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

Sustainable manufacturing requires schedules that balance environmental responsibility with delivery reliability. This paper studies the Carbon-Aware Flexible Job Shop Scheduling Problem with Tardiness Penalty (CAFJSP-T), where total carbon emissions and total tardiness penalty are the primary objectives. We propose a Policy-based Rough Optimization with a Large Neighborhood Search (Pro-LNS) framework integrating Proximal Policy Optimization (PPO) and adaptive Large Neighborhood Search (LNS). PPO constructs a feasible schedule by selecting operation-machine assignments from job-readiness, machine-availability, earliest-completion, and critical-path features. This policy-generated schedule provides a structurally informed incumbent, enabling LNS to avoid unguided search and focus destroy-and-repair refinement on high-impact operations. Both phases use the same normalized scalarized carbon-tardiness objective, which guides PPO rewards and LNS removal, reinsertion, and acceptance while preserving precedence, eligibility, and capacity constraints. Experiments on small, medium, and large workcenter benchmarks show strong due-date performance and controlled carbon emissions. Under equal objective weighting, Pro-LNS achieves a median optimality gap of 6.12% relative to the exact formulation, with all instances within 14%, while requiring 4.08 s on average and at most 10.51 s. Comparisons with PPO-only, Advantage Actor-Critic (A2C), Soft Actor-Critic (SAC), and Genetic Algorithm (GA) schedulers show that Pro-LNS attains the best weighted scalarized objective across representative instance-weight settings. Friedman and Holm-corrected Wilcoxon tests confirm significant improvements over all competitors, with average weighted-objective gains of 4.90%, 7.25%, 8.81%, and 9.51% over PPO-only, A2C, SAC, and GA, respectively. These results demonstrate that Pro-LNS is an effective and computationally practical hybrid approach for carbon-aware, tardiness-sensitive flexible job shop scheduling.