Makespan minimization of multi-slot just-in-time scheduling on single and parallel machines
The paper addresses the problem of multi-slot just-in-time scheduling. Unlike the existing literature on this subject, it studies a more general criterion—the minimization of the schedule makespan rather than the minimization of the number of slots used by schedule. It gives an O ( n log 2 n )-time...
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| Published in: | Journal of scheduling Vol. 13; no. 5; pp. 479 - 492 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Boston
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01.10.2010
Springer Science + Business Media Springer Nature B.V |
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| ISSN: | 1094-6136, 1099-1425 |
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| Abstract | The paper addresses the problem of multi-slot just-in-time scheduling. Unlike the existing literature on this subject, it studies a more general criterion—the minimization of the schedule makespan rather than the minimization of the number of slots used by schedule. It gives an
O
(
n
log
2
n
)-time optimization algorithm for the single machine problem. For arbitrary number of
m
>1 identical parallel machines it presents an
O
(
n
log
n
)-time optimization algorithm for the case when the processing time of each job does not exceed its due date. For the general case on
m
>1 machines, it proposes a polynomial time constant factor approximation algorithm. |
|---|---|
| AbstractList | The paper addresses the problem of multi-slot just-in-time scheduling. Unlike the existing literature on this subject, it studies a more general criterion—the minimization of the schedule makespan rather than the minimization of the number of slots used by schedule. It gives an
O
(
n
log
2
n
)-time optimization algorithm for the single machine problem. For arbitrary number of
m
>1 identical parallel machines it presents an
O
(
n
log
n
)-time optimization algorithm for the case when the processing time of each job does not exceed its due date. For the general case on
m
>1 machines, it proposes a polynomial time constant factor approximation algorithm. Issue Title: Special Issue: New Challenges in Scheduling Theory The paper addresses the problem of multi-slot just-in-time scheduling. Unlike the existing literature on this subject, it studies a more general criterion--the minimization of the schedule makespan rather than the minimization of the number of slots used by schedule. It gives an O(nlog^sup 2^n)-time optimization algorithm for the single machine problem. For arbitrary number of m>1 identical parallel machines it presents an O(nlogn)-time optimization algorithm for the case when the processing time of each job does not exceed its due date. For the general case on m>1 machines, it proposes a polynomial time constant factor approximation algorithm.[PUBLICATION ABSTRACT] |
| Author | Kubiak, Wiesław Dereniowski, Dariusz |
| Author_xml | – sequence: 1 givenname: Dariusz surname: Dereniowski fullname: Dereniowski, Dariusz email: deren@eti.pg.gda.pl organization: Department of Algorithms and System Modeling, Gdańsk University of Technology – sequence: 2 givenname: Wiesław surname: Kubiak fullname: Kubiak, Wiesław organization: Faculty of Business Administration, Memorial University |
| BackLink | http://www.econis.eu/PPNSET?PPN=640042171$$DView this record in ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften |
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| Cites_doi | 10.1023/A:1026200209386 10.1093/ietfec/e88-a.5.1192 10.1007/BF01585506 10.1007/978-3-662-03217-6 10.1007/978-3-540-30182-0_25 10.1016/0012-365X(92)90646-W 10.1016/S0305-0548(00)00086-1 10.1016/0166-218X(95)80003-M 10.1287/opre.12.5.655 10.1137/0117039 10.1137/S0097539703434966 |
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| DOI | 10.1007/s10951-009-0139-3 |
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| Keywords | Just-in-time scheduling Multi-slot Makespan minimization |
