An efficient polynomial-time approximation scheme for parallel multi-stage open shops
Various new scheduling problems have been arising from real-world applications and spawning new research areas in the scheduling field. We study the parallel multi-stage open shops problem, which generalizes the classic open shop scheduling and parallel machine scheduling problems. Given m identical...
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| Published in: | Discrete Applied Mathematics Vol. 377; pp. 390 - 401 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
31.12.2025
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| ISSN: | 0166-218X |
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| Abstract | Various new scheduling problems have been arising from real-world applications and spawning new research areas in the scheduling field. We study the parallel multi-stage open shops problem, which generalizes the classic open shop scheduling and parallel machine scheduling problems. Given m identical k-stage open shops and a set of n jobs, we aim to process all jobs on these open shops with the minimum makespan, i.e., the completion time of the last job, under the constraint that job preemption is not allowed. We present an efficient polynomial-time approximation scheme (EPTAS) for the case when both m and k are constant. The main idea for our EPTAS is the combination of several categorization, scaling, and linear programming rounding techniques. Jobs and/or operations are first scaled and then categorized carefully into multiple types so that different types of jobs and/or operations are scheduled appropriately without increasing the makespan too much.
•Proposed first EPTAS for parallel multi-stage open shops scheduling.•Combined categorization, scaling, and linear programming rounding methods.•Demonstrated effective gap-filling strategy for small job scheduling.•Achieved near-optimal makespan within polynomial runtime complexity. |
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| AbstractList | Various new scheduling problems have been arising from real-world applications and spawning new research areas in the scheduling field. We study the parallel multi-stage open shops problem, which generalizes the classic open shop scheduling and parallel machine scheduling problems. Given m identical k-stage open shops and a set of n jobs, we aim to process all jobs on these open shops with the minimum makespan, i.e., the completion time of the last job, under the constraint that job preemption is not allowed. We present an efficient polynomial-time approximation scheme (EPTAS) for the case when both m and k are constant. The main idea for our EPTAS is the combination of several categorization, scaling, and linear programming rounding techniques. Jobs and/or operations are first scaled and then categorized carefully into multiple types so that different types of jobs and/or operations are scheduled appropriately without increasing the makespan too much.
•Proposed first EPTAS for parallel multi-stage open shops scheduling.•Combined categorization, scaling, and linear programming rounding methods.•Demonstrated effective gap-filling strategy for small job scheduling.•Achieved near-optimal makespan within polynomial runtime complexity. |
| Author | Tong, Weitian Xu, Yao Lin, Guohui Su, Bing Dong, Jianming Jin, Ruyan |
| Author_xml | – sequence: 1 givenname: Jianming surname: Dong fullname: Dong, Jianming email: djm226@163.com organization: School of Management and E-Business, Contemporary Business and Trade Research Center, Zhejiang Gongshang University, Hangzhou, Zhejiang, 310018, China – sequence: 2 givenname: Ruyan surname: Jin fullname: Jin, Ruyan email: jry623@163.com organization: Public Course Teaching and Research Office, Taizhou Vocational and Technical College, Taizhou, Zhejiang, 318000, China – sequence: 3 givenname: Guohui surname: Lin fullname: Lin, Guohui email: guohui@alberta.ca organization: Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada, T6G 2E8 – sequence: 4 givenname: Bing surname: Su fullname: Su, Bing email: subing684@sohu.com organization: School of Economics and Management, Xi’an Technological University, Xi’an, China – sequence: 5 givenname: Weitian orcidid: 0000-0002-9815-2330 surname: Tong fullname: Tong, Weitian email: wtong.research@gmail.com organization: Department of Computer Science, Georgia Southern University, Statesboro, GA, 30458, USA – sequence: 6 givenname: Yao surname: Xu fullname: Xu, Yao email: yxu@georgiasouthern.edu organization: Department of Computer Science, Georgia Southern University, Statesboro, GA, 30458, USA |
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| Cites_doi | 10.1007/3-540-46541-3_38 10.1007/s10479-015-1934-1 10.1016/S0167-6377(99)00005-X 10.1016/j.ejor.2025.01.034 10.1016/j.cor.2015.10.012 10.1016/j.ipl.2013.01.009 10.1016/j.tcs.2016.04.046 10.1007/BF01585871 10.1080/0020754031000106443 10.1016/j.tcs.2017.09.018 10.1016/j.ejor.2019.08.019 10.1080/07408179608966258 10.1016/j.robot.2020.103560 10.1057/jors.1994.99 10.1145/321978.321985 10.1016/j.ejor.2021.03.026 10.1016/j.ejor.2011.08.007 10.1080/07408170008967427 10.1007/s10479-024-05860-6 10.1057/s41278-019-00122-w 10.1016/j.tcs.2019.01.017 10.1007/s10878-018-0314-6 10.1007/BF01585870 10.1287/opre.45.2.288 10.1016/j.tcs.2018.04.005 10.1145/321921.321934 10.1007/s10878-020-00591-3 10.1016/j.tcs.2019.08.028 10.1007/s10845-015-1149-y 10.1016/0377-2217(93)90249-M 10.1016/j.tcs.2018.04.017 10.1287/msom.2016.0591 10.1002/j.1538-7305.1966.tb01709.x 10.1145/7531.7535 10.1016/j.cor.2022.105732 |
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| Keywords | Linear programming Scheduling Makespan Efficient polynomial-time approximation scheme Parallel multi-stage open shops |
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| Title | An efficient polynomial-time approximation scheme for parallel multi-stage open shops |
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