Scheduling with jobs at fixed positions
In this paper, we study classical single machine scheduling problems with the additional constraint that a set of special jobs must be scheduled at certain positions in the job sequence. In other words, a special job must start when a certain number of jobs have finished on the machine. We analyze s...
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| Published in: | European journal of operational research Vol. 318; no. 2; pp. 388 - 397 |
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| Format: | Journal Article |
| Language: | English |
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16-10-2024
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| Abstract | In this paper, we study classical single machine scheduling problems with the additional constraint that a set of special jobs must be scheduled at certain positions in the job sequence. In other words, a special job must start when a certain number of jobs have finished on the machine. We analyze several classical objective functions for this more general setting with the additional constraint of fixed positioned jobs. We show that for some of them they are still polynomially solvable. Then, we focus on the objective of minimizing the number of tardy jobs. Considering the case of just one special job, this allows for a polynomial-time algorithm.
•A practical constraint that fixes certain jobs in the job sequence is introduced to classical scheduling problems.•The analyzed models can be motivated by maintenance scheduling.•The complexity of several one-machine problems with this constraint is analyzed.•Polynomial-time algorithms are presented for some scenarios. |
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| AbstractList | In this paper, we study classical single machine scheduling problems with the additional constraint that a set of special jobs must be scheduled at certain positions in the job sequence. In other words, a special job must start when a certain number of jobs have finished on the machine. We analyze several classical objective functions for this more general setting with the additional constraint of fixed positioned jobs. We show that for some of them they are still polynomially solvable. Then, we focus on the objective of minimizing the number of tardy jobs. Considering the case of just one special job, this allows for a polynomial-time algorithm.
•A practical constraint that fixes certain jobs in the job sequence is introduced to classical scheduling problems.•The analyzed models can be motivated by maintenance scheduling.•The complexity of several one-machine problems with this constraint is analyzed.•Polynomial-time algorithms are presented for some scenarios. |
| Author | Jaehn, Florian |
| Author_xml | – sequence: 1 givenname: Florian orcidid: 0000-0003-1778-1723 surname: Jaehn fullname: Jaehn, Florian email: florian.jaehn@hsu-hh.de organization: Management Science and Operations Research, Helmut Schmidt University, University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany |
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| Keywords | Maintenance scheduling polynomial-time algorithms |
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parallel identical machines publication-title: Computers & Industrial Engineering doi: 10.1016/j.cie.2019.03.043 contributor: fullname: Żurowski – volume: 51 start-page: 7140 issue: 23–24 year: 2013 ident: 10.1016/j.ejor.2024.05.029_b7 article-title: Variable very large neighbourhood algorithms for truck sequencing at transshipment terminals publication-title: International Journal of Production Research doi: 10.1080/00207543.2013.849825 contributor: fullname: Briskorn – volume: 235 start-page: 319 issue: 1 year: 2015 ident: 10.1016/j.ejor.2024.05.029_b15 article-title: Approximability of scheduling problems with resource consuming jobs publication-title: Annals of Operations Research doi: 10.1007/s10479-015-1993-3 contributor: fullname: Györgyi – volume: 16 start-page: 105 issue: 1 year: 2013 ident: 10.1016/j.ejor.2024.05.029_b5 article-title: Exact algorithms for inventory constrained scheduling on a single machine publication-title: Journal of Scheduling doi: 10.1007/s10951-011-0261-x contributor: fullname: Briskorn – volume: 55 start-page: 257 issue: 3 year: 2004 ident: 10.1016/j.ejor.2024.05.029_b1 article-title: Scheduling jobs with position-dependent processing times publication-title: Journal of the Operational Research Society doi: 10.1057/palgrave.jors.2601689 contributor: fullname: Bachman – volume: 565 start-page: 63 year: 2015 ident: 10.1016/j.ejor.2024.05.029_b16 article-title: Reductions between scheduling problems with non-renewable resources and knapsack problems publication-title: Theoretical Computer Science doi: 10.1016/j.tcs.2014.11.007 contributor: fullname: Györgyi – volume: 15 start-page: 565 issue: 5 year: 2012 ident: 10.1016/j.ejor.2024.05.029_b3 article-title: Scheduling flexible maintenance activities subject to job-dependent machine deterioration publication-title: Journal of Scheduling doi: 10.1007/s10951-011-0248-7 contributor: fullname: Bock – volume: 91 start-page: 290 year: 2016 ident: 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Journal of Scheduling doi: 10.1007/s10951-015-0433-1 contributor: fullname: Morsy – volume: 20 start-page: 183 issue: 2 year: 2017 ident: 10.1016/j.ejor.2024.05.029_b13 article-title: Scheduling jobs and maintenance activities subject to job-dependent machine deteriorations publication-title: Journal of Scheduling doi: 10.1007/s10951-016-0502-0 contributor: fullname: Grigoriu – volume: 17 start-page: 135 issue: 2 year: 2014 ident: 10.1016/j.ejor.2024.05.029_b14 article-title: Approximation schemes for single machine scheduling with non-renewable resource constraints publication-title: Journal of Scheduling doi: 10.1007/s10951-013-0346-9 contributor: fullname: Györgyi – volume: 13 start-page: 123 issue: 2 year: 2010 ident: 10.1016/j.ejor.2024.05.029_b18 article-title: Minimizing the total weighted completion time in the relocation problem publication-title: Journal of Scheduling doi: 10.1007/s10951-009-0151-7 contributor: fullname: Kononov |
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