Multi-Criteria Optimization for Medical Physics Scheduling: A Soft-Constraint–Driven System with Superior Coverage and Quality-of-Life Performance
Abstract
Purpose
Automating medical physics scheduling is challenging due to the need to balance clinical coverage, fairness, employee preferences, and quality-of-life considerations. This work presents a multi-criteria optimization (MCO)–based scheduling system designed to replace manual and commercial scheduling approaches by efficiently incorporating a large set of hard and soft constraints. The system was evaluated against both manually generated schedules and a state-of-the-art commercial scheduling platform.
Methods
A large-scale constrained integer programming model was developed using the CP-SAT solver from the OR-Tools library. The model encodes mandatory requirements as hard constraints while representing fairness objectives, employee preferences, and quality-of-life considerations as soft constraints with configurable penalties. This formulation allows the optimizer to prioritize full task coverage while flexibly trading off competing objectives. A robustness metric was additionally introduced to quantify schedule vulnerability to employee unavailability. Performance was compared against manually created schedules and schedules generated by a leading commercial scheduling system.
Results
The proposed system successfully filled 99% of all scheduling tasks, substantially outperforming the commercial system, which filled 89% under the same constraints. The optimizer incorporated 13 quality-of-life constraints not supported by the commercial platform, including preferences related to workload balance, protected time, and scheduling patterns. Compared to manual scheduling, the automated approach reduced planning time by approximately a factor of 50 and produced more equitable task distributions. Soft-constraint modeling enabled high coverage while maintaining employee satisfaction without violating critical requirements. The robustness analysis identified assignments most sensitive to staffing disruptions, supporting proactive contingency planning.
Conclusion
A CP-SAT–based scheduling system with explicit soft-constraint modeling provides superior coverage, fairness, and flexibility compared to both manual and commercial scheduling approaches. This framework enables high-quality, transparent, and resilient scheduling while accommodating complex quality-of-life considerations that are otherwise impractical to manage manually.