Single machine scheduling with a generalized job-dependent cumulative effect

We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these pa...

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Veröffentlicht in:	Journal of scheduling Jg. 20; H. 6; S. 583 - 592
Hauptverfasser:	Rustogi, Kabir, Strusevich, Vitaly A.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.12.2017 Springer Nature B.V
Schlagworte:	Artificial Intelligence Boolean algebra Business and Management Calculus of Variations and Optimal Control; Optimization Job shops Mathematical models Operations Research/Decision Theory Optimization Precedence constraints Production scheduling Scheduling Supply Chain Management Precedence constraints Maintenance Approximation scheme Half-product problem Deterioration Single machine
ISSN:	1094-6136, 1099-1425
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Abstract	We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these parameters are assumed to be equal to the normal processing times of jobs, which seriously limits the practical application of this model. We further generalize this model by allowing every job to respond differently to these cumulative effects. For the introduced model, we solve the problem of minimizing the makespan, with and without precedence constraints. For the problem without precedence constraints, we also consider a situation in which a maintenance activity is included in the schedule, which can improve the processing conditions of the machine, not necessarily to its original state. The resulting problem is reformulated as a variant of a Boolean programming problem with a quadratic objective, known as a half-product, which allows us to develop a fully polynomial-time approximation scheme with the best possible running time.
AbstractList	We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these parameters are assumed to be equal to the normal processing times of jobs, which seriously limits the practical application of this model. We further generalize this model by allowing every job to respond differently to these cumulative effects. For the introduced model, we solve the problem of minimizing the makespan, with and without precedence constraints. For the problem without precedence constraints, we also consider a situation in which a maintenance activity is included in the schedule, which can improve the processing conditions of the machine, not necessarily to its original state. The resulting problem is reformulated as a variant of a Boolean programming problem with a quadratic objective, known as a half-product, which allows us to develop a fully polynomial-time approximation scheme with the best possible running time.
Author	Rustogi, Kabir Strusevich, Vitaly A.
Author_xml	– sequence: 1 givenname: Kabir surname: Rustogi fullname: Rustogi, Kabir organization: Department of Mathematical Sciences, University of Greenwich – sequence: 2 givenname: Vitaly A. surname: Strusevich fullname: Strusevich, Vitaly A. email: V.Strusevich@greenwich.ac.uk organization: Department of Mathematical Sciences, University of Greenwich
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Cites_doi	10.1016/j.omega.2011.12.007 10.1007/s10951-008-0064-x 10.1016/j.ejor.2012.04.037 10.1016/j.ejor.2005.03.020 10.1287/moor.23.3.649 10.1137/0211023 10.1016/j.apm.2014.11.002 10.1007/s10479-015-2018-y 10.1142/S0129054110007301 10.1016/S0377-2217(99)00066-1 10.1016/j.omega.2013.05.005 10.1016/j.cor.2010.06.004 10.1016/j.ins.2009.02.015 10.1007/978-3-642-41880-8 10.1016/j.ipl.2004.12.018 10.1007/s10951-012-0287-8 10.1287/moor.4.3.215 10.1016/j.dam.2008.01.018 10.1057/jors.2014.18 10.1016/S0167-5060(08)70323-6 10.1007/s10288-011-0180-x 10.1016/j.ipl.2005.09.007 10.1007/BF01581240
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Copyright	Springer Science+Business Media New York 2016 Journal of Scheduling is a copyright of Springer, (2016). All Rights Reserved.
