船舶专业外文文献.docx

船舶专业外文文献.docx

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船舶专业外文文献

Spatialschedulingforlargeassemblyblocksinshipbuilding

令狐采学

Abstract:

Thispaperaddressesthespatialschedulingproblem（SPP）forlargeassemblyblocks,whicharisesinashipyardassemblyshop.Thespatialschedulingproblemistoscheduleasetofjobs,ofwhicheachrequiresitsphysicalspaceinarestrictedspace.Thisproblemiscomplicatedbecauseboththeschedulingofassemblieswithdifferentduedatesandearlieststartingtimesandthespatialallocationofblockswithdifferentsizesandloadsmustbeconsideredsimultaneously.Thisproblemunderconsiderationaimstotheminimizationofboththemakespanandtheloadbalanceandincludesvariousreal-worldconstraints,whichincludesthepossibledirectionalrotationofblocks,theexistenceofsymmetricblocks,andtheassignmentofsomeblockstodesignatedworkplacesorworkteams.Theproblemisformulatedasamixedintegerprogramming（MIP）modelandsolvedbyacommerciallyavailablesolver.Atwo-stageheuristicalgorithmhasbeendevelopedtousedispatchingpriorityrulesandadiagonalfillspaceallocationmethod,whichisamodificationofbottom-left-fillspaceallocationmethod.ThecomparisonandcomputationalresultsshowstheproposedMIPmodelaccommodatesvariousconstraintsandtheproposedheuristicalgorithmsolvesthespatialschedulingproblemseffectivelyandefficiently.

Keywords:

Largeassemblyblock;Spatialscheduling;Loadbalancing;Makespan;Shipbuilding

1.Introduction

Shipbuildingisacomplexproductionprocesscharacterizedbyheavyandlargeparts,variousequipment,skilledprofessionals,prolongedleadtime,andheterogeneousresourcerequirements.Theshipbuildingprocessisdividedintosubprocessesintheshipyard,includingshipdesign,cuttingandbendingoperations,blockassembly,outfitting,painting,pre-erectionanderection.Theassemblyblocksarecalledtheminorassemblyblock,thesubassemblyblock,andthelargeassemblyblockaccordingtotheirsizeandprogressesinthecourseofassemblyprocesses.Thispaperfocusesonthespatialschedulingproblemoflargeassemblyblocksinassemblyshops.Fig.1showsasnapshotoflargeassemblyblocksinashipyardassemblyshop.

Recently,theresearchersandpractitionersatacademiaandshipbuildingindustriesrecentlygottogetherat“SmartProductionTechnologyForuminShipbuildingandOceanPlantIndustries”torecognizethattherearevariousspatialschedulingproblemsineveryaspectofshipbuildingduetothelimitedspace,facilities,equipment,laborandtime.TheSPPsoccurinvariousworkingareassuchascuttingandblastshops,assemblyshops,outfittingshops,pre-erectionyard,anddrydocks.TheSPPatdifferentareashasdifferentrequirementsandconstraintstocharacterizetheuniqueSPPs.Inaddition,thedepletionofenergyresourcesonlandputmoreemphasisontheoceandevelopment.Theshipbuildingindustriesfacethetransitionoffocusfromthetraditionalshipbuildingtooceanplantmanufacturing.Therefore,thediversityofassemblyblocks,materials,facilitiesandoperationsinshipyardsincreasesrapidly.

TherearesomesolutionproviderssuchasSiemens™andDassultSystems™toprovideintegratedsoftwareincludingproductlifemanagement,enterpriseresourceplanningsystem,simulationandetc.Theyindicatedtheneedsofefficientalgorithmstosolvemedium-tolarge-sizedSPPproblemsin20 min,sothattheshopcanquicklyre-optimizetheproductionplanuponthefrequentandunexpectedchangesinshopfloorswiththeongoingoperationsonexitingblocksintact.

Therearemanydifferentapplicationswhichrequireefficientschedulingalgorithmswithvariousconstraintsandcharacteristics（KimandMoon,2003,Kimetal.,2013,NguyenandYun,2014 and Yanetal.,2014）.However,thespatialschedulingproblemwhichconsidersspatiallayoutanddynamicjobschedulinghasnotbeenstudiedextensively.Untilnow,spatialschedulinghastobecarriedoutbyhumanschedulersonlywiththeirexperiencesandhistoricaldata.Evenwhenhumanexpertshavemuchexperienceinspatialscheduling,ittakesalongtimeandintensiveefforttoproduceasatisfactoryschedule,duetothecomplexityofconsideringblocks’geometricshapes,loads,requiredfacilities,etc.Inpractice,spatialschedulingformorethanasix-monthperiodisbeyondthehumanschedulers’capacity.Moreover,thespaceintheworkingareastendstobethemostcriticalresourceinshipbuilding.Therefore,theeffectivemanagementofspatialresourcesthroughautomationofthespatialschedulingprocessisacriticalissueintheimprovementofproductivityinshipbuildingplants.

