Handling processing time uncertainty in flexible job shop scheduling with variable sublots: a CVaR-enhanced MILP and multi-agent reinforcement learning approach

The utilisation of variable sublots in scheduling increases machine efficiency through operation overlap, yet its performance is vulnerable to processing time uncertainty, which can propagate delays and erode robustness. This paper tackles the flexible job shop scheduling problem with variable sublots (FJSP-VS) under such uncertainty, seeking to harness lot streaming efficiency while rigorously managing downside risk. We propose a risk-aware, integrated framework coupling multi-agent reinforcement learning (MARL) for adaptive coordination with a scenario-based, conditional value-at-risk(CVaR)-enhanced mixed-integer program (MILP) for robust sublot planning. The MARL component handles dynamic, operation-level scheduling across flexible routes, while the CVaR-enhanced MILP provides a formal hedge against severe makespan outcomes in sublot partitioning, machine assignment, and timing decisions. Computational results on established benchmarks reveal that the proposed framework consistently surpasses risk-neutral and alternative robust schedulers. The method reduces the CVaR0.9 of makespan by up to about 2% while maintaining competitive average makespan performance, resulting in more stable scheduling outcomes under processing-time uncertainty.