Single machine batch scheduling with two non-disjoint agents and splitable jobs

We investigate the scheduling problem on a single bounded parallel-batch machine where jobs belong to two non-disjoint agents (called agent A and agent B) and are of equal length but different size. Each job’s size can be arbitrarily split into two parts and processed in the consecutive batches. It...

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Published in:	Journal of combinatorial optimization Vol. 40; no. 3; pp. 774 - 795
Main Authors:	Geng, Zhichao, Liu, Jiayu
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.10.2020 Springer Nature B.V
Subjects:	Algorithms Combinatorics Completion time Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Pareto optimum Polynomials Schedules Scheduling Theory of Computation Splitable jobs Polynomial-time algorithm Parallel-batch Pareto optimal
ISSN:	1382-6905, 1573-2886
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Abstract	We investigate the scheduling problem on a single bounded parallel-batch machine where jobs belong to two non-disjoint agents (called agent A and agent B) and are of equal length but different size. Each job’s size can be arbitrarily split into two parts and processed in the consecutive batches. It is permitted to process the jobs from different agents in a common batch. We show that it is unary NP-hard for the problem of minimizing the total weighted completion time of the jobs of agent A subject to the maximum cost of the jobs of agent B being upper bounded by a given threshold. For the case of the jobs of agent A having identical weights, we study the version of Pareto problem, and give a polynomial-time algorithm to generate all Pareto optimal points and a Pareto optimal schedule corresponding to each Pareto optimal point.
AbstractList	We investigate the scheduling problem on a single bounded parallel-batch machine where jobs belong to two non-disjoint agents (called agent A and agent B) and are of equal length but different size. Each job’s size can be arbitrarily split into two parts and processed in the consecutive batches. It is permitted to process the jobs from different agents in a common batch. We show that it is unary NP-hard for the problem of minimizing the total weighted completion time of the jobs of agent A subject to the maximum cost of the jobs of agent B being upper bounded by a given threshold. For the case of the jobs of agent A having identical weights, we study the version of Pareto problem, and give a polynomial-time algorithm to generate all Pareto optimal points and a Pareto optimal schedule corresponding to each Pareto optimal point.
Author	Geng, Zhichao Liu, Jiayu
Author_xml	– sequence: 1 givenname: Zhichao orcidid: 0000-0002-1443-9554 surname: Geng fullname: Geng, Zhichao email: zcgeng@zzu.edu.cn organization: School of Mathematics and Statistics, Zhengzhou University – sequence: 2 givenname: Jiayu surname: Liu fullname: Liu, Jiayu organization: Henan College of Transportation
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References	YangDHouYKuoWA note on a single-machine lot scheduling problem with indivisible ordersCompu Oper Res2017793438359581410.1016/j.cor.2016.10.004 LiSYuanJUnbounded parallel-batching scheduling with two competitive agentsJ Sched201215629640297165610.1007/s10951-011-0253-x AgnetisAMirchandaniPBPacciarelliDPacificiAScheduling problems with two competing agentsOper Res200452229242206639810.1287/opre.1030.0092 HoogeveenJAVan de VeldeSLMinimizing total completion time and maximum cost simultaneously is solvable in polynomial timeOper Res Lett199517205208135707610.1016/0167-6377(95)00023-D HouYYangDKuoWLot scheduling on a single machineInf Process Lett2014114718722324718510.1016/j.ipl.2014.06.016 LawlerELOptimal sequencing of a single machine subject to precedence constraintsManag Sci19731954454610.1287/mnsc.19.5.544 GengZYuanJPareto optimization scheduling of family jobs on a p-batch machine to minimize makespan and maximum latenessTheor Comput20155702229330294610.1016/j.tcs.2014.12.020 SantosCMagazineMBatching in single operation manufacturing systemsOper Res Lett198549910310.1016/0167-6377(85)90011-2 ZhangGCaiXLeeCWongCMinimizing makespan on a single batch processing machine with nonidentical job sizesNav Res Log200148226240181765110.1002/nav.4 WangJFanGZhangYZhangCLeungJYTTwo-agent scheduling on a single parallel-batching machine with equal processing time and non-identical job sizesEur J Oper Res2017258478490358235810.1016/j.ejor.2016.10.024 WangJFanGLinZMixed batch scheduling on identical machinesJ Sched201910.1007/s10951-019-00623-9 ZhangELiuMZhengFXuYSingle machine lot scheduling to minimize the total weighted (discounted) completion timeInf Process Lett20191424651387296010.1016/j.ipl.2018.10.002 BakerKRSmithJCA multiple-criterion model for machine schedulingJ Sched20036716199998710.1023/A:1022231419049 GareyMJohnsonDComputers and Intractability: a guide to the theory of NP-completeness1979New YorkW. H. Freeman0411.68039 BruckerPGladkyAHoogeveenHKovalyovMYPottsCNTautenhahnTScheduling a batching machineJ Sched199813154164226110.1002/(SICI)1099-1425(199806)1:1<31::AID-JOS4>3.0.CO;2-R LeeCUzsoyRMartin-VegaLAEfficient algorithms for scheduling semiconductor burn-in operationsOper Res199240764775117980210.1287/opre.40.4.764 HoogeveenHMulticriteria schedulingEur J Oper Res2005167592623215706110.1016/j.ejor.2004.07.011 LawlerELA pseudopolynomial algorithm for sequencing jobs to minimize total tardniessAnn Discrete Math19771313420353.68071 MorBMosheiovGBatch scheduling of identical jobs on parallel identical machinesInf Process Lett2012112762766295520910.1016/j.ipl.2012.06.020 NelsonRTSarinRKDanielsRLScheduling with multiple performance measures: the one-machine caseManag Sci19863246447910.1287/mnsc.32.4.464 AgnetisABillautJCGawiejnowiczSPacciarelliDSoukhalAMultiagent scheduling: models and algorithms2014BerlinSpringer10.1007/978-3-642-41880-8 HoogeveenJASingle-machine scheduling to minimize a function of two or three maximum cost criteriaJ Algorithms199621415433140568710.1006/jagm.1996.0051 KR Baker (626_CR4) 2003; 6 JA Hoogeveen (626_CR9) 1995; 17 S Li (626_CR14) 2012; 15 A Agnetis (626_CR2) 2004; 52 M Garey (626_CR5) 1979 Y Hou (626_CR10) 2014; 114 C Lee (626_CR11) 1992; 40 EL Lawler (626_CR12) 1973; 19 B Mor (626_CR15) 2012; 112 P Brucker (626_CR3) 1998; 1 RT Nelson (626_CR17) 1986; 32 J Wang (626_CR19) 2019 Z Geng (626_CR6) 2015; 570 EL Lawler (626_CR13) 1977; 1 JA Hoogeveen (626_CR7) 1996; 21 J Wang (626_CR18) 2017; 258 G Zhang (626_CR22) 2001; 48 A Agnetis (626_CR1) 2014 C Santos (626_CR16) 1985; 4 E Zhang (626_CR21) 2019; 142 H Hoogeveen (626_CR8) 2005; 167 D Yang (626_CR20) 2017; 79
References_xml	– reference: WangJFanGZhangYZhangCLeungJYTTwo-agent scheduling on a single parallel-batching machine with equal processing time and non-identical job sizesEur J Oper Res2017258478490358235810.1016/j.ejor.2016.10.024 – reference: LiSYuanJUnbounded parallel-batching scheduling with two competitive agentsJ Sched201215629640297165610.1007/s10951-011-0253-x – reference: YangDHouYKuoWA note on a single-machine lot scheduling problem with indivisible ordersCompu Oper Res2017793438359581410.1016/j.cor.2016.10.004 – reference: BruckerPGladkyAHoogeveenHKovalyovMYPottsCNTautenhahnTScheduling a batching machineJ Sched199813154164226110.1002/(SICI)1099-1425(199806)1:1<31::AID-JOS4>3.0.CO;2-R – reference: LawlerELOptimal sequencing of a single machine subject to precedence constraintsManag Sci19731954454610.1287/mnsc.19.5.544 – reference: SantosCMagazineMBatching in single operation manufacturing systemsOper Res Lett198549910310.1016/0167-6377(85)90011-2 – reference: AgnetisABillautJCGawiejnowiczSPacciarelliDSoukhalAMultiagent scheduling: models and algorithms2014BerlinSpringer10.1007/978-3-642-41880-8 – reference: HoogeveenJASingle-machine scheduling to minimize a function of two or three maximum cost criteriaJ Algorithms199621415433140568710.1006/jagm.1996.0051 – reference: LeeCUzsoyRMartin-VegaLAEfficient algorithms for scheduling semiconductor burn-in operationsOper Res199240764775117980210.1287/opre.40.4.764 – reference: BakerKRSmithJCA multiple-criterion model for machine schedulingJ Sched20036716199998710.1023/A:1022231419049 – reference: LawlerELA pseudopolynomial algorithm for sequencing jobs to minimize total tardniessAnn Discrete Math19771313420353.68071 – reference: AgnetisAMirchandaniPBPacciarelliDPacificiAScheduling problems with two competing agentsOper Res200452229242206639810.1287/opre.1030.0092 – reference: ZhangGCaiXLeeCWongCMinimizing makespan on a single batch processing machine with nonidentical job sizesNav Res Log200148226240181765110.1002/nav.4 – reference: GengZYuanJPareto optimization scheduling of family jobs on a p-batch machine to minimize makespan and maximum latenessTheor Comput20155702229330294610.1016/j.tcs.2014.12.020 – reference: MorBMosheiovGBatch scheduling of identical jobs on parallel identical machinesInf Process Lett2012112762766295520910.1016/j.ipl.2012.06.020 – reference: HoogeveenJAVan de VeldeSLMinimizing total completion time and maximum cost simultaneously is solvable in polynomial timeOper Res Lett199517205208135707610.1016/0167-6377(95)00023-D – reference: WangJFanGLinZMixed batch scheduling on identical machinesJ Sched201910.1007/s10951-019-00623-9 – reference: NelsonRTSarinRKDanielsRLScheduling with multiple performance measures: the one-machine caseManag Sci19863246447910.1287/mnsc.32.4.464 – reference: HouYYangDKuoWLot scheduling on a single machineInf Process Lett2014114718722324718510.1016/j.ipl.2014.06.016 – reference: HoogeveenHMulticriteria schedulingEur J Oper Res2005167592623215706110.1016/j.ejor.2004.07.011 – reference: ZhangELiuMZhengFXuYSingle machine lot scheduling to minimize the total weighted (discounted) completion timeInf Process Lett20191424651387296010.1016/j.ipl.2018.10.002 – reference: GareyMJohnsonDComputers and Intractability: a guide to the theory of NP-completeness1979New YorkW. H. Freeman0411.68039 – volume: 6 start-page: 7 year: 2003 ident: 626_CR4 publication-title: J Sched doi: 10.1023/A:1022231419049 – volume: 258 start-page: 478 year: 2017 ident: 626_CR18 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2016.10.024 – volume: 142 start-page: 46 year: 2019 ident: 626_CR21 publication-title: Inf Process Lett doi: 10.1016/j.ipl.2018.10.002 – volume: 570 start-page: 22 year: 2015 ident: 626_CR6 publication-title: Theor Comput doi: 10.1016/j.tcs.2014.12.020 – volume-title: Multiagent scheduling: models and algorithms year: 2014 ident: 626_CR1 doi: 10.1007/978-3-642-41880-8 – volume: 17 start-page: 205 year: 1995 ident: 626_CR9 publication-title: Oper Res Lett doi: 10.1016/0167-6377(95)00023-D – volume: 32 start-page: 464 year: 1986 ident: 626_CR17 publication-title: Manag Sci doi: 10.1287/mnsc.32.4.464 – volume: 1 start-page: 31 year: 1977 ident: 626_CR13 publication-title: Ann Discrete Math – volume: 114 start-page: 718 year: 2014 ident: 626_CR10 publication-title: Inf Process Lett doi: 10.1016/j.ipl.2014.06.016 – volume: 19 start-page: 544 year: 1973 ident: 626_CR12 publication-title: Manag Sci doi: 10.1287/mnsc.19.5.544 – volume: 4 start-page: 99 year: 1985 ident: 626_CR16 publication-title: Oper Res Lett doi: 10.1016/0167-6377(85)90011-2 – year: 2019 ident: 626_CR19 publication-title: J Sched doi: 10.1007/s10951-019-00623-9 – volume: 48 start-page: 226 year: 2001 ident: 626_CR22 publication-title: Nav Res Log doi: 10.1002/nav.4 – volume-title: Computers and Intractability: a guide to the theory of NP-completeness year: 1979 ident: 626_CR5 – volume: 21 start-page: 415 year: 1996 ident: 626_CR7 publication-title: J Algorithms doi: 10.1006/jagm.1996.0051 – volume: 40 start-page: 764 year: 1992 ident: 626_CR11 publication-title: Oper Res doi: 10.1287/opre.40.4.764 – volume: 52 start-page: 229 year: 2004 ident: 626_CR2 publication-title: Oper Res doi: 10.1287/opre.1030.0092 – volume: 167 start-page: 592 year: 2005 ident: 626_CR8 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2004.07.011 – volume: 79 start-page: 34 year: 2017 ident: 626_CR20 publication-title: Compu Oper Res doi: 10.1016/j.cor.2016.10.004 – volume: 15 start-page: 629 year: 2012 ident: 626_CR14 publication-title: J Sched doi: 10.1007/s10951-011-0253-x – volume: 112 start-page: 762 year: 2012 ident: 626_CR15 publication-title: Inf Process Lett doi: 10.1016/j.ipl.2012.06.020 – volume: 1 start-page: 31 year: 1998 ident: 626_CR3 publication-title: J Sched doi: 10.1002/(SICI)1099-1425(199806)1:1<31::AID-JOS4>3.0.CO;2-R
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SubjectTerms	Algorithms Combinatorics Completion time Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Pareto optimum Polynomials Schedules Scheduling Theory of Computation
Title	Single machine batch scheduling with two non-disjoint agents and splitable jobs
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