Just-in-Time Systems

311 Pages·2011·4.284 MB·English

by  Roger Rios, Yasmín A. Ríos-Solís

Springer Optimization and Its Applications
VOLUME60
ManagingEditor
PanosM.Pardalos(UniversityofFlorida)
Editor–CombinatorialOptimization
Ding-ZhuDu(UniversityofTexasatDallas)
AdvisoryBoard
J.Birge(UniversityofChicago)
C.A.Floudas(PrincetonUniversity)
F.Giannessi(UniversityofPisa)
H.D.Sherali(VirginiaPolytechnicandStateUniversity)
T.Terlaky(McMasterUniversity)
Y.Ye(StanfordUniversity)
AimsandScope
Optimizationhasbeenexpandinginalldirectionsatanastonishingratedur-
ing the last few decades. New algorithmic and theoretical techniques have
beendeveloped,thediffusionintootherdisciplineshasproceededatarapid
pace, and our knowledge of all aspects of the field has grown even more
profound.Atthe sametime, oneofthe moststriking trendsin optimization
is the constantly increasing emphasis on the interdisciplinary nature of the
field.Optimizationhasbeenabasictoolinallareasofappliedmathematics,
engineering,medicine,economics,andothersciences.
The series Springer Optimization and Its Applications publishes under-
graduate and graduate textbooks, monographs and state-of-the-art exposi-
tory work that focus on algorithms for solving optimization problems and
alsostudyapplicationsinvolvingsuchproblems.Someofthetopicscovered
includenonlinearoptimization(convexandnonconvex),networkflowprob-
lems,stochasticoptimization,optimalcontrol,discreteoptimization,multi-
objective programming, description of software packages, approximation
techniquesandheuristicapproaches.
Forfurthervolumes:
http://www.springer.com/series/7393

Roger Z. R´ıos-Mercado • Yasm´ın A. R´ıos-Sol´ıs
Editors
Just-in-Time Systems
123
Editors
RogerZ.R´ıos-Mercado Yasm´ınA.R´ıos-Sol´ıs
DepartmentofMechanicalandElectrical DepartmentofMechanicalandElectrical
Engineering Engineering
GraduatePrograminSystemsEngineering GraduatePrograminSystemsEngineering
UniversidadAuto´nomadeNuevoLeo´n UniversidadAuto´nomadeNuevoLeo´n
66450SanNicola´sdelosGarza 66450SanNicola´sdelosGarza
NuevoLeo´n NuevoLeo´n
Mexico Mexico
[email protected] yasmin@yalma.fime.uanl.mx
ISSN1931-6828
ISBN978-1-4614-1122-2 e-ISBN978-1-4614-1123-9
DOI10.1007/978-1-4614-1123-9
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2011938811
MathematicsSubjectClassification(2010):37M10,92B20,68M20,68Q15,68Q25,82C32,9002,9008,
90B05,90B25,90B30,90B35,90B36,90B50,90B90,90C10,90C11,90C27,90C39,90C59,90C60,
90C90,91A80,91B50
(cid:2)c SpringerScience+BusinessMedia,LLC2012
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Preface
Just-in-time(JIT)philosophywasintroducedinthe1950s.Itsaimwastoreducein-
ventoryanditsassociatedcosts.Nowadays,JITisassociatedwithefficiency,contin-
uousimprovement,quality,andoptimalflow.JITstartedinindustriesbutitquickly
attracted the interest of the researchers since its implementation involves difficult
problemsthathavebeen,andwillbe,challengingthescientificcommunity.
There is a large community dealing with JIT scheduling. As we show in the
first part of this book, the scheduling models, their analysis, and their resolution
methodsarevastandarecontinuouslyexpanding.Nevertheless,JITiscoveringand
integrating other parts of the supply chain as presented in the second part of the
book.Ifwedefineasystemasasetofinteractingcomponentsforminganintegrated
whole,thenthetitleofthisbookemerges:“JITsystems”.Indeed,notonlyoneofthe
mainobjectivesforusistopresentstate-of-the-artarticlesinJITschedulingbutalso
is to show thatJIT includeslot-sizing,forecasting,gametheory,mass production,
andtransferlines.