Ashipyardassemblyshopisconsistedofpinnedworkplaces,equipment,andoverhangcranes.Duetotheheavyweightoflargeassemblyblock,overhangcranesareusedtoaccessanyareasoverotherobjectswithoutanyhindranceintheassemblyshop.Theheightofcranescanlimittheheightofblocksthatcanbeassembledintheshop.Theshopcanbeconsideredasatwo-dimensionalspace.Theblocksareplacedonpreciselypinnedworkplaces.

Oncetheblockisallocatedtoacertainareainaworkplace,itisdesirablenottomovetheblockagaintodifferentlocationsduetothesizeandweightofthelargeassemblyblocks.Therefore,itisimportanttoallocatetheworkspacetoeachblockcarefully,sothattheworkspaceinanassemblyshopcanbeutilizedinamostefficientway.Inaddition,sinceeachblockhasitsduedatewhichispre-determinedatthestageofshipdesign,thetardinessofablockassemblycanleadtoseveredelayinthefollowingoperations.Therefore,inthespatialschedulingproblemforlargeassemblyblocks,theschedulingofassemblyprocessesforblocksandtheallocationofblockstospecificlocationsinworkplacesmustbeconsideredatthesametime.Astheterminologysuggests,spatialschedulingpursuestheoptimalspatiallayoutandthedynamicschedulewhichcanalsosatisfytraditionalschedulingconstraintssimultaneously.Inaddition,therearemanyconstraintsorrequirementswhichareseriousconcernsonshopfloorsandthesecomplicatetheSPP.Theconstraintsorrequirementsthisstudyconsideredareexplainedhere:

（1）Blockscanbeputineitherdirections,horizontalorvertical.

（2）Sincetheshipissymmetricaroundthecenterline,thereexistsymmetricblocks.Thesesymmetricblocksarerequiredtobeputnexttoeachotheronthesameworkplace.（3）Someblocksarerequiredtobeputonacertainspecialareaoftheworkplace,becausetheworkteamsonthatareahasspecialequipmentorskillstoachieveacertainlevelofqualityorcompletethenecessarytasks.（4）Frequently,theproductionplanmaynotbeimplementedasplanned,sothatfrequentmodificationsinproductionplansarerequiredtocopewiththechangesintheshop.Atthesemodifications,itisrequiredtoproduceanewmodifiedproductionplanwhichdoesnotremoveormovethepre-existingblocksintheworkplacetocompletetheongoingoperations.（5）Ifpossibleatanytime,theloadbalancingovertheworkteams,i.e.,workplacesaredesirableinordertokeepalltaskassignmentstoworkteamsfairanduniform.

Lee,Lee,andChoi（1996）studiedaspatialschedulingthatconsidersnotonlytraditionalschedulingconstraintslikeresourcecapacityandduedates,butalsodynamicspatiallayoutoftheobjects.Theyusedtwo-dimensionalarrangementalgorithmdevelopedbyLozano-Perez（1983）todeterminethespatiallayoutofblocksinshipbuilding.Koh,Park,Choi,andJoo（1999）developedablockassemblyschedulingsystemforashipbuildingcompany.Theyproposedatwo-phaseapproachthatincludesaschedulingphaseandaspatiallayoutphase.Koh,Eom,andJang（2008）extendedtheirpreciousworks（Kohetal.,1999）byproposingthelargestcontactareapolicytoselectabetterallocationofblocks.Cho,Chung,Park,Park,andKim（2001）proposedaspatialschedulingsystemforblockpaintingprocessinshipbuilding,includingblockscheduling,fourarrangementalgorithmsandblockassignmentalgorithm.Parketal.（2002）extendedChoetal.（2001）utilizingstrategysimulationintwoconsecutiveoperationsofblastingandpainting.Shin,Kwon,andRyu（2008）proposedabottom-left-fillheuristicmethodforspatialplanningofblockassembliesandsuggestedaplacementalgorithmforblocksbydifferentialevolutionarrangementalgorithm.Liu,Chua,andWee（2011）proposedasimulationmodelwhichenabledmultiplepriorityrulestobecompared.Zheng,Jiang,andChen（2012）proposedamathematicalprogrammingmodelforspatialschedulingandusedseveralheuristicspatialschedulingstrategies（gridsearchingandgeneticalgorithm）.ZhangandChen（2012）proposedanothermathematicalprogrammingmodelandproposedtheagglomerationalgorithm.

Thisstudypresentsanovelmixedintegerprogramming（MIP）formulationtoconsiderblockrotations,symmetricalblocks,pre-existingblocks,loadbalancingandallocationofcertainblockstopre-determinedworkspace.TheproposedMIPmodelswereimplementedbycommerciallyavailablesoftware,LINGO®andproblemsofvarioussizesaretested.ThecomputationalresultsshowthattheMIPmodelisextremelydifficulttosolveasthesizeofproblemsgrows.Toefficientlysolvetheproblem,atwo-stageheuristicalgorithmhasbeenproposed.

Section2describesspatialschedulingproblemsandassumptionswhichareusedinthisstudy.Section3presentsamixedintegerprogrammingformulation.InSection4,atwo-stageheuristicalgorithmhasbeenproposed,includingblockdispatchingpriorityrulesandadiagonalfillspaceallocationheuristicmethod,whichismodifiedfromthebottom-left-fillspaceallocationmethod.ComputationalresultsareprovidedinSection5.Theconclusionsa