Bicriteria scheduling of equal length jobs on uniform parallel machines

We study the bicriteria scheduling of equal length jobs on uniform parallel machines. By introducing a new scheduling model, called single-machine scheduling with generated completion times (shortly, GCT-scheduling), we show that the scheduling of equal length jobs on uniform parallel machines can b...

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Published in:	Journal of combinatorial optimization Vol. 39; no. 3; pp. 637 - 661
Main Authors:	Zhao, Qiulan, Yuan, Jinjiang
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2020 Springer Nature B.V
Subjects:	Combinatorics Completion time Convex and Discrete Geometry Job shops Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Polynomials Production scheduling Sarin Scheduling Theory of Computation Uniform parallel machines NP-hardness Generated completion times Bicriteria scheduling Polynomial time algorithm
ISSN:	1382-6905, 1573-2886
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Abstract	We study the bicriteria scheduling of equal length jobs on uniform parallel machines. By introducing a new scheduling model, called single-machine scheduling with generated completion times (shortly, GCT-scheduling), we show that the scheduling of equal length jobs on uniform parallel machines can be polynomially transformed into the single-machine GCT-scheduling with a special setting of generated completion times. In the GCT-scheduling, a sequence of completion times is given in advance and the job scheduled at the i -th position will be assigned the i -th completion time. We present a comprehensive study on the complexities of the bicriteria single-machine GCT-scheduling problems with respect to various regular criteria. We then turn these complexity results into the forms of bicriteria scheduling of equal length jobs on uniform (or identical) parallel machines. Our research generalizes the existing results on bicriteria scheduling of equal length jobs in the literature. Particularly, one of our results solves the open problem posed by Sarin and Prakash (J Comb Optim 8:227–240, 2004), which asks for minimizing the total weighted completion time subject to the optimality of minimizing the total number of tardy jobs on identical parallel machines, and we show that this problem is solvable in polynomial time.
AbstractList	We study the bicriteria scheduling of equal length jobs on uniform parallel machines. By introducing a new scheduling model, called single-machine scheduling with generated completion times (shortly, GCT-scheduling), we show that the scheduling of equal length jobs on uniform parallel machines can be polynomially transformed into the single-machine GCT-scheduling with a special setting of generated completion times. In the GCT-scheduling, a sequence of completion times is given in advance and the job scheduled at the i-th position will be assigned the i-th completion time. We present a comprehensive study on the complexities of the bicriteria single-machine GCT-scheduling problems with respect to various regular criteria. We then turn these complexity results into the forms of bicriteria scheduling of equal length jobs on uniform (or identical) parallel machines. Our research generalizes the existing results on bicriteria scheduling of equal length jobs in the literature. Particularly, one of our results solves the open problem posed by Sarin and Prakash (J Comb Optim 8:227–240, 2004), which asks for minimizing the total weighted completion time subject to the optimality of minimizing the total number of tardy jobs on identical parallel machines, and we show that this problem is solvable in polynomial time. We study the bicriteria scheduling of equal length jobs on uniform parallel machines. By introducing a new scheduling model, called single-machine scheduling with generated completion times (shortly, GCT-scheduling), we show that the scheduling of equal length jobs on uniform parallel machines can be polynomially transformed into the single-machine GCT-scheduling with a special setting of generated completion times. In the GCT-scheduling, a sequence of completion times is given in advance and the job scheduled at the i -th position will be assigned the i -th completion time. We present a comprehensive study on the complexities of the bicriteria single-machine GCT-scheduling problems with respect to various regular criteria. We then turn these complexity results into the forms of bicriteria scheduling of equal length jobs on uniform (or identical) parallel machines. Our research generalizes the existing results on bicriteria scheduling of equal length jobs in the literature. Particularly, one of our results solves the open problem posed by Sarin and Prakash (J Comb Optim 8:227–240, 2004), which asks for minimizing the total weighted completion time subject to the optimality of minimizing the total number of tardy jobs on identical parallel machines, and we show that this problem is solvable in polynomial time.
