Abstract

Optimal scheduling of patients waiting for radiation treatments is a quite challenging operational problem in radiotherapy clinics. Long waiting times for radiotherapy treatments is mainly due to imbalanced supply and demand of radiotherapy services, which negatively affects the effectiveness and efficiency of the healthcare delivered. On the other hand, variations in the time required to set-up machines for each individual patient as well as patient treatment times make this problem even more involved. Efficient scheduling of patients on the waiting list is essential to reduce the waiting time and its possible adverse direct and indirect impacts on the patient. This research is focused on the problem of scheduling patients on a prioritized radiotherapy waiting list while the rescheduling of already booked patients is also possible. The aforementioned problem is formulated as a mixed-integer program that aims for maximizing the number of newly scheduled patients such that treatment time restrictions, scheduling of patients on consecutive days on the same machine, covering all required treatment sessions, as well as the capacity restriction of machines are satisfied. Afterwards, with the goal of protecting the schedule against treatment time perturbations, the problem is reformulated as a cardinality-constrained robust optimization model. This approach provides some insights into the adjustment of the level of robustness of the patients schedule over the planning horizon and protection against uncertainty. Further, three metaheuristics, namely Whale Optimization Algorithm, Particle Swarm Optimization, and Firefly Algorithm are proposed as alternative solution methods. Our numerical experiments are designed based on a case study inspired from a real radiotherapy clinic. The first goal of experiments is to analyze the performance of proposed robust radiotherapy appointment scheduling (ASP) model in terms of feasibility of schedule and the number of scheduled patients by the aid of Monte-Carlo simulation. Our second goal is to compare the solution quality and CPU time of the proposed metaheuristics with a commercial solver. Our experimental results indicate that by only considering half of patients treatment times as worst-case scenario, the schedule proposed by the robust RAS model is feasible in the presence of all randomly generated scenarios for this uncertain parameter. On the other hand, protecting the schedule against uncertainty at the aforementioned level would not significantly reduce the number of scheduled patients. Finally, our numerical results on the three metaheuristics indicate the high quality of their converged solution as well as the reduced CPU time comparing to a commercial solver.