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Keywords	Precedence constraints Maintenance Approximation scheme Half-product problem Deterioration Single machine
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References	RustogiKStrusevichVACombining time and position dependent effects on a single machine subject to rate-modifying activitiesOmega20144216617810.1016/j.omega.2013.05.005 Kellerer, H., & Strusevich, V. A. (2012). The symmetric quadratic knapsack problem: Approximation and scheduling applications. 4OR, 10, 111–161. LawlerELSequencing jobs to minimize total weighted completion time subject to precedence constraintsAnnals of Discrete Mathematics19782759010.1016/S0167-5060(08)70323-6 GawiejnowiczSTime-dependent scheduling2008BerlinSpringer TamirAA strongly polynomial algorithm for minimum convex separable quadratic cost flow problems on two-terminal series-parallel networksMathematical Programming19935911713210.1007/BF01581240 SmithWEVarious optimizers for single state productionNaval Research Logistics Quarterly195636669 WangJ-BXiaZ-QScheduling jobs under decreasing linear deteriorationInformation Processing Letters200594636910.1016/j.ipl.2004.12.018 AgnetisABillautJ-CGawiejnowiczSPacciarelliDSoukhalAMultiagent scheduling. Models and algorithms2014BerlinSpringer10.1007/978-3-642-41880-8 YinYXuDSunKLiHSome scheduling problems with general position-dependent and time-dependent learning effectsInformation Sciences20091792416242510.1016/j.ins.2009.02.015 KellererHStrusevichVAMinimizing total weighted earliness-tardiness on a single machine around a small common due date: An FPTAS using quadratic knapsackInternational Journal of Foundations of Computer Science20102135738310.1142/S0129054110007301 MonmaCLSidneyJBSequencing with series-parallel precedence constraintsMathematics of Operations Research1979421523410.1287/moor.4.3.215 RustogiKStrusevichVASingle machine scheduling with general positional deterioration and rate-modifying maintenanceOmega20124079180410.1016/j.omega.2011.12.007 ErelEGhoshJBFPTAS for half-products minimization with scheduling applicationsDiscrete Applied Mathematics20081563046305610.1016/j.dam.2008.01.018 Huang, X., & Wang, J.-J. (2015). Machine scheduling problems with a position-dependent deterioration. Applied Mathematical Modelling, 39, 2897–2908. RustogiKStrusevichVASimple matching vs linear assignment in scheduling models with positional effects: A critical reviewEuropean Journal of Operational Research201222239340710.1016/j.ejor.2012.04.037 Tanaev, V. S., Gordon, V. S., & Shafransky, Y. M. (1984). Scheduling theory. Single-stage systems. Moscow: Nauka (in Russian; translated into English by Kluwer Academic, Dordrecht, 1994). BadicsTBorosEMinimization of half-productsMathematics of Operations Research19983364966010.1287/moor.23.3.649 Kellerer, H., & Strusevich, V. A. (2016). Optimizing the half-product and related quadratic Boolean functions: Approximation and scheduling applications. Annals of Operations Research, 240, 39–94. KellererHRustogiKStrusevichVAApproximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenanceJournal of Scheduling20131667568310.1007/s10951-012-0287-8 KuoW-HYangD-LMinimizing the makespan in a single machine scheduling problem with a time-based learning effectInformation Processing Letters200697646710.1016/j.ipl.2005.09.007 ValdesJRTarjanELawlerELThe recognition of series-parallel digraphsSIAM Journal on Computing19821136137010.1137/0211023 GordonVSPottsCNStrusevichVAWhiteheadJDSingle machine scheduling models with deterioration and learning: Handling precedence constraints via priority generationJournal of Scheduling20081135737010.1007/s10951-008-0064-x DolguiAGordonVStrusevichVSingle machine scheduling with precedence constraints and positionally dependent processing timesComputers & Operations Research2012391218122410.1016/j.cor.2010.06.004 LeeC-YLeonVJMachine scheduling with a rate-modifying activityEuropean Journal of Operational Research200112811912810.1016/S0377-2217(99)00066-1 RustogiKStrusevichVASingle machine scheduling with time-dependent linear deterioration and rate-modifying maintenanceJournal of Operational Research Society20156650051510.1057/jors.2014.18 KuoW-HYangD-LMinimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effectEuropean Journal of Operational Research20061741184119010.1016/j.ejor.2005.03.020 497_CR7 A Tamir (497_CR22) 1993; 59 497_CR23 S Gawiejnowicz (497_CR5) 2008 K Rustogi (497_CR19) 2014; 42 Y Yin (497_CR26) 2009; 179 A Dolgui (497_CR3) 2012; 39 WE Smith (497_CR21) 1956; 3 H Kellerer (497_CR8) 2013; 16 W-H Kuo (497_CR12) 2006; 97 C-Y Lee (497_CR15) 2001; 128 H Kellerer (497_CR9) 2010; 21 K Rustogi (497_CR18) 2012; 222 VS Gordon (497_CR6) 2008; 11 497_CR11 CL Monma (497_CR16) 1979; 4 EL Lawler (497_CR14) 1978; 2 E Erel (497_CR4) 2008; 156 497_CR10 W-H Kuo (497_CR13) 2006; 174 K Rustogi (497_CR20) 2015; 66 J-B Wang (497_CR25) 2005; 94 A Agnetis (497_CR1) 2014 K Rustogi (497_CR17) 2012; 40 T Badics (497_CR2) 1998; 33 JR Valdes (497_CR24) 1982; 11
