起重机调度与空间限制中英文翻译Word格式.docx

起重机调度与空间限制中英文翻译Word格式.docx

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CraneSchedulingwithSpatialConstraints

AndrewLim,BrianRodrigues,FeiXiao,andYiZhu

Abstract

Inthiswork,weexamineportcraneschedulingwithspatialandseparationconstraints.Althoughcommontomostportoperations,theseconstraintshavenotbeenpreviouslystudied.Weassumethatcranescannotcross,thereisaminimumdistancebetweencranesandjobscannotbedonesimultaneously.Theobjectiveistofindacrane-to-jobmatchingwhichmaximizesthroughputundertheseconstraints.Weprovidedynamicprogrammingalgorithms,aprobabilistictabusearchandasqueakywheeloptimizationheuristicforsolution.ExperimentsshowtheheuristicsperformwellcomparedwithoptimalsolutionsobtainedbyCPLEXforsmallscaleinstanceswhereasqueakywheeloptimizationwithlocalsearchapproachgivesgoodresultswithinshorttimes.

1Introduction

ThePortofSingaporeAuthority（PSA）isalargeportoperatorlocatedinSingapore,oneofthebusiestportsintheworld.PSAhandles17.04millionTEU’sannuallyorninepercentofglobalcontainertrafficinSingapore,theworld’slargesttransshipmenthub.PSAisconcernedwithmaximizingthroughputatitsportduetolimitedportsize,highcargotransshipmentvolumesandlimitedphysicalfacilitiesandequipment.Craneschedulingandworkschedulesarecriticalinportmanagementsincecranesareattheinterfacebetweenlandandwatersectionsofanyport,eachwithitsowntrafficlanes,intersections,andvehicleflowcontrolsystems.Inthismulti-channelinterfacewearelikelytofindbottleneckswherecranesandothercargo-handlingequipment（forklifts,conveyorsetc.）converge.

SabriaandDaganzostudiedportoperationswhichfocusedonberthingandcargo-handlingsystems.Inberthing,whichisawidely-analyzedportactivity,queuingtheoryhasbeenusedwidely.Trafficandvehicle-flowschedulingonlandinportshasalsobeenwellstudied.Danganzostudiedastaticcraneschedulingcasewherecranescouldmovefreelyfromholdtoholdandonlyonecraneisallowedtoworkononeholdatanyonetime.Theobjectivewastominimizetheaggregatecostofdelay.In[13],containerhandlingismodelledas“work”whichcranesperformatconstantratesandcranescaninterruptworkwithoutlossofefficiency.Thisconstitutedan“openshop”parallelandidenticalmachinesproblem,wherejobsconsistofindependent,single-stageandpre-emptabletasks.Abranch-and-boundmethodwasusedtominimizedelaycostsforthisproblem.Craneschedulinghasalsobeenstudiedinthemanufacturingenvironmentcontext.

Commonly-foundconstraintsaffectingcraneoperationsareabsentinstudiesavailableonthesubject.Suchconstraintsaffectcraneworkschedulingandneedtobefactoredintooperationalmodels.Theseincludethebasicrequirementthatoperatingcranesdonotcrossovereachother.Also,aminimumseparatingdistancebetweencranesisnecessarysincecranesrequiresomespatialflexibilityinperformingjobs.Finally,thereisaneedforjobsarrivingforstackingatyardstobeseparatedinarrivaltimetoavoidcongestion.

Wefoundthatoperationaldecision-makingatPSAwasbasedlargelyonexperienceandsimulationtechniques.Whilethelatterisofvalue,analyticmodelsareanadvantageandarenotlimitedbyexperience-generatedrules-of-thumbsorsimulation.Theobjectofthisworkistoaddresstheneedforsuchmodelswhichtakeintoaccountcommonspatialandseparationrequirementsintheschedulingcranes.ThisworkaugmentsPeterkofskyandDaganzostudy.

2ProblemDescription

Duringthetimeshipsareberthed,variouscargo-handlingequipmentisusedtounloadcargo,mostlyintheformofcontainers.Differenttypesofcargorequiredifferenthandlingandmanyportshavebulk,container,dryandliquid-bulkterminals.Cargothatiscontainerizedcanbeloadedandunloadedinafewernumberofmovesbycranesoperatingdirectlyovershipholdsorbycranearmsmovingoverholdsordeckareas.

Cargostackedinyardsismovedbycranesontomoversandtransportedforloadingontoships.”Cargo”herecomprisescontainersofdifferentcapacities,which,whetherinshipsorinyards,areparcelledintofixedareasforaccesstocranes.Forexample,cargoplacedinspecificholdsordecksectionsonships,orinsectionswithinyards.

