Scheduling theory is an important branch of operations research. Problems studied within the framework of that theory have numerous applications in various fields of human activity. As an independent discipline scheduling theory appeared in the middle of the fifties, and has attracted the attention of researchers in many countries. In the Soviet Union, research in this direction has been mainly related to production scheduling, especially to the development of automated systems for production control. In 1975 Nauka ("Science") Publishers, Moscow, issued two books providing systematic descriptions of scheduling theory. The first one was the Russian translation of the classical book Theory of Scheduling by American mathematicians R. W. Conway, W. L. Maxwell and L. W. Miller. The other one was the book Introduction to Scheduling Theory by Soviet mathematicians V. S. Tanaev and V. V. Shkurba. These books well complement each other. Both. books well represent major results known by that time, contain an exhaustive bibliography on the subject. Thus, the books, as well as the Russian translation of Computer and Job-Shop Scheduling Theory edited by E. G. Coffman, Jr., (Nauka, 1984) have contributed to the development of scheduling theory in the Soviet Union. Many different models, the large number of new results make it difficult for the researchers who work in related fields to follow the fast development of scheduling theory and to master new methods and approaches quickly.

Klappentext

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. br/ 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 emNP/em-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. br/ For researchers and graduate students of management science and operations research interested in production planning and flexible manufacturing. br/

Zusammenfassung
` These two volumes dedicated to the theory and complexity of scheduling problems are a valuable source of information to researchers and graduate students of operations research, management, and computer sciences. Readers with particular interests in production planning and flexible manufacturing are very well served by this fine set. '
Journal of Global Optimization, 7, 1995

Inhalt
1 Elements of Graph Theory and Computational Complexity of Algorithms.- 1. Sets, Orders, Graphs.- 2. Balanced 2-3-Trees.- 3. Polynomial Reducibility of Discrete Problems. Complexity of Algorithms.- 4. Bibliography and Review.- 2 Polynomially Solvable Problems.- 1. Preemption.- 2. Deadline-Feasible Schedules.- 3. Single Machine. Maximal Cost.- 4. Single Machine. Total Cost.- 5. Identical Machines. Maximal Completion Time. Equal Processing Times.- 6. Identical Machines. Maximal Completion Time. Preemption.- 7. Identical Machines. Due Dates. Equal Processing Times.- 8. Identical Machines. Maximal Lateness..- 9. Uniform and Unrelated Parallel Machines. Total and Maximal Cost.- 10. Bibliography and Review.- 3 Priority-Generating Functions. Ordered Sets of Jobs.- 1. Priority-Generating Functions.- 2. Elimination Conditions.- 3. Tree-like Order.- 4. Series-Parallel Order.- 5. General Case.- 6. Convergence Conditions.- 7. l-Priority-Generating Functions.- 8. Bibliography and Review.- 4 NP-Hard Problems.- 1. Reducibility of the Partition Problem.- 2. Reducibility of the 3-Partition Problem.- 3. Reducibility of the Vertex Covering Problem.- 4. Reducibility of the Clique Problem.- 5. Reducibility of the Linear Arrangement Problem.- 6. Bibliographic Notes.- Appendix Approximation Algorithms.- References.- Additional References.- Also of Interest.