The book is comprised of invitation-onlyarticles written by experts in the JIT
field. Each manuscripthas beenstrictly peer-reviewedto ensure the qualityof the
work.Theaimofthebookistopresentmodels,methods,algorithms,applications,
orcasestudiesofJITsystems.Thetargetaudienceofthisbookwillbeprofessionals,
researchers,andgraduatestudentsfromdiversefieldssuchasOperationsResearch,
ManagementScience,ComputerScience,andDiscreteMathematics.
PartIofthebookdealswithasurprisingvarietyofJITschedulingmodels.First,
asurveyofschedulingtomaximizingthenumberofJITjobsispresentedbyShab-
tay and Steiner. It deals from the single machine case to the shop cases. Then,
Tanaka contributed an article dealing with the exact resolution of the single ma-
chineearliness–tardinessscheduling.Indeed,earlinesspenaltiescanbeconsidered
asinventorycostswhiletardinessonesarerelatedtothedispleasureofthecustomer
when a delay occurs. Yang and Yang present another field studied in scheduling
thatariseswhenthejobsortaskshavedeterioratingandlearningeffectsonasingle
machine.
In the scheduling literature, the single machine problem has received most of
the attention. Nevertheless, the parallel machine case is interesting and closer to
v
vi Preface
the real problems industries have. Vallada and Ruiz present a genetic algorithm
for the parallel machine earliness–tardiness problem with setup times. Moreover,
Ronconi and Birgin deal with the exact resolution of the flowshop earliness–
tardiness scheduling case. Soukhal and Hyunh Toung analyse the particular but
challengingcaseofhavingjobswithequalprocessingtimes.LastarticleofPartIis
byOulamaraandfocusonschedulingproblemswherethejobsmustbeprocessed
inbatchesasitoftenhappensintherealword.
PartIIofthisbookisintendedto problemsthatincludeorintegrateotherparts
of the production system. First, Jo´sefowska deals with the mass production envi-
ronmentwhereitistoocostlytodefineandcontrolduedatesforindividualitems.
Instead, the objective is to construct schedules with minimum deviation from an
ideal product rate. Absi, Dauze`re-Pe´rez, and Kedad-Sidhoum show that JIT sys-
temsintegratingthelot-sizingandtheschedulingphasesareactuallyinterestingand
challenging.Gourve`s,Monnot,andTelelisexamineanalgorithmicgame-theoretic
approach to optimizing the performance of distributed systems utilized by au-
tonomous self-interested users. They focus on scheduling with parallel machines
withsetuptimes.
For a JIT system to work properly,accurate forecasts are sought. In particular,
neuralnetworkscan be extremely useful. This subject is treated by Cabrera-R´ıos,
Salazar-Aguilar, Villareal-Marroqu´ın, and Anaya Salazar. The paper of Low and
JayawickramapresentareallifebuildingprojectthatismanagedwiththeJITsys-
tem.Finally,Go¨kc¸e,Dinc¸er,andO¨rnekstudythethroughputratesoftransferlines
withpullsystems.
Collectively, this book describes recent advancesin JIT systems. We acknowl-
edgethattherearemanytopicsthatarenotcoveredduetothelimitationsofspace.
Nevertheless,wetrustthatthosethatareincludedherewillprovideinformationand
motivationtoexplorethisresearcharea.
Wethankforemosttheauthorsfortheiroutstandingcontributionsandtheircoop-
erationforthisproject.Furthermore,wethankProfessorPanosPardalos,editorof
theSpringerSeriesonOptimizationandItsApplications,foracceptingandencour-
agingthisproject.WealsothankVaishaliDamleandMeredithRichfromSpringer
fortheirsupportthroughouttheeditionprocessofthisbook.Wespeciallythankthe
anonymousreviewers who have greatly improved the quality of the chapters. We
are also grateful to Omar Ibarra-Rojasand Mo´nica Elizondo-Amayafrom UANL
fortheirhelpduringtheeditionofthebook.