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| References | BłażewiczJ.EckerK.PeschE.SchmidtG.WęglarzJ.Scheduling computer and manufacturing processes1996New YorkSpringer CarlisleM. C.LloydE. L.On the k-coloring of intervalsDiscrete Applied Mathematics19955922523510.1016/0166-218X(93)E0174-W HiraishiK.LevnerE.VlachM.Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobsComputers and Operations Research200229784184810.1016/S0305-0548(00)00086-1 Sung, S.-Ch., Čepek, O., & Hiraishi, K. (2007a). Algorithm for multislot just-in-time scheduling. In ISME’07: international symposium on management engineering. Barth, D., Cohen, J., Gastal, L., Mautor, T., & Rousseau, S. (2004). Fixed size and variable size packet models in an optical ring network: complexity and simulations. In ISCIS (pp. 238–246). KubiakW.Proportional optimization and fairness2009New YorkSpringer KumarA.KleinbergJ.Fairness measures for resource allocationSIAM Journal on Computing200636365768010.1137/S0097539703434966 GilmoreP. C.GomoryR. E.Sequencing a one state-variable machine: A solvable case of the traveling salesman problemOperations Research196412565567910.1287/opre.12.5.655 MegiddoN.Optimal flows in networks with multiple sources and sinksMathematical Programming197479710710.1007/BF01585506 JózefowskaJ.Just-in-time scheduling2007New YorkSpringer BiróM.HujterM.TuzaZs.Precoloring extension. i: interval graphsDiscrete Mathematics19921001–326727910.1016/0012-365X(92)90646-W Hiraishi, K. (2001). Just-in-time scheduling of parallel identical machines with multiple time slots. In Proceedings of the 4th Czech–Japan seminar on data analysis and decision making under uncertainty, Jindrichuv Hradec. GrahamR. L.Bounds on multiprocessing timing anomaliesSIAM Journal on Applied Mathematics196917241642910.1137/0117039 ChibaE.HiraishiK.A heuristic algorithm for one-machine just-in-time scheduling problem with periodic time slotsIEICE Transactions on Fundamentals of Electronics, Communications and Computer Science2005E88-A51192119910.1093/ietfec/e88-a.5.1192 LawlerE. L.LenstraJ. K.Rinnooy KanA. H. G.ShmoysD. B.The travelling salesman problem1985New YorkWiley VairaktarakisG. L.Simple algorithms for Gilmore–Gomory’s traveling salesman and related problemsJournal of Scheduling20036649952010.1023/A:1026200209386 ČepekO.SungS.-Ch.Just-in-time scheduling with periodic time slotsScientiae Mathematicae Japonicae Online200410431437 SungS.-Ch.ČepekO.HiraishiK.Algorithm for multislot just-in-time scheduling on identical parallel machinesICICIC’07: Proceedings of the second international conference on innovative computing, information and control2007Los AlamitosIEEE Computer Society12010.1109/ICICIC.2007.123 R. L. Graham (139_CR8) 1969; 17 M. C. Carlisle (139_CR4) 1995; 59 E. Chiba (139_CR6) 2005; E88-A 139_CR9 J. Błażewicz (139_CR3) 1996 139_CR16 K. Hiraishi (139_CR10) 2002; 29 S.-Ch. Sung (139_CR17) 2007 E. L. Lawler (139_CR14) 1985 G. L. Vairaktarakis (139_CR18) 2003; 6 O. Čepek (139_CR5) 2004; 10 M. Biró (139_CR2) 1992; 100 P. C. Gilmore (139_CR7) 1964; 12 N. Megiddo (139_CR15) 1974; 7 A. Kumar (139_CR13) 2006; 36 139_CR1 J. Józefowska (139_CR11) 2007 W. Kubiak (139_CR12) 2009 |
| References_xml | – reference: Hiraishi, K. (2001). Just-in-time scheduling of parallel identical machines with multiple time slots. In Proceedings of the 4th Czech–Japan seminar on data analysis and decision making under uncertainty, Jindrichuv Hradec. – reference: MegiddoN.Optimal flows in networks with multiple sources and sinksMathematical Programming197479710710.1007/BF01585506 – reference: BłażewiczJ.EckerK.PeschE.SchmidtG.WęglarzJ.Scheduling computer and manufacturing processes1996New YorkSpringer – reference: KumarA.KleinbergJ.Fairness measures for resource allocationSIAM Journal on Computing200636365768010.1137/S0097539703434966 – reference: Barth, D., Cohen, J., Gastal, L., Mautor, T., & Rousseau, S. (2004). Fixed size and variable size packet models in an optical ring network: complexity and simulations. In ISCIS (pp. 238–246). – reference: ChibaE.HiraishiK.A heuristic algorithm for one-machine just-in-time scheduling problem with periodic time slotsIEICE Transactions on Fundamentals of Electronics, Communications and Computer Science2005E88-A51192119910.1093/ietfec/e88-a.5.1192 – reference: VairaktarakisG. L.Simple algorithms for Gilmore–Gomory’s traveling salesman and related problemsJournal of Scheduling20036649952010.1023/A:1026200209386 – reference: SungS.