关于转炉炼钢外文翻译转炉炼钢生产调度铸造厂.docx
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关于转炉炼钢外文翻译转炉炼钢生产调度铸造厂.docx
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关于转炉炼钢外文翻译转炉炼钢生产调度铸造厂
原文
Productionschedulinginasteelmaking-continuouscastingplant
Abstract
Inthispaperwedescribeanoptimizationprocedureforplanningtheproductionofsteelingotsinasteelmakingcontinuouscastingplant.Thestrictrequirementsoftheproductionprocessdefeatedmostoftheearlierapproachestosteelmakingcontinuouscastingproductionscheduling,mainlyduetothelackofinformationintheoptimizationmodels.Ourformulationoftheproblemisbasedonthealternativegraph,whichisageneralizationofthedisjunctivegraphofRoyandSussman.Thealternativegraphformulationallowustodescribeindetailalltheconstraintsthatarerelevantfortheschedulingproblem.Wethensolvetheproblembyusingabeamsearchprocedure,andcompareourresultswithalowerboundoftheoptimalsolutionsandwiththeactualperformanceobtainedintheplant.Computationalexperienceshowstheeffectivenessofthisapproach.
Keywords:
Scheduling;Productionplanning;Steelmaking
1.Introduction:
Steelindustryisveryrichintermsofoperationalproblemsthatcanbemodeledandsolvedbyusingcomputerizedtechniques.Infact,duetothecompetitivepressure,manyinternationalironandsteelcorporationsaremovingtothejust-in-time(JIT)productionconcepts.CommonfeaturesoftheJITmanufacturingsystemsarethesmallsizeofthelotsandtherequestsforhighqualityproducts,timingdelivery,increasedproductivityandreducedcosts.
Toalargeextent,inthesteelindustry,schedulingandrelatedissuesarestillcarriedoutbyhumanschedulerswhosecomputersupportmainlyconsistsofasimulatoroftheplant,whichisusedtoevaluateandcomparedifferentscenarios.Ontheotherhand,manycompaniesarenowdevelopingandimplementingcomputerizedsystemsforaddressingsuchoperationalproblems,asreflectedintheprofessionalmeetingsonthesubject.Thesesystemshelptoincreaseproductivityandtimingdelivery,whilereducingenergyconsumptionandproductioncosts.Steelschedulingisknowntobeoneofthemostdifficultindustrialschedulingproblems.Researchersandpractitionershaveapproachedtherelatedschedulingproblemsusingtheformulationsandtoolsofvariousdisciplines,mostlyartificialintelligenceDornetal,1996,DornandShams,1996,TürksenandFazelZarandi,1998andSantosetal,2003andmathematicalprogrammingDuttaandFourer,2001,Naphadeetal,2001,Tangetal,2000,MoonandHrymak,1999,HarjunkoskiandGrossmann,2001andTangetal,2002.
InthispaperwedealinparticularwiththeproblemofschedulingtheproductionofstainlesssteelingotsinaproductionlinelocatedincentralItaly.Theplantproducesalargevarietyofingots,tobeusedinawidesetofapplications,characterizedbythesizeandchemicalcomposition,or“grade”.Theingotformationprocess,orsteelmakingcontinuouscastingprocess,hasextremelystrictrequirementsofmaterialcontinuityandflowtimetofulfillinordertoachievesuitablepropertiesonthefinalproduct,thusmakingtheproductionschedulingproblemparticularlychallenging.Showthelayoutoftheproductionline.Theproductionisorganizedinlots,eachlotbeingcomposedofagivennumberofladlestobecastconsecutively.Theladlesbelongingtothesamelotareidenticalandareassociatedtoaspecificproductionorder.Theproductionschedulingproblemconsistsofdeterminingtheschedulingofoperationstobeperformedonmoltensteelatthedifferentproductionstagesfromsteelmakingtocontinuouscasting.Inparticular,theprocessingofstainlesssteelconsistsofasequenceofhightemperatureoperationsstartingwiththeloadingofscrapironinanelectricarcfurnace(EAF).Thetimetomeltthescrapironrangesfrom70to80 minutes,includingafewminutesforsetupandfurnacemaintenanceoperations.
