Title: Select and Schedule: An Efficient Hierarchical Optimizer for Blocking Job Shop Scheduling Problem with Massive Jobs
Primary area: optimization
Keywords: Blocking Job Shop Scheduling Problem，Efficient，massive jobs

Abstract: The Blocking Job Shop Scheduling Problem (BJSP) is a widely studied variant of the classic Job Shop Scheduling Problem. In BJSP, the blocking constraint requires a job to remain on its current machine until the next machine is available. This constraint substantially increases problem complexity, which in turn limits most existing scheduling algorithms to small-scale instances.  However, we observe that this blocking constraint also has merit: it naturally restricts the number of jobs processed concurrently, thereby reducing the number of candidate jobs that must be considered at almost any decision point. Building on this insight, we propose a novel hierarchical optimization framework. The higher layer employs a neural network to select a small subset of jobs from a large candidate pool, while the lower layer uses a solver to schedule the selected jobs. Compared with traditional approaches that directly schedule large sets of jobs, our method achieves significantly lower computational complexity and scales almost linearly with the number of jobs. This scalability enables us to efficiently handle larger instances that are previously intractable. Experimental results demonstrate that, on large-scale benchmarks and under comparable runtime budgets, our approach improves solution quality by an average of 11\%, while continuing to deliver high-quality solutions within reasonable runtimes for even larger instances.