging. In addition to the treatments themselves, also preparation times and exiting times have to be considered, which are uncertain as well. To address and analyze this type of problems, the current study develops a model for planning appointment times under uncertain activity durations for a medical unit with a single “core resource” (in our application case a radiotherapy beam device), several treatment rooms, and required preparation and exiting phases for each patient. We employ a novel buffer concept based on quantiles of duration distributions and introduce a reactive procedure that adapts a pre-determined baseline schedule to the actual patient flow. For heuristically solving the resulting stochastic optimization model, a combination of a Genetic Algorithm and Monte Carlo simulation is proposed. A case study uses real-world data on activity durations gathered from an ion beam therapy facility in Austria. Experimental results comparing different variants of the method are carried out. In particular, comparisons of the stochastic optimization approach to a simpler deterministic approach are given.
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