Theliquidsteelispouredintoladlesthatacranetransportstoasubsequentmachine,calledargonoxygendecarburizationunit(AOD),wherenickel,chromiumandotherelementsareaddedtothesteelinordertomeetthechemicalqualityrequirements.UsuallythedurationoftheoperationontheAODrangesbetween70and80 minutes.BetweenEAFandAODthereisroomforstoringuptothreeladlesbut,sincethestoredsteelcoolsdown,itmustbereheatedintheAOD.AftertheAODtheladlesaretransportedtoaladlefurnace(LF)whichcanhostatmosttwoladles.EvenifsomeoperationsareexecutedintheLF(nomorethan30 minutes),inpracticeitactsasabuffertomaintaintheladlesatthepropertemperaturebeforethelastoperation,tobeexecutedinthecontinuouscaster(CC).BetweentheLFandtheCCthereisabufferthatcanholdatmostoneladle.Aladlecanstayinthebufferatmost10 minutes,otherwisetheliquidsteelcouldcooldown.IntheCCtheliquidsteeliscastandcooledtoformslabs,thetimerequiredforcastingoneladlerangesfrom60to70 minutes.MoreovertheCCneedstobetooledwithaparticulartool,calledflyingtundish,whichdeterminestheformatofslabs.Iftwosubsequentladlesbelongtothesamelot,theymustbecastwithoutinterruption,otherwisethetundishdeteriorates,andasetupisnecessaryinordertosubstituteit.However,thetundishmustbechangedanywaywhenswitchingfromalottoanother,aswellasafteragivennumberofladles,rangingfromthreetoseven,whichdependsonthesteelquality.Thesizeofalotmayvary,therefore,fromonetosevenladles.Thesetuptimeneedsabout60 minutes,duringwhichtheCCisblocked.Theproblemistoscheduletheproductionofagivennumberoflotswiththeobjectiveofminimizingthecompletiontimeofthelastscheduledlot,i.e.minimizingthemakespan.Werefertothisproblemassteelmakingcontinuouscasting(SCC)problem.Thetimehorizonforaplanningperiodis1week,whichcorrespondstoanaverageof120ladlesand30lotsforatypicalrealsizeproblem.Fig.2showstheGanttchartofascheduleinwhichtwolotsareproduced.Thefirstlotiscomposedofthreeladles,andthesecondiscomposedoftwoladles.Theprocessingtimesarenotrealistic,butareusefultohighlighttheproductionrequirementsofafeasibleschedule.
Summarizingtheabovediscussion,theSCCproblemcanbemodeledasapermutationflowshopwithlimitedbuffersandthefollowingadditionalconstraints:
•Allpartsinalotmustbesequencedconsecutively.
•Therearesequenceindependentsetuptimesonthelastmachine(CC)betweentwoconsecutivelots.
•Thereisano-waitconstraintbetweenanytwoconsecutivecastingoperationsinthesamelot.
Thereisaperishabilityconstraintinthebufferbeforethelastmachine(CC).
Thepaperisorganizedasfollows.InSection2webrieflyreviewtheliteraturerelatedtotheSCCproblem,inSection3weintroducethenotationand,inSection4,wediscusstwomodelsfortheSCCproblem.InSection5,wedescribesomeproceduresforcomputinglowerboundstotheoptimalsolution,InSection6wedescribeourbeamsearchprocedurefortheSCCproblemand,inSection7,weillustratethecomputationalexperience.ConclusionsfollowinSection8.
2.Literaturereview
Inthissectionwebrieflyreviewtheliteraturerelatedtothispaper.Inparticular,inthefirstpartofthissectionwediscusstheliteratureonproblemsarisinginsteelmakingplants.Inthesecondpartwereviewsomegeneralapproachesforsolvingschedulingproblemsthatcanbeappliedtoindustrialcases,includingtheSCCproblemasaspecialcase.Inthelastpartofthissectionwebrieflyreviewsomerelevantpapersdealingwiththebeamsearchtechnique,analgorithmicprocedurethatweuseinthispapertosolvetheSCCproblem.
2.1Schedulingprobleminsteelmakingplants
Inanextensivesurveypaper,DuttaandFourer(2001)discussseveralproblemsarisinginasteelmakingplant.Theproblemsrangefromproductmixandblendingtoproductionschedulingandcuttingstock.Foralltheseproblems,mathematicalprogrammingapproachesarepresented.Inviewoftheirextensivesurvey,weprovideonlyabriefsummaryofrecentworkshere.
Naphadeetal.(2001)formulatetheschedulingprobleminasteelmakingplantusingamixedintegerformulationandsolveitusingatwolevelheuristicapproach.Tangetal.(2000)formulatetheSCCproblemusinganon-linearprogrammingmodel,andthenconvertitintoalinearprogrammingmodel,solvableusingstandardsoftwarepackages.InanotherrecentworkofTangetal.(2002),theSCCproblemisformulatedbyusinganintegerprogrammingmodelanditissolvedcombiningLagrangianrelaxation,dynamicprogrammingandheuristics.
HarjunkoskiandGrossmann(2001)considertheschedulingproblems,arisingintheproductionofsteel,foralinecomposedoftwoparallelEAFs,anAOD,anLFandaCC.Theydevelopadecompositionstrategy,whichisabletoreducethecomputationeffortdrastically.Thisstrategyallowstotackleindustrial-sizeproblems,basedon1weektimehorizonand80ladles,obtainingfeasiblesolutionswhicharealwayswithin3%fromalowerboundoftheoptimum.ThemainlayoutdifferencesbetweenoursettingandthesettingconsideredinHarjunkoskiandGrossmann(2001)arethatinourproblemtheladlesaregroupedinlotswhereasinHarjunkoskiandGrossmanneachladleisindependentoftheothers,andanotherdifferenceisduetothepresenceoftwoparallelEAFsintheirproductionline.OtherrelevantworksfocusontheoptimizationoftheCCmachineSantosetal.,2003andSchwindtandTrautmann,2003orfurnaces,coolersandcraneoperations(Moon&Hrymak,1999).
2.2Machineschedulingwithcomplicatingconstraints
AdifferentstreamofresearchrelatedtoSCCproblemdeals,moreingeneral,withothermachineschedulingproblemsexhibitingthesamecomplicatingconstraintsoftheSCCproblem.Forexample,
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