Author	Yuan, Jinjiang Zhao, Qiulan
Author_xml	– sequence: 1 givenname: Qiulan surname: Zhao fullname: Zhao, Qiulan organization: Department of Mathematics, Nanjing University – sequence: 2 givenname: Jinjiang orcidid: 0000-0002-9814-615X surname: Yuan fullname: Yuan, Jinjiang email: yuanjj@zzu.edu.cn organization: School of Mathematics and Statistics, Zhengzhou University
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Cites_doi	10.1023/B:JOCO.0000038909.06086.ed 10.1111/j.1467-9574.1990.tb01276.x 10.1016/j.disopt.2019.06.002 10.1016/j.ejor.2020.07.064 10.1002/nav.3800030106 10.1287/opre.1030.0092 10.1016/j.ejor.2004.07.011 10.1016/j.disopt.2017.01.001 10.1016/j.ejor.2015.01.003 10.1007/978-3-642-41880-8 10.1016/S0305-0548(98)80005-1 10.1007/s10951-010-0201-1 10.1007/s10479-012-1099-0
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References	TuzikovAMakhaniokMMannerRBicriterion scheduling of identical processing time jobs by uniform processorsComput Oper Res1998253135160715510.1016/S0305-0548(98)80005-1 OronDShabtayDSteinerGSingle machine scheduling with two competing agents and equal job processing timesEur J Oper Res20152448699332076810.1016/j.ejor.2015.01.003 AgnetisAMirchandaniPBPacciarelliDPacificiAScheduling problems with two competing agentsOper Res200452229242206639810.1287/opre.1030.0092 DessoukyMILagewegBJLenstraJKVan de VeldeSLScheduling identical jobs on uniform parallel machinesStat Neerl199044115123109435310.1111/j.1467-9574.1990.tb01276.x ChenRBYuanJJLuLFSingle-machine scheduling with positional due indices and positional deadlinesDiscrete Optim2019402872610.1016/j.disopt.2019.06.00207138072 SarinSCPrakashDEqual processing time bicriteria scheduling on parallel machinesJ Comb Optim20048227240209225910.1023/B:JOCO.0000038909.06086.ed Wan L, Du JZ, Lai KK (2019) CO-agent scheduling to minimize total weighted completion time and total weighted number of tardy jobs with unit processing times. In submission SadiFSoukhalAmulti-agent scheduling problems with a global agent and equal length jobsDiscrete Optim20172393104361096810.1016/j.disopt.2017.01.001 HoogeveenHMulticriteria schedulingEur J Oper Res2005167592623215706110.1016/j.ejor.2004.07.011 ElvikisDHamacherHWT’kindtVScheduling two agents on uniform parallel machines with makespan and cost functionsJ Sched201114471481283444210.1007/s10951-010-0201-1 SmithWEVarious optimizers for single-stage productionNav Res Logist Q1956159668910910.1002/nav.3800030106 ElvikisDT’kindtVTwo-agent scheduling on uniform parallel machines with min–max criteriaAnn Oper Res20142137994315287310.1007/s10479-012-1099-0 LawlerELCombinatorial optimization: networks and matroids1976New YorkHolt, Rinehart and Winston0413.90040 AgnetisABillautJCGawiejnowiczSPacciarelliDSoukhalAMultiagent scheduling: models and algorithms2014BerlinSpringer10.1007/978-3-642-41880-8 T’kindtVBillautJCMulticriteria scheduling: theory, models and algorithms20062BerlinSpringer1126.90002 D Elvikis (507_CR5) 2011; 14 EL Lawler (507_CR8) 1976 F Sadi (507_CR10) 2017; 23 WE Smith (507_CR12) 1956; 1 D Elvikis (507_CR6) 2014; 213 H Hoogeveen (507_CR7) 2005; 167 A Agnetis (507_CR2) 2004; 52 507_CR15 MI Dessouky (507_CR4) 1990; 44 V T’kindt (507_CR13) 2006 D Oron (507_CR9) 2015; 244 RB Chen (507_CR3) 2019 A Agnetis (507_CR1) 2014 SC Sarin (507_CR11) 2004; 8 A Tuzikov (507_CR14) 1998; 25
References_xml	– reference: ElvikisDT’kindtVTwo-agent scheduling on uniform parallel machines with min–max criteriaAnn Oper Res20142137994315287310.1007/s10479-012-1099-0 – reference: SadiFSoukhalAmulti-agent scheduling problems with a global agent and equal length jobsDiscrete Optim20172393104361096810.1016/j.disopt.2017.01.001 – reference: LawlerELCombinatorial optimization: networks and matroids1976New YorkHolt, Rinehart and Winston0413.90040 – reference: ChenRBYuanJJLuLFSingle-machine scheduling with positional due indices and positional deadlinesDiscrete Optim2019402872610.1016/j.disopt.2019.06.00207138072 – reference: SarinSCPrakashDEqual processing time bicriteria scheduling on parallel machinesJ Comb Optim20048227240209225910.1023/B:JOCO.0000038909.06086.ed – reference: T’kindtVBillautJCMulticriteria scheduling: theory, models and algorithms20062BerlinSpringer1126.90002 – reference: AgnetisABillautJCGawiejnowiczSPacciarelliDSoukhalAMultiagent scheduling: models and algorithms2014BerlinSpringer10.1007/978-3-642-41880-8 – reference: SmithWEVarious optimizers for single-stage productionNav Res Logist Q1956159668910910.1002/nav.3800030106 – reference: TuzikovAMakhaniokMMannerRBicriterion scheduling of identical processing time jobs by uniform processorsComput Oper Res1998253135160715510.1016/S0305-0548(98)80005-1 – reference: Wan L, Du JZ, Lai KK (2019) CO-agent scheduling to minimize total weighted completion time and total weighted number of tardy jobs with unit processing times. In submission – reference: AgnetisAMirchandaniPBPacciarelliDPacificiAScheduling problems with two competing agentsOper Res200452229242206639810.1287/opre.1030.0092 – reference: ElvikisDHamacherHWT’kindtVScheduling two agents on uniform parallel machines with makespan and cost functionsJ Sched201114471481283444210.1007/s10951-010-0201-1 – reference: DessoukyMILagewegBJLenstraJKVan de VeldeSLScheduling identical jobs on uniform parallel machinesStat Neerl199044115123109435310.1111/j.1467-9574.1990.tb01276.x – reference: HoogeveenHMulticriteria schedulingEur J Oper Res2005167592623215706110.1016/j.ejor.2004.07.011 – reference: OronDShabtayDSteinerGSingle machine scheduling with two competing agents and equal job processing timesEur J Oper Res20152448699332076810.1016/j.ejor.2015.01.003 – volume: 8 start-page: 227 year: 2004 ident: 507_CR11 publication-title: J Comb Optim doi: 10.1023/B:JOCO.0000038909.06086.ed – volume: 44 start-page: 115 year: 1990 ident: 507_CR4 publication-title: Stat Neerl doi: 10.1111/j.1467-9574.1990.tb01276.x – year: 2019 ident: 507_CR3 publication-title: Discrete Optim doi: 10.1016/j.disopt.2019.06.002 – ident: 507_CR15 doi: 10.1016/j.ejor.2020.07.064 – volume: 1 start-page: 59 year: 1956 ident: 507_CR12 publication-title: Nav Res Logist Q doi: 10.1002/nav.3800030106 – volume-title: Combinatorial optimization: networks and matroids year: 1976 ident: 507_CR8 – volume: 52 start-page: 229 year: 2004 ident: 507_CR2 publication-title: Oper Res doi: 10.1287/opre.1030.0092 – volume: 167 start-page: 592 year: 2005 ident: 507_CR7 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2004.07.011 – volume: 23 start-page: 93 year: 2017 ident: 507_CR10 publication-title: Discrete Optim doi: 10.1016/j.disopt.2017.01.001 – volume: 244 start-page: 86 year: 2015 ident: 507_CR9 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2015.01.003 – volume-title: Multicriteria scheduling: theory, models and algorithms year: 2006 ident: 507_CR13 – volume-title: Multiagent scheduling: models and algorithms year: 2014 ident: 507_CR1 doi: 10.1007/978-3-642-41880-8 – volume: 25 start-page: 31 year: 1998 ident: 507_CR14 publication-title: Comput Oper Res doi: 10.1016/S0305-0548(98)80005-1 – volume: 14 start-page: 471 year: 2011 ident: 507_CR5 publication-title: J Sched doi: 10.1007/s10951-010-0201-1 – volume: 213 start-page: 79 year: 2014 ident: 507_CR6 publication-title: Ann Oper Res doi: 10.1007/s10479-012-1099-0
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SubjectTerms	Combinatorics Completion time Convex and Discrete Geometry Job shops Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Polynomials Production scheduling Sarin Scheduling Theory of Computation
Title	Bicriteria scheduling of equal length jobs on uniform parallel machines
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