A Policy-Based Rough Optimization with Large Neighborhood Search for Carbon‑Aware Flexible Job Shop Scheduling with Tardiness Penalty

Sustainable manufacturing increasingly requires production schedules that balance environmental responsibility with delivery reliability. In flexible job shop environments, this challenge is especially difficult because machine assignment and sequencing decisions affect both the carbon footprint of production and the risk of missing job due dates. Motivated by this trade-off, this paper studies the Carbon-Aware Flexible Job Shop Scheduling Problem with Tardiness Penalty (CAFJSP-T), a flexible job shop formulation in which total carbon emissions and total tardiness penalty are treated as the two primary objectives, while energy consumption and makespan are retained as supporting performance indicators. To solve this problem, we propose a Policy-based Rough Optimization with Large Neighborhood Search (Pro-LNS) framework that combines Proximal Policy Optimization for fast, policy-guided construction of feasible schedules with an adaptive large neighborhood search procedure for targeted refinement. The two phases are aligned through a normalized scalarized objective that balances carbon emissions and tardiness penalty while preserving all precedence, eligibility, and machine-capacity constraints. Computational experiments on benchmark instances spanning small, medium, and large workcenter categories show that Pro-LNS produces high-quality schedules with strong due-date performance and controlled carbon emissions. Under equal objective weighting, the method achieves a median optimality gap of 6.12% relative to the exact formulation, with all reported instances remaining within 14%, while requiring only 4.08 seconds on average and at most 10.51 seconds. These results indicate that Pro-LNS is an effective and computationally practical approach for carbon-aware, tardiness-sensitive flexible job shop scheduling.