This is one of two volumes devoted to single and multistage systems in scheduling theory respectively. The main emphasis throughout is on the analysis of the computational complexity of scheduling problems. This volume is devoted to the problems of determining optimal schedules for systems consisting of either a single machine or several parallel machines. The most important statements and algorithms which relate to scheduling are described and discussed in detail. The book has an introduction followed by four chapters dealing with the elements of graph theory and the computational complexity of algorithms, polynomially solvable problems, priority-generating functions, and NP-Hard problems, respectively. Each chapter concludes with a comprehensive biobliography and review. The volume also includes an appendix devoted to approximation algorithms and extensive reference sections. For researchers and graduate students of management science and operations research interested in production planning and flexible manufacturing.