-Ch.ČepekO.HiraishiK.Algorithm for multislot just-in-time scheduling on identical parallel machinesICICIC’07: Proceedings of the second international conference on innovative computing, information and control2007Los AlamitosIEEE Computer Society12010.1109/ICICIC.2007.123 – reference: CarlisleM. C.LloydE. L.On the k-coloring of intervalsDiscrete Applied Mathematics19955922523510.1016/0166-218X(93)E0174-W – reference: BiróM.HujterM.TuzaZs.Precoloring extension. i: interval graphsDiscrete Mathematics19921001–326727910.1016/0012-365X(92)90646-W – reference: JózefowskaJ.Just-in-time scheduling2007New YorkSpringer – reference: HiraishiK.LevnerE.VlachM.Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobsComputers and Operations Research200229784184810.1016/S0305-0548(00)00086-1 – reference: KubiakW.Proportional optimization and fairness2009New YorkSpringer – reference: ČepekO.SungS.-Ch.Just-in-time scheduling with periodic time slotsScientiae Mathematicae Japonicae Online200410431437 – reference: GilmoreP. C.GomoryR. E.Sequencing a one state-variable machine: A solvable case of the traveling salesman problemOperations Research196412565567910.1287/opre.12.5.655 – reference: Sung, S.-Ch., Čepek, O., & Hiraishi, K. (2007a). Algorithm for multislot just-in-time scheduling. In ISME’07: international symposium on management engineering. – reference: GrahamR. L.Bounds on multiprocessing timing anomaliesSIAM Journal on Applied Mathematics196917241642910.1137/0117039 – reference: LawlerE. L.LenstraJ. K.Rinnooy KanA. H. G.ShmoysD. B.The travelling salesman problem1985New YorkWiley – volume-title: The travelling salesman problem year: 1985 ident: 139_CR14 – volume: 6 start-page: 499 issue: 6 year: 2003 ident: 139_CR18 publication-title: Journal of Scheduling doi: 10.1023/A:1026200209386 – volume: 10 start-page: 431 year: 2004 ident: 139_CR5 publication-title: Scientiae Mathematicae Japonicae Online – ident: 139_CR9 – ident: 139_CR16 – volume: E88-A start-page: 1192 issue: 5 year: 2005 ident: 139_CR6 publication-title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science doi: 10.1093/ietfec/e88-a.5.1192 – volume-title: Proportional optimization and fairness year: 2009 ident: 139_CR12 – volume: 7 start-page: 97 year: 1974 ident: 139_CR15 publication-title: Mathematical Programming doi: 10.1007/BF01585506 – volume-title: Scheduling computer and manufacturing processes year: 1996 ident: 139_CR3 doi: 10.1007/978-3-662-03217-6 – ident: 139_CR1 doi: 10.1007/978-3-540-30182-0_25 – volume: 100 start-page: 267 issue: 1–3 year: 1992 ident: 139_CR2 publication-title: Discrete Mathematics doi: 10.1016/0012-365X(92)90646-W – volume-title: Just-in-time scheduling year: 2007 ident: 139_CR11 – volume: 29 start-page: 841 issue: 7 year: 2002 ident: 139_CR10 publication-title: Computers and Operations Research doi: 10.1016/S0305-0548(00)00086-1 – volume: 59 start-page: 225 year: 1995 ident: 139_CR4 publication-title: Discrete Applied Mathematics doi: 10.1016/0166-218X(95)80003-M – volume: 12 start-page: 655 issue: 5 year: 1964 ident: 139_CR7 publication-title: Operations Research doi: 10.1287/opre.12.5.655 – volume: 17 start-page: 416 issue: 2 year: 1969 ident: 139_CR8 publication-title: SIAM Journal on Applied Mathematics doi: 10.1137/0117039 – volume: 36 start-page: 657 issue: 3 year: 2006 ident: 139_CR13 publication-title: SIAM Journal on Computing doi: 10.1137/S0097539703434966 – start-page: 120 volume-title: ICICIC’07: Proceedings of the second international conference on innovative computing, information and control year: 2007 ident: 139_CR17 |
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| SubjectTerms | Approximation Artificial Intelligence Business and Management Calculus of Variations and Optimal Control; Optimization Just in time Operations Research/Decision Theory Optimization Optimization algorithms Polynomials Production controls Schedules Scheduling Supply Chain Management Supply chains |
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| Title | Makespan minimization of multi-slot just-in-time scheduling on single and parallel machines |
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