Containersareunloadedfromshipsbyquaycranesontomoversortrailerswhichcarrythemtoassignedyardlocationswheretheyareloadedontostacksbyyardcranes.Containersdestinedforimportaresetaside,andrestacking,ifrequired,iscarriedout.Inthemovementofcontainers,sequencingiscrucialbecausecontainersarestoredinstacksintheshipandontheyardandlanesmaybedesignatedtospecifictrailersatcertaintimes.Inaddition,themovementofcontainersinvolvesroutingandcraneoperationswheretimingsmaybeuncertain.Infact,craneschedulingisoneactivityamongmanythatdeterminethemovementofcontainers.Othersuchactivitiesincludeberthing,yardstorage,shipstowageandvehicleallocationandrouting,allofwhichcanbeuncertain.Becauseoftheuncertaintypresentoverallactivities,itisalmostimpossibletoimplementaplanoveranylengthoftime.Thisdifficultyispresentinschedulingcranes.Forexample,althoughasetofjobsmaybeassignedtoacertaincrane,itmaynotbepossibleforthecranetocompleteprocessingajobinthissetontomoversonceitwasknownthattheroutethesemoversaretotakewascongested.Asanotherexample,althoughwecanspecifythatjobsboundforthesameyardspacearenotunloadedfromshipssimultaneously,wecannotexpectsuchcontainerstobeunloadedatatimeotherthantheallottedtimeinterval,sincearequiredresourcetocompletethejobmaybecomeunavailableafterthistime,asforexample,iftheyardcranebecomesunavailable.Inviewofthedynamicallychangingenvironment,acentralcontroldevisesandmaintainsajobassignmentplanthatisperiodicallyupdatedinordertocoordinateoperations,includingcranescheduling.Thesystemwillallocatealljobsandresourcesperiodically.

Intheportwestudied,ajobparcelcanincludeanumberofshipsandanumberofcranestogetherwithjobs.Typically,therecanbeuptofiveshipswithfourtosevencranespershipandanumberofjobsdependingonthesizeandconfigurationofships.Jobshaveaprofitvalueassignedtothemandresources,e.g.,cranes,movers,lanesetc.,areassignedtoeachofthejobsdependingontheirvaluetotheoveralloperationsplanwhichaimstooptimizetotalthroughput.Whenanassignmentplanisupdated,thecentralsystemreassessesthecurrentstateofoperationstoregroupandreassignjobparcels.Becauseofthis,timeisaccommodatedbyconstantadjustmentsofjobparcelsandassignmentsbasedonthecurrentstateofalloperations.Hence,oncejobsandresourcesareassignedforthetimeperiodnoupdateisnecessary.

Jobscomeindifferentsizes,andcraneshavedifferenthandlingcapacities.Sincewemaketheassumptionthatanycraneassignedtoajobcompletesit,thethroughputorprofit,foragivencrane-to-jobassignment,isafixedvalueindependentofothercrane-to-jobassignments.

Theproblemisnaturallyrepresentedbyabipartitegraphmatchingproblemwhenwetakecranesandjobstobetheverticesanddefinetheweightsofconnectingedgestobecrane-to-jobthroughput.ThisrepresentationisshowninFigure1.

Figure1

Thismatchingproblemisinterestingbecause,inpractice,anumberofspatialconstraintsariseforcranesandjobs.Wefirstintroducequalitativenotionsofthreeparticularlycommonconstraintswhichwecall“spatial”constraintssincetheyarerelatedtotherelativepositionsofcranesandjobs.Ourobjectiveistofindacrane-to-jobassignmentschemewhich

maximizesthroughputundertheseconstraints.Forreasonsgivenabove,weassumethatcrane-to-jobassignmentsareperformedinagiventimeinterval,i.e.,thereisnotemporalcomponentintheproblem.Detaileddefinitionswillbegivenintherelevantsectionsofthispaper.

1.Non-crossingconstraint:

Cranescannotcrossovereachother.Thisisastructuralconstraintoncranesandcranetracks.

2.Neighborhoodconstraint:

Thereisaminimumdistancebetweencranes.Thisarises,forexample,sincecranesrequireflexibilityinspacetoperformjobsand/orforsafetyreasons.Theeffectofthisconstraintisthatneighboringjobsmaybeaffectedandmaynotbeassignabletoothercranes.

3.Job-separationconstraint:

Certainjobscannotbedonesimultaneously.Forexample,jobsboundforthesameyardmayrequireseparationintimetoavoidtrailercongestioninlanes.

Inthefollowingsections,wefirstconsidertheseconstraintsseparatelyandthensimultaneously.Insection3,anO（mn）dynamicprogramming（DP）algorithmisgiventosolvetheproblemwithonlytheNon-crossingconstraintwheremisthenumberofcranesandnisthenumberofjobs.Insection4,weuseanO（m2n）dynamicprogrammingalgorithmtoachieveanoptimalsolutionfortheproblemwithboththeNon-crossingandNeighborhoodconstraints.Insection5,assumingallthreespatialconstraints,weshowtheproblemtobeNP-completeandgivetwoheuristicapproachestosolvetheproblem—aprobabilistictabusearchandasqueakywheeloptimizationwithlocalsearchmethod.Insection6,weprovideexperimentalresultsandcomparethedifferentapproaches.

3SchedulingwiththeNon-CrossingConstraint

3.1TheProblem

Throughoutthiswork,C={c1,c2,...,cm}isasetofcranesandJ={j1,j2,...,jn}asetofjobs.Theorderofsubscriptsassignedtothecranesandjobsrepresentstheirspatial（assumedlinear）distribution,i.e.,theneighborofj1isj2,theneighborsofj2arej1andj3,...,andtheneighborofj