References_xml	– reference: AgnetisABillautJ-CGawiejnowiczSPacciarelliDSoukhalAMultiagent scheduling. Models and algorithms2014BerlinSpringer10.1007/978-3-642-41880-8 – reference: RustogiKStrusevichVASimple matching vs linear assignment in scheduling models with positional effects: A critical reviewEuropean Journal of Operational Research201222239340710.1016/j.ejor.2012.04.037 – reference: Kellerer, H., & Strusevich, V. A. (2016). Optimizing the half-product and related quadratic Boolean functions: Approximation and scheduling applications. Annals of Operations Research, 240, 39–94. – reference: SmithWEVarious optimizers for single state productionNaval Research Logistics Quarterly195636669 – reference: Tanaev, V. S., Gordon, V. S., & Shafransky, Y. M. (1984). Scheduling theory. Single-stage systems. Moscow: Nauka (in Russian; translated into English by Kluwer Academic, Dordrecht, 1994). – reference: YinYXuDSunKLiHSome scheduling problems with general position-dependent and time-dependent learning effectsInformation Sciences20091792416242510.1016/j.ins.2009.02.015 – reference: LawlerELSequencing jobs to minimize total weighted completion time subject to precedence constraintsAnnals of Discrete Mathematics19782759010.1016/S0167-5060(08)70323-6 – reference: RustogiKStrusevichVASingle machine scheduling with general positional deterioration and rate-modifying maintenanceOmega20124079180410.1016/j.omega.2011.12.007 – reference: KuoW-HYangD-LMinimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effectEuropean Journal of Operational Research20061741184119010.1016/j.ejor.2005.03.020 – reference: WangJ-BXiaZ-QScheduling jobs under decreasing linear deteriorationInformation Processing Letters200594636910.1016/j.ipl.2004.12.018 – reference: TamirAA strongly polynomial algorithm for minimum convex separable quadratic cost flow problems on two-terminal series-parallel networksMathematical Programming19935911713210.1007/BF01581240 – reference: Kellerer, H., & Strusevich, V. A. (2012). The symmetric quadratic knapsack problem: Approximation and scheduling applications. 4OR, 10, 111–161. – reference: RustogiKStrusevichVACombining time and position dependent effects on a single machine subject to rate-modifying activitiesOmega20144216617810.1016/j.omega.2013.05.005 – reference: KuoW-HYangD-LMinimizing the makespan in a single machine scheduling problem with a time-based learning effectInformation Processing Letters200697646710.1016/j.ipl.2005.09.007 – reference: ValdesJRTarjanELawlerELThe recognition of series-parallel digraphsSIAM Journal on Computing19821136137010.1137/0211023 – reference: Huang, X., & Wang, J.-J. (2015). Machine scheduling problems with a position-dependent deterioration. Applied Mathematical Modelling, 39, 2897–2908. – reference: ErelEGhoshJBFPTAS for half-products minimization with scheduling applicationsDiscrete Applied Mathematics20081563046305610.1016/j.dam.2008.01.018 – reference: GordonVSPottsCNStrusevichVAWhiteheadJDSingle machine scheduling models with deterioration and learning: Handling precedence constraints via priority generationJournal of Scheduling20081135737010.1007/s10951-008-0064-x – reference: LeeC-YLeonVJMachine scheduling with a rate-modifying activityEuropean Journal of Operational Research200112811912810.1016/S0377-2217(99)00066-1 – reference: DolguiAGordonVStrusevichVSingle machine scheduling with precedence constraints and positionally dependent processing timesComputers & Operations Research2012391218122410.1016/j.cor.2010.06.004 – reference: RustogiKStrusevichVASingle machine scheduling with time-dependent linear deterioration and rate-modifying maintenanceJournal of Operational Research Society20156650051510.1057/jors.2014.18 – reference: KellererHStrusevichVAMinimizing total weighted earliness-tardiness on a single machine around a small common due date: An FPTAS using quadratic knapsackInternational Journal of Foundations of Computer Science20102135738310.1142/S0129054110007301 – reference: BadicsTBorosEMinimization of half-productsMathematics of Operations Research19983364966010.1287/moor.23.3.649 – reference: KellererHRustogiKStrusevichVAApproximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenanceJournal of Scheduling20131667568310.1007/s10951-012-0287-8 – reference: MonmaCLSidneyJBSequencing with series-parallel precedence constraintsMathematics of Operations Research1979421523410.1287/moor.4.3.215 – reference: GawiejnowiczSTime-dependent scheduling2008BerlinSpringer – volume: 40 start-page: 791 year: 2012 ident: 497_CR17 publication-title: Omega doi: 10.1016/j.omega.2011.12.007 – volume: 11 start-page: 357 year: 2008 ident: 497_CR6 publication-title: Journal of Scheduling doi: 10.1007/s10951-008-0064-x – volume: 222 start-page: 393 year: 2012 ident: 497_CR18 publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2012.04.037 – volume: 174 start-page: 1184 year: 2006 ident: 497_CR13 publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2005.03.020 – volume: 33 start-page: 649 year: 1998 ident: 497_CR2 publication-title: Mathematics of Operations Research doi: 10.1287/moor.23.3.649 – volume: 11 start-page: 361 year: 1982 ident: 497_CR24 publication-title: SIAM Journal on Computing doi: 10.1137/0211023 – ident: 497_CR7 doi: 10.1016/j.apm.2014.11.002 – volume: 3 start-page: 66 year: 1956 ident: 497_CR21 publication-title: Naval Research Logistics Quarterly – ident: 497_CR11 doi: 10.1007/s10479-015-2018-y – volume: 21 start-page: 357 year: 2010 ident: 497_CR9 publication-title: International Journal of Foundations of Computer Science doi: 10.1142/S0129054110007301 – volume: 128 start-page: 119 year: 2001 ident: 497_CR15 publication-title: European Journal of Operational Research doi: 10.1016/S0377-2217(99)00066-1 – volume: 42 start-page: 166 year: 2014 ident: 497_CR19 publication-title: Omega doi: 10.1016/j.omega.2013.05.005 – volume: 39 start-page: 1218 year: 2012 ident: 497_CR3 publication-title: Computers & Operations Research doi: 10.1016/j.cor.2010.06.004 – volume: 179 start-page: 2416 year: 2009 ident: 497_CR26 publication-title: Information Sciences doi: 10.1016/j.ins.2009.02.015 – volume-title: Multiagent scheduling. Models and algorithms year: 2014 ident: 497_CR1 doi: 10.1007/978-3-642-41880-8 – volume: 94 start-page: 63 year: 2005 ident: 497_CR25 publication-title: Information Processing Letters doi: 10.1016/j.ipl.2004.12.018 – volume: 16 start-page: 675 year: 2013 ident: 497_CR8 publication-title: Journal of Scheduling doi: 10.1007/s10951-012-0287-8 – volume: 4 start-page: 215 year: 1979 ident: 497_CR16 publication-title: Mathematics of Operations Research doi: 10.1287/moor.4.3.215 – volume: 156 start-page: 3046 year: 2008 ident: 497_CR4 publication-title: Discrete Applied Mathematics doi: 10.1016/j.dam.2008.01.018 – volume: 66 start-page: 500 year: 2015 ident: 497_CR20 publication-title: Journal of Operational Research Society doi: 10.1057/jors.2014.18 – ident: 497_CR23 – volume: 2 start-page: 75 year: 1978 ident: 497_CR14 publication-title: Annals of Discrete Mathematics doi: 10.1016/S0167-5060(08)70323-6 – ident: 497_CR10 doi: 10.1007/s10288-011-0180-x – volume: 97 start-page: 64 year: 2006 ident: 497_CR12 publication-title: Information Processing Letters doi: 10.1016/j.ipl.2005.09.007 – volume-title: Time-dependent scheduling year: 2008 ident: 497_CR5 – volume: 59 start-page: 117 year: 1993 ident: 497_CR22 publication-title: Mathematical Programming doi: 10.1007/BF01581240
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Snippet	We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which...
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SubjectTerms	Artificial Intelligence Boolean algebra Business and Management Calculus of Variations and Optimal Control; Optimization Job shops Mathematical models Operations Research/Decision Theory Optimization Precedence constraints Production scheduling Scheduling Supply Chain Management
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Title	Single machine scheduling with a generalized job-dependent cumulative effect
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