This book outlines the results of a systematic, long-term research effort aimed at developing effective scheduling algorithms for complex manufacturing facilities. The book focuses on a specific industrial context, that of semiconductor manufacturing. The authors combine knowledge of the specific physical production system with the methods and results of previous scheduling research to develop effective, approximate solution procedures for scheduling problems. The decomposition methods developed in this book constitute a broad family of heuristic approaches to large, NP-hard scheduling problems which can be applied to other manufacturing environments in addition to semiconductor production manufacturing facilities. The results reported in this book indicate that properly designed decomposition methods can obtain significantly better schedules than the dispatching rules that currently form the core of industrial scheduling practice.