SanNicola´sdelosGarza,Mexico Yasm´ınA.R´ıos-Sol´ıs
RogerZ.R´ıos-Mercado
Contents
PartI Just-in-TimeSchedulingSystems
1 SchedulingtoMaximizetheNumber
ofJust-in-TimeJobs:ASurvey ................................ 3
DvirShabtayandGeorgeSteiner
1.1 Introduction.............................................. 3
1.2 TheJIT ProblemonaSingleMachine........................ 7
1.2.1 ConstantProcessingTimes.......................... 7
1.2.2 ControllableProcessingTimes ...................... 8
1.3 TheJIT SchedulingProblemonParallelMachines ............. 10
1.3.1 ConstantProcessingTimes.......................... 10
1.3.2 ControllableProcessingTimes ...................... 12
1.4 TheJIT SchedulingProbleminOtherMulti-machineSystems ... 12
1.4.1 FlowShops ...................................... 12
1.4.2 JobShopsandOpenShops ......................... 17
1.5 Summary ................................................ 17
References..................................................... 19
2 AnExactAlgorithmfortheSingle-MachineEarliness–Tardiness
SchedulingProblem ......................................... 21
ShunjiTanaka
2.1 Introduction.............................................. 21
2.2 ProblemFormulation ...................................... 23
2.2.1 Time-IndexedFormulation.......................... 23
2.2.2 NetworkRepresentation............................ 24
2.3 LagrangianRelaxation..................................... 26
2.3.1 LagrangianRelaxationoftheNumberofJob
Occurrences...................................... 26
2.3.2 ConstraintsonSuccessiveJobs ...................... 27
2.3.3 ConstraintsonAdjacentPairsofJobs................. 29
2.3.4 ConstraintsonState-SpaceModifiers................. 29
vii
viii Contents
2.4 NetworkReduction........................................ 30
2.4.1 NetworkReductionbyUpperBound ................. 31
2.4.2 NetworkReductionbyDominanceofSuccessiveJobs... 31
2.5 AlgorithmOverview....................................... 33
2.6 UpperBoundComputation ................................. 34
2.6.1 LagrangianHeuristic............................... 34
2.6.2 ImprovementbyNeighborhoodSearch ............... 35
2.6.3 InitialUpperBound ............................... 35
2.7 NumericalExperiments .................................... 35
2.8 Conclusion............................................... 38
References..................................................... 38
3 Single-Machine Scheduling Problems Simultaneous with
Deteriorating and Learning Effects Under a Deteriorating
MaintenanceConsideration................................... 41
Suh-JenqYangandDar-LiYang
3.1 Introduction.............................................. 41
3.2 ProblemFormulation ...................................... 45
3.3 Problem1/p =(p +λt)ra, ma/∑n (αE +βT +γd+δD).. 46
jr j j=1 j j
3.3.1 PreliminaryAnalysis............................... 46
3.3.2 OptimalSolutions ................................. 52
3.4 Problem1/p =(p +λt)ra, ma/C ...................... 58
jr j max
3.5 Problem1/p =(p +λt)ra, ma/TC........................ 59
jr j
3.6 Problem1/p =(p +λt)ra, ma/TADC..................... 60
jr j
3.7 Conclusions.............................................. 61
References..................................................... 62
4 SchedulingUnrelatedParallelMachineswithSequenceDependent
SetupTimesandWeightedEarliness–TardinessMinimization...... 67
EvaValladaandRube´nRuiz
4.1 Introduction.............................................. 67
4.2 LiteratureReview ......................................... 70
4.3 ExactMixedIntegerLinearProgrammingModel............... 71
4.4 ProposedMethods ........................................ 74
4.4.1 Representation of Solutions, Initialization
ofthePopulation,andSelectionProcedure ............ 75
4.4.2 CrossoverOperator................................ 76
4.4.3 LocalSearch ..................................... 76
4.4.4 IdleTimeInsertion ................................ 77
4.5 ComputationalandStatisticalEvaluation...................... 79
4.5.1 TestingtheMathematicalModels .................... 80
4.5.2 ComputationalEvaluationforSmallInstances ......... 82
4.5.3 ComputationalEvaluationforLargeInstances ......... 83
4.6 ConclusionsandFutureResearch............................ 85
References..................................................... 88
Contents ix
5 Mixed-IntegerProgrammingModelsforFlowshopScheduling
ProblemsMinimizingtheTotalEarlinessandTardiness ........... 91
De´boraP.RonconiandErnestoG.Birgin
5.1 Introduction.............................................. 91
5.2 MILPModelsforFlowshopwithUnlimitedBuffer ............. 92
5.3 MILPModelsforFlowshopwithZeroBuffer.................. 97
5.4 NumericalExperiments ....................................101
5.5 ConcludingRemarks ......................................103
References.....................................................104
6 Just-in-TimeSchedulingwithEqual-SizeJobs ................... 107
AmeurSoukhalandNguyenHuynhToung
6.1 Introduction..............................................107
6.2 PreliminaryResults .......................................109
6.2.1 AssignmentProblem...............................111
6.3 RestrictiveCommonDueDateandJust-in-TimeScheduling .....112
6.3.1 1|p =p,d =d|∑(αE +βT ) ....................112
j j j j j j
6.3.2 1|p =p,d ∈D,|D|=l,l fixed|∑(αE +βT) ......117
j j j j j j
6.3.3 Qm|p =p,d ∈D,|D|=l,l fixed|∑(αE +βT ) ....122
j j j j j j
6.4 Non-RestrictiveCommonDueDateandJust-in-Time
Scheduling...............................................122
6.4.1 Qm|p =p,d =d,non-restrictive|∑(αE +βT) .....123
j j j j
6.4.2 Qm|p =p,d =d,non-restrictive|∑(αE +βT ) ....128
j j j j j j
6.5 UnknownCommonDueDateandJust-in-TimeScheduling ......129
6.5.1 JobAssignmentCostMatrixforaGivenDueDate......130
6.5.2 1|p =p,d =d unknown|∑(αE +βT +γd)........132
j j j j j j
6.5.3 1|p = p,d ∈D,|D|≤l,D unknown,l fixed|
j j
∑(αE +βT +γd ) .............................133
j j j j j j
6.5.4 P|p = p,d ∈D,|D|≤l,D unknown,l fixed|
j j
∑(αE +βT +γd ) .............................135
j j j j j j
6.5.5 AdditionalConstraintandNotDependingWeights
onJobs ..........................................141
6.6 Conclusion...............................................142
References.....................................................143
7 No-WaitSchedulingProblemswithBatchingMachines............ 147
A.Oulamara
7.1 Introduction..............................................147
7.2 No-WaitFlowshopwithMixedBatchingMachines.............150
7.2.1 NP-Hardness .....................................150
7.2.2 EqualProcessingTimesonM ......................153
1
7.2.3 EqualProcessingTimesonM ......................156
2
7.2.4 Approximation ...................................158
7.3 No-WaitFlowshopwithTwos-BatchingMachines .............160
7.3.1 NP-Hardness .....................................160
7.3.2 IntegerProgrammingFormulation ...................162
x Contents
7.3.3 LagrangianRelaxationHeuristic.....................163
7.3.4 ComputationalExperiments ........................165
7.4 Conclusion...............................................167
References.....................................................167
PartII Just-in-TimePhilosophy:InteractionwithOtherAreas
8 Just-in-TimeSchedulinginModernMassProduction
Environment ............................................... 171
JoannaJo´zefowska
8.1 Introduction..............................................171
8.2 MathematicalModel.......................................173
8.2.1 BasicModel......................................174
8.2.2 Just-in-TimeSchedulingandtheApportionment
Problem .........................................175
8.3 SolutionAlgorithms.......................................177
8.3.1 MinimizingtheTotalDeviation......................178
8.3.2 MinimizingtheMaximumDeviation .................181
8.4 MultipleParallelMachines .................................185
8.4.1 TotalDeviation ...................................186
8.4.2 MaximumDeviation...............................187
8.5 Conclusions..............................................189
References.....................................................190
9 Just-in-TimePlanningandLot-Sizing .......................... 191
NabilAbsi,Ste´phaneDauze`re-Pe´re`s,andSafiaKedad-Sidhoum
9.1 Introduction..............................................191
9.2 SetupOptimization........................................194
9.3 DemandBacklogs.........................................197
9.4 LostSalesandOvertimes...................................198
9.5 TimeWindowsConstraintsandEarlyProductions..............199
9.6 BoundedProductionandInventory...........................201
9.7 DealingwithCapacityConstraints ...........................202
9.8 IntegratedLot-SizingandScheduling ........................204
9.9 ConclusionandNewResearchDirections.....................204
References.....................................................205
10 StrategicSchedulingGames:EquilibriaandEfficiency............ 209
LaurentGourve`s,Je´roˆmeMonnot,andOrestisA.Telelis
10.1 Introduction..............................................209
10.1.1 Contents .........................................212
10.2 PreliminariesandNotation .................................212
10.2.1 StrategicGamesandEquilibria ......................212
10.2.2 SocialCost-EfficiencyofEquilibria ..................213
10.2.3 SelfishSchedulingandCoordinationMechanisms ......216