Design of a Lagrangian Relaxation-Based Hierarchical Production Scheduling Environment for Semiconductor Wafer Fabrication

Abstract—This paper describes the design of a two-level hierarchical production scheduling engine, which captures the industrial practice of mass production semiconductor fabrication factories (fabs). The two levels of the hierarchy consist of a mid-term scheduler and a short-term scheduler, and are aimed at achieving coordination between the fab-wide objectives and local shop-floor operations. The mid-term scheduler maximizes weighted production flow to reduce the fab-wide cycle time and ensure on-time delivery by properly setting daily production target volumes and reference work-in-process (WIP) levels for individual part types and stages. Mid-term scheduling results are further broken down into more detailed schedules by the short-term scheduler. In addition to the same set of operational constraints in mid-term scheduling, the short-term scheduler includes the consideration of batching effects. It maximizes weighted production flow while tracking the daily production targets and the reference WIP levels specified by mid-term scheduling. The schedulers adopt a solution methodology with three ingredients; the Lagrange relaxation approach, network flow optimization, and Frank–Wolfe method. The methodology is optimization-based, exploits the separability of the scheduling problem formulations, and facilitates quick answers to “what if ” analysis. Test results using field data indicate that the two-level scheduling tool is reasonably efficient in computation and leads to throughput increase and reduction of output variations. The scheduling results can further be utilized in variability analysis for cycle time reduction. Index Terms—Hierarchical scheduling, Lagrangian relaxation, reentrant line, target generation