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115995118 综述123.docx
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115995118综述123
EuropeanJournalofOperationalResearch202(2010)615–627
ContentslistsavailableatScienceDirect
EuropeanJournalofOperationalResearch
journalhomepage:
www.else
InvitedReview
Asurveyofberthallocationandquaycraneschedulingproblemsincontainerterminals
ChristianBierwirth*,FrankMeisel
SchoolofEconomicsandBusiness,Martin-Luther-UniversityHalle-Wittenberg,Germany
articleinfo
Articlehistory:
Received17December2008
Accepted15May2009
Availableonline28May2009
Keywords:
Containerterminaloperations
Berthallocation
QuaycraneassignmentQuaycraneschedulingProblemclassification
Integratedplanning
abstract
Duetothevarietyoftechnicalequipmentsandterminallayouts,researchhasproducedamultitudeofoptimizationmodelsforseasideoperationsplanningincontainerterminals.Toprovideasupportinmod-elingproblemcharacteristicsandinsuggestingapplicablealgorithmsthispaperreviewstherelevantlit-erature.Forthispurposenewclassificationschemesforberthallocationproblemsandquaycraneschedulingproblemsaredeveloped.Particularfocusisputonintegratedsolutionapproacheswhichreceiveincreasingimportancefortheterminalmanagement.
2009ElsevierB.V.Allrightsreserved.
1.Introduction
Inrecentyears,ORmethodshavereceivedconsiderableimpor-tancefortheoperationsmanagementincontainerterminals(CTs).Comprehensiveoverviewsonapplicationsandoptimizationmod-elsinthisfieldaregivenbyMeersