Scheduling Theory Single-Stage Systems (Mathematics and Its Applications) （1994）

Tanaev, V./ Gordon, W./ Shafransky, Yakov M.

Springer（1994/05発売）

• ページ数 800 p.
• 言語 ENG
• 商品コード 9780792328728
• DDC分類 515

Full Description

This two-volume set is devoted to single and multistage systems in scheduling theory. The main emphasis throughout is on the analysis of the computational complexity of scheduling problems. The first 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. It 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. The second volume is concerned with the problems of finding optimal schedules for systems comprising several sequential machines. More specifically, attention is largely given in separate chapters to three classical processing systems: the flow shop, the job shop, and the open shop.
A final chapter deals with mixed graph problems. Each of the four chapters concludes with a comprehensive bibliography and review. The volume also has an introduction and finishes with an extensive reference section. These volumes are suitable for researchers and graduate students of management science and operations research interested in production planning and flexible manufacturing.

Contents

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.