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外文原文（出自JOURNALOFCONSTRUCTIONENGINEEINGANDMANAGEMENTMARCH/APRIL/115--121）LOCATIONOPTIMIZATIONFORAGROUPOFTOWERCRANESABSTRACT:Acomputerizedmodeltooptimizelocationofagroupoftowercranesispresented.Locationcriteriaarebalancedworkload,minimumlikelihoodofconflictswitheachother,andhighefficiencyofoperations.Threesubmodelsarealsopresented.First,theinitiallocationmodelclassifiestasksintogroupsandidentifiesfeasiblelocationforeachcraneaccordingtogeometric‘‘closeness.’’Second,theformertaskgroupsareadjustedtoyieldsmoothworkloadsandminimalconflicts.Finally,asingle-tower-craneoptimizationmodelisappliedcranebycranetosearchforoptimallocationintermsofminimalhooktransportationtime.Experimentalresultsandthestepsnecessaryforimplementationofthemodelarediscussed.INTRODUCTIONOnlargeconstructionprojectsseveralcranesgenerallyundertaketransportationtasks,particularlywhenasinglecranecannotprovideoverallcoverageofalldemandandsupplypoints,and/orwhenitscapacityisexceededbytheneedsofatightconstructionschedule.Manyfactorsinfluencetowercranelocation.Intheinterestsofsafetyandefficientoperation,cranesshouldbelocatedasfarapartaspossibletoavoidinterferenceandcollisions,ontheconditionthatallplannedtaskscanbeperformed.However,thisidealsituationisoftendifficulttoachieveinpractice;constrainedworkspaceandlimitationsofcranecapacitymakeitinevitablethatcraneareasoverlap.Subsequently,interferenceandcollisionscanoccurevenifcranejibsworkatdifferentlevels.Craneposition(s)tendtobedeterminedthroughtrialanderror,basedonsitetopography/shapeandoverallcoverageoftasks.Thealternativesforcranelocationcanbecomplex,somanagersremainconfrontedbymultiplechoicesandlittlequantitativereference.Cranelocationmodelshaveevolvedoverthepast20years.Warszawski(1973)establishedatime-distanceformulabywhichquantitativeevaluationoflocationwaspossible.FurusakaandGray(1984)presentedadynamicprogrammingmodelwiththeobjectivefunctionbeinghirecost,butwithoutconsiderationoflocation.GrayandLittle(1985)optimizedcranelocationinirregular-shapedbuildingswhileWijesunderaandHarris(1986)designedasimulationmodeltoreconstructoperationtimesandequipmentcycleswhenhandlingconcrete.FarrellandHover(1989)developedadatabasewithagraphicalinterfacetoassistincraneselectionandlocation.ChoiandHarris(1991)introducedanothermodeltooptimizesingletowercranelocationbycalculatingtotaltransportationtimesincurred.Emsley(1992)proposedseveralimprovementstotheChoiandHarrismodel.Apartfromthesealgorithmicapproaches,rule-basedsystemshavealsoevolvedtoassistdecisionsoncranenumbersandtypesaswellastheirsitelayout。AssumptionsSitemanagerswereinterviewedtoidentifytheirconcernsandobservecurrentapproachestothetaskathand.Further,operationswereobservedon14siteswherecraneswereintensivelyused(fourinChina,sixinEngland,andfourinScotland).Timestudieswerecarriedoutonfoursitesforsixweeks,twositesfortwoweekseach,andtwoforoneweekeach.Findingssuggestedinteraliathatfullcoverageofworkingarea,balancedworkloadwithnointerference,andgroundconditionsaremajorconsiderationsindetermininggrouplocation.Therefore,effortswereconcentratedonthesefactors(exceptgroundconditionsbecausesitemanagerscanspecifyfeasiblelocationareas).Thefollowingfourassumptionswereappliedtomodeldevelopment(detailedlater):1.Geometriclayoutofallsupply(S)anddemand(D)points,togetherwiththetypeandnumberofcranes,arepredetermined.2.ForeachS-Dpair,demandlevelsfortransportationareknown,e.g.,totalnumberoflifts,numberofliftsforeachbatch,maximumload,unloadingdelays,andsoon.3.Thedurationofconstructionisbroadlysimilarovertheworkingareas.4.ThematerialtransportedbetweenanS-Dpairishandledbyonecraneonly.MODELDESCRIPTIONThreestepsareinvolvedindeterminingoptimalpositionsforacranegroup.First,alocationgenerationmodelproducesanapproximatetaskgroupforeachcrane.Thisisthenadjustedbyataskassignmentmodel.Finally,anoptimizationmodelisappliedtoeachtowerinturntofindanexactcranelocationforeachtaskgroup.InitialLocationGenerationModelLiftCapacityand‘‘Feasible’’AreaCraneliftcapacityisdeterminedfromaradius-loadcurvewherethegreatertheload,thesmallerthecrane’soperatingradius.Assumingaloadatsupplypoint(S)withtheweightw,itscorrespondingcraneradiusisr.Acraneisthereforeunabletoliftaloadunlessitislocatedwithinacirclewithradiusr[Fig.1(a)].Todeliveraloadfrom(S)todemandpoint(D),thecranehastobepositionedwithinanellipticalarea(a)FIG.1.FeasibleAreaofCraneLocationforTaskFIG.2.Task“Closenness”enclosedbytwocircles,showninFig.1(b).Thisiscalledthefeasibletaskarea.ThesizeoftheareaisrelatedtothedistancebetweenSandD,theweightoftheload,andcranecapacity.Thelargerthefeasiblearea,themoreeasilythetaskcanbehandled.Measurementof‘‘Closeness’’ofTasksThreegeometricrelationshipsexistforanytwofeasibletaskareas,asillustratedinFig.2;namely,(a)onefullyenclosedbyanother(tasks1and2);(b)twoareaspartlyintersected(tasks1and3);and(c)twoareasseparated(tasks2and3).Asindicatedincases(a)and(b),bybeinglocatedinareaA,acranecanhandlebothtasks1and2,andsimilarly,withinB,tasks1and3.However,case(c)showsthattasks2and3aresofarfromeachotherthatasingletowercraneisunabletohandlebothwi