Multiple orders per job batch scheduling with incompatible jobs

The growth in demand for semiconductors has been accompanied by intense competition between semiconductor manufacturers to satisfy customer on-time delivery needs. This paper is motivated by scheduling the wafer fabrication phase of 300-mm semiconductor manufacturing, as it contains both batch processing operations and multiple customer orders being grouped into production jobs. The resulting multiple orders per job (MOJ) scheduling problem is presented for the batch-processing environment as exemplified by a diffusion oven. A mixed-integer programming formulation is presented for incompatible job families wherein only jobs that belong to the same family may be grouped together in a batch. This formulation is analyzed using an experimental design to minimize total weighted tardiness. While optimal solutions are attainable for small problem instances in a reasonable amount of computation time, heuristic development is warranted to support the analysis of larger, more practical MOJ batch scheduling problems. Promising heuristic approaches are identified that find near-optimal solutions very quickly.