[Paper Review] An Integer Linear Programming Model for the Radiotherapy Treatment Scheduling Problem

Edmund Burke, Pedro Leite Rocha+1 more|arXiv (Cornell University)|Mar 17, 2011

Healthcare Operations and Scheduling OptimizationHealth Professions19 references16 citations

TL;DR

This paper proposes a new integer linear programming (ILP) model for scheduling radiotherapy treatments at Nottingham University Hospitals NHS Trust, optimizing for patient waiting times and schedule quality. Using real-world data and CPLEX, the model demonstrates that delaying schedule creation until patients' release dates are closer (e.g., 7 days in advance for routine patients) significantly improves key performance metrics, including reduced late patients and better adherence to target dates.

ABSTRACT

Radiotherapy represents an important phase of treatment for a large number of cancer patients. It is essential that resources used to deliver this treatment are employed effectively. This paper presents a new integer linear programming model for real-world radiotherapy treatment scheduling and analyses the effectiveness of using this model on a daily basis in a hospital. Experiments are conducted varying the days on which schedules can be created. Results obtained using real-world data from the Nottingham University Hospitals NHS Trust, UK, are presented and show how the proposed model can be used with different policies in order to achieve good quality schedules.

Motivation & Objective

• To address the challenge of inefficient radiotherapy treatment scheduling in the UK, where long waiting times persist despite treatment advances.
• To develop a practical, mathematically rigorous scheduling model that reflects real-world constraints in a hospital radiotherapy department.
• To evaluate the impact of different scheduling policies—particularly timing of schedule creation—on schedule quality and patient waiting times.
• To provide a decision-support tool for hospital schedulers using optimization, improving fairness and efficiency in linac allocation.
• To lay the foundation for future integration of robustness, rescheduling, and patient preference constraints into the model.

Proposed method

• Formulates a new integer linear programming (ILP) model with four optimization criteria: breach date, JCCO maximum acceptable target date, JCCO good practice target date, and squared waiting time.
• Uses real-world data from Nottingham University Hospitals NHS Trust, including patient categories (urgent, routine), release dates, treatment durations, and linac availability.
• Implements a myopic scheduling approach, where schedules are created daily based only on current patient availability, not future predictions.
• Employs CPLEX as the optimization engine to solve the ILP model and generate high-quality daily schedules.
• Tests various scheduling policies by varying the number of days in advance (MNDA) that schedules are created for patients relative to their release date.
• Incorporates constraints such as non-consecutive treatment days, linac eligibility, and deterministic treatment durations with fixed intervals.

Experimental results

Research questions

• RQ1 What is the optimal timing for creating radiotherapy schedules relative to patient release dates to minimize late patients and improve schedule quality?
• RQ2 How do different scheduling policies—based on patient urgency and release date proximity—affect key performance metrics like waiting time and target date adherence?
• RQ3 Can an ILP model effectively handle real-world constraints such as linac eligibility, non-consecutive treatments, and variable release dates?
• RQ4 How does the quality of schedules change when schedules are created earlier (e.g., 14 days before release) versus closer to the release date?
• RQ5 What is the trade-off between immediate scheduling and delayed scheduling in terms of robustness and patient waiting time?

Key findings

• Creating schedules for routine patients only when their release date is within 7 days (MNDA = 7) yields the best results for the breach criterion, significantly reducing the number of patients treated after their target date.
• The policy of creating schedules for urgent patients when their release date is within 14 or more days and for routine patients on their release date or later (MNDA = 14/0) achieves the best values for the JCCO maximum acceptable and good practice target dates.
• The squared waiting time criterion is minimized when schedules are created for urgent patients 14+ days in advance and routine patients on their release date or later, indicating fewer patients experience excessively long waits.
• Using MNDA values of ∞/7 (i.e., infinite look-ahead for urgent, 7-day look-ahead for routine) achieves the best breach date performance and near-optimal results for other criteria, making it the recommended policy.
• The policy of creating schedules immediately upon patient arrival (MNDA = 0) results in the worst performance across all criteria, especially for the breach and JCCO good practice targets.
• The experiments confirm that delaying schedule creation improves overall schedule quality, supporting the recommendation to avoid immediate scheduling despite patient preference for early confirmation.