A System-of-Systems Approach to Flexible Job-Shop Scheduling Using Column Generation

In the era of smart manufacturing, scheduling techniques play a crucial role in optimizing industrial processes. Among the various scheduling problems, the Flexible Job-Shop Scheduling Problem (FJSSP) represents a fundamental challenge due to the diversity of machines and production chains. The simultaneous management of routing and scheduling significantly increases complexity, making exact optimization methods impractical for large instances. This paper proposes a column generation approach to efficiently explore the solution space and improve makespan while significantly reducing computational time. The method iteratively refines the solution by generating promising columns, ensuring a trade-off between optimality and efficiency. Preliminary tests on medium and large instances, considering equivalent processing times, demonstrate that the proposed approach achieves near-optimal solutions at a considerably higher speed compared to traditional methods. These results highlight the potential of column generation as a viable strategy for addressing large-scale FJSSP instances in industrial applications.