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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.
Table des matières
Preface. Introduction.
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. 1-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. Index.
