Total completion time minimization in two-machine flow shop scheduling problems with a fixed job sequence
This paper addresses scheduling n jobs in a two-machine flow shop to minimize the total completion time, subject to the condition that the jobs are processed in the same given sequence on both machines. A new concept of optimal schedule block is introduced, and polynomial time dynamic programming al...
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| Published in | Discrete optimization Vol. 9; no. 1; pp. 29 - 39 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.02.2012
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1572-5286 1873-636X |
| DOI | 10.1016/j.disopt.2011.11.001 |
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| Abstract | This paper addresses scheduling n jobs in a two-machine flow shop to minimize the total completion time, subject to the condition that the jobs are processed in the same given sequence on both machines. A new concept of optimal schedule block is introduced, and polynomial time dynamic programming algorithms employing this concept are derived for two specific problems. In the first problem, the machine-2 processing time of a job is a step increasing function of its waiting time between the machines, and a decision about machine-1 idle time insertion has to be made. This problem is solved in O(n2) time. In the second problem, the jobs are processed in batches and each batch is preceded by a machine-dependent setup time. An O(n5) algorithm is developed to find an optimal batching decision. |
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| AbstractList | This paper addresses scheduling n jobs in a two-machine flow shop to minimize the total completion time, subject to the condition that the jobs are processed in the same given sequence on both machines. A new concept of optimal schedule block is introduced, and polynomial time dynamic programming algorithms employing this concept are derived for two specific problems. In the first problem, the machine-2 processing time of a job is a step increasing function of its waiting time between the machines, and a decision about machine-1 idle time insertion has to be made. This problem is solved in O(n2) time. In the second problem, the jobs are processed in batches and each batch is preceded by a machine-dependent setup time. An O(n5) algorithm is developed to find an optimal batching decision. |
| Author | Hwang, F.J. Kovalyov, M.Y. Lin, B.M.T. |
| Author_xml | – sequence: 1 givenname: F.J. surname: Hwang fullname: Hwang, F.J. email: fengjanghwang@gmail.com organization: Institute of Information Management, Department of Information and Finance Management, National Chiao Tung University, Taiwan – sequence: 2 givenname: M.Y. surname: Kovalyov fullname: Kovalyov, M.Y. email: kovalyov_my@newman.bas-net.by organization: United Institute of Informatics Problems, National Academy of Sciences of Belarus, Belarus – sequence: 3 givenname: B.M.T. surname: Lin fullname: Lin, B.M.T. email: bmtlin@mail.nctu.edu.tw, bmtlin@gmail.com organization: Institute of Information Management, Department of Information and Finance Management, National Chiao Tung University, Taiwan |
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| Keywords | Dynamic programming Fixed sequence Total completion time Two-machine flow shop |
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| SubjectTerms | Dynamic programming Fixed sequence Total completion time Two-machine flow shop |
| Title | Total completion time minimization in two-machine flow shop scheduling problems with a fixed job sequence |
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