A matheuristic approach to multi-objective batch scheduling of parallel diffusion furnaces with slot-eligibility and non-product wafers

Diffusion processes in semiconductor manufacturing are frequently identified as primary bottlenecks due to their extensive processing times and complex batching requirements. This study investigates a multi-objective batch scheduling problem for identical parallel diffusion furnaces, explicitly incorporating two practically important constraints: slot-eligibility and the strategic usage of non-product wafer (NPW) lots. Slot-eligibility constraints are imposed to ensure thermal uniformity and process stability within the furnace, while NPW lots are employed to satisfy minimum loading requirements, resulting in capacity loss. We formulate a Mixed-Integer Linear Programming (MILP) model to minimise a weighted sum of the makespan, the number of tardy lots, and NPW usage. To address large-scale industrial instances that are computationally intractable for exact methods, we propose Product-based Reconstruction and Iterative Sequencing Matheuristic (PRISM), which integrates product-based decomposition, MILP-based batch reconstruction, and iterative sequencing refinement to navigate the complex solution space efficiently. Numerical experiments on benchmark instances generated to reflect practical fab operating characteristics demonstrate that the proposed approach significantly outperforms the direct solution of the MILP formulation and conventional metaheuristics, providing high-quality schedules within practical computational time limits.