Two-machine flow shop scheduling with a common due date to maximize total early work
•Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully polynomial time approximation scheme (FPTAS) is developed.•The approximation results work for the weighted model - if a specific constraint is satis...
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| Vydáno v: | European journal of operational research Ročník 300; číslo 2; s. 504 - 511 |
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| Jazyk: | angličtina |
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Elsevier B.V
16.07.2022
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully polynomial time approximation scheme (FPTAS) is developed.•The approximation results work for the weighted model - if a specific constraint is satisfied.
This paper considers scheduling in a two-machine flow shop to maximize the total early work subject to a common due date. The early work of a job is a parameter defined as the total amount of the job that is processed before the specified due date. We mainly focus on the unweighted model in this paper, and propose a dynamic programming approach running in O(n2d2) time (compared with the previous result in O(n2d4) time for the weighted case discussed in the literature). Then we analyse the problem from an approximation point of view, in which we first show that Johnson’s algorithm, one of the most classical ones in flow shop scheduling, can only achieve the worst performance ratio for the considered problem (although it is an optimal one for makespan minimization). With the motivation of proposing better approximation algorithms, we further design a fully polynomial time approximation scheme (FPTAS). Finally, we point out that the approximation results also work for the weighted model - if a specific constraint is satisfied. |
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| AbstractList | •Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully polynomial time approximation scheme (FPTAS) is developed.•The approximation results work for the weighted model - if a specific constraint is satisfied.
This paper considers scheduling in a two-machine flow shop to maximize the total early work subject to a common due date. The early work of a job is a parameter defined as the total amount of the job that is processed before the specified due date. We mainly focus on the unweighted model in this paper, and propose a dynamic programming approach running in O(n2d2) time (compared with the previous result in O(n2d4) time for the weighted case discussed in the literature). Then we analyse the problem from an approximation point of view, in which we first show that Johnson’s algorithm, one of the most classical ones in flow shop scheduling, can only achieve the worst performance ratio for the considered problem (although it is an optimal one for makespan minimization). With the motivation of proposing better approximation algorithms, we further design a fully polynomial time approximation scheme (FPTAS). Finally, we point out that the approximation results also work for the weighted model - if a specific constraint is satisfied. |
| Author | Chen, Xin Lin, Bertrand M.T. Blazewicz, Jacek Sterna, Malgorzata Miao, Qian |
| Author_xml | – sequence: 1 givenname: Xin surname: Chen fullname: Chen, Xin organization: Liaoning University of Technology, School of Electronics and Information Engineering, Shiying 169, Jinzhou 121001, China – sequence: 2 givenname: Qian surname: Miao fullname: Miao, Qian organization: Dalian University of Technology, School of Software, Tuqiang 321, Dalian 116023, China – sequence: 3 givenname: Bertrand M.T. orcidid: 0000-0003-0456-296X surname: Lin fullname: Lin, Bertrand M.T. email: bmtlin@mail.nctu.edu.tw organization: National Yang Ming Chiao Tung University, Institute of Information Management, Shinchu 300, Taiwan – sequence: 4 givenname: Malgorzata orcidid: 0000-0002-3845-8194 surname: Sterna fullname: Sterna, Malgorzata organization: Poznan University of Technology, Institute of Computing Science, Piotrowo 2, Poznan 60-965, Poland – sequence: 5 givenname: Jacek surname: Blazewicz fullname: Blazewicz, Jacek organization: Poznan University of Technology, Institute of Computing Science, Piotrowo 2, Poznan 60-965, Poland |
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| Keywords | Early and late work Dynamic programming Combinatorial optimization FPTAS Flow shop scheduling |
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| SubjectTerms | Combinatorial optimization Dynamic programming Early and late work Flow shop scheduling FPTAS |
| Title | Two-machine flow shop scheduling with a common due date to maximize total early work |
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