Radiotherapy treatment scheduling considering time window preferences

Abstract

External-beam radiotherapy treatments are delivered by a linear accelerator (linac) in a series of high-energy radiation sessions over multiple days. With the increase in the incidence of cancer and the use of radiotherapy (RT), the problem of automatically scheduling RT sessions while satisfying patient preferences regarding the time of their appointments becomes increasingly relevant. While most literature focuses on timeliness of treatments, several Dutch RT centers have expressed their need to include patient preferences when scheduling appointments for irradiation sessions. In this study, we propose a mixed-integer linear programming (MILP) model that solves the problem of scheduling and sequencing RT sessions considering time window preferences given by patients. The MILP model alone is able to solve the problem to optimality, scheduling all sessions within the desired window, in reasonable time for small size instances up to 66 patients and 2 linacs per week. For larger centers, we propose a heuristic method that pre-assigns patients to linacs to decompose the problem in subproblems (clusters of linacs) before using the MILP model to solve the subproblems to optimality in a sequential manner. We test our methodology using real-world data from a large Dutch RT center (8 linacs). Results show that, combining the heuristic with the MILP model, the problem can be solved in reasonable computation time with as few as 2.8% of the sessions being scheduled outside the desired time window.

Radiotherapy treatment scheduling: Implementing operations research into clinical practice

“…Although actual patient preferences could not be obtained from the NKI clinic as they were not being recorded in practice, our model was able to fulfill the estimated preferences a total of 98% of the times. A sensitivity analysis on the impact of varying the preferential time window distributions may be useful to further assess the robustness of the model [ 21 ]. Moreover, the number of gaps in the schedule decreased by 72% in the BVI, with the daily number of treatment sessions being delivered earlier in the day during the whole week.…”

“…We estimate the complete process can be finalized in a time frame of 2–4 hours, and the final solutions would be considerably more efficient that the ones currently produced manually in RT clinics. In very large RT centers where problem size increases complexity to a significant degree, a heuristic procedure may be applied to pre-allocate patients to (subgroups of) linacs before the MILP model is applied to solve the problem for each subgroup of linacs independently [ 21 ]. By providing a decision-making tool that generates a schedule in an automated way, we not only save planners the burden of having to produce a feasible schedule in due time, but also allows them to prioritize their activities more easily.…”

“…In this study, we have used and adapted the mixed-integer linear programming (MILP) model proposed by Vieira et al [ 17 ] to improve the RT treatment scheduling based on historic off-line data of two Dutch RT centers. MILP is a mathematical programming framework that involves the use of integer and continuous variables to model a decision problem by means of linear inequalities [ 17 ]. The process of adjusting the existent model to ensure that it produces a feasible schedule for each RT center was completed iteratively following a structured sequence of steps ( Fig 1 ).…”

“…In the NKI case, patients are given the possibility of choosing a preferential time window for the time of their treatment sessions. The objective of the NKI is then to find a schedule that maximizes the fulfillment of those patient preferences requests [ 17 ]. Thus, we use objective function (1a) of the MILP model ( S1 Appendix ) to maximize the number of sessions that are scheduled within the time window given by patients as a preference.…”

“…In this paper, we study the implementation of a weekly schedule for radiotherapy treatments obtained by using an earlier developed mathematical programming model [ 17 ]. In our previous publication, we proposed a theoretical model and tested it using fictitious data generated from datasets of a one-year period.…”