Approximation Algorithms on Multiple Two-Stage Flowshops
This paper considers the problem of scheduling multiple two-stage flowshops that minimizes the makespan, where the number of flowshops is part of the input. We study the relationship between the problem and the classical makespan problem. We prove that if there exists an $$\alpha $$ -approximation a...
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| Published in | Computing and Combinatorics Vol. 10976; pp. 713 - 725 |
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| Main Authors | , |
| Format | Book Chapter |
| Language | English |
| Published |
Switzerland
Springer International Publishing AG
2018
Springer International Publishing |
| Series | Lecture Notes in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783319947754 3319947753 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/978-3-319-94776-1_59 |
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| Summary: | This paper considers the problem of scheduling multiple two-stage flowshops that minimizes the makespan, where the number of flowshops is part of the input. We study the relationship between the problem and the classical makespan problem. We prove that if there exists an $$\alpha $$ -approximation algorithm for the makespan problem, then for the multiple two-stage flowshop scheduling problem, we can construct a $$2 \alpha $$ -approximation algorithm for the general case, and $$(\alpha + 1/2)$$ -approximation algorithms for two restricted cases. As a result, we get a $$(2 + \epsilon )$$ -approximation algorithm for the general case and a $$(1.5 + \epsilon )$$ -approximation algorithm for the two restricted cases, which significantly improve the previous approximation ratios 2.6 and 11/6, respectively. |
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| Bibliography: | Original Abstract: This paper considers the problem of scheduling multiple two-stage flowshops that minimizes the makespan, where the number of flowshops is part of the input. We study the relationship between the problem and the classical makespan problem. We prove that if there exists an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-approximation algorithm for the makespan problem, then for the multiple two-stage flowshop scheduling problem, we can construct a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2 \alpha $$\end{document}-approximation algorithm for the general case, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha + 1/2)$$\end{document}-approximation algorithms for two restricted cases. As a result, we get a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2 + \epsilon )$$\end{document}-approximation algorithm for the general case and a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1.5 + \epsilon )$$\end{document}-approximation algorithm for the two restricted cases, which significantly improve the previous approximation ratios 2.6 and 11/6, respectively. This work is supported by the National Natural Science Foundation of China under grants 61420106009, 61672536 and 61472449, Scientific Research Fund of Hunan Provincial Education Department under grant 16C1660. |
| ISBN: | 9783319947754 3319947753 |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-319-94776-1_59 |