An Integer Programming Method for Maintenance Schedule Optimization in Nuclear Power Plants

Maintenance scheduling in nuclear power plants (NPPs) is challenging because multicomponent systems exhibit strong interdependencies and must satisfy strict safety requirements. We present a two-tier framework that couples a mixed-integer programming (MIP) model with a probabilistic risk assessment (PRA) layer for at-power maintenance scheduling.The PRA module evaluates incumbent schedules, and through a solver callback, triggers additional constraints that exclude configurations violating PRA-derived risk thresholds, technical specification limits (e.g., limiting condition for operation windows), and physical work control rules, thereby guiding the MIP toward cost-optimal, safety-compliant solutions.We construct anonymized test sets by mapping real maintenance work packages onto a hypothetical high-pressure injection system comprised of three trains. The framework is validated on three weekly workloads (A-, B-, and C-train task sets), each examined under three backlog policies.With a 16-h wall-clock limit and interim checkpoints at 30 min, the framework proves optimality in three of nine scenarios and terminates within 10% of the best bound in all nine, with the backlog-enabled scenarios remaining the most numerically challenging (gaps of 3.32% to 9.10%), reflecting the added combinatorial difficulty of optional task selection.In a representative comparison against a schedule hand constructed by methods used in current practice, the optimized A-train plan satisfies all operational requirements at substantially lower labor cost ($28 920 versus $36 612) while respecting out-of-service limits and PRA guardrails.These results demonstrate that integrating MIP with configuration risk screening can reduce operating and maintenance costs without sacrificing safety margins, and represent a promising direction for further development toward routine, cost aware maintenance planning in NPPs.