关于转炉炼钢外文翻译转炉炼钢生产调度铸造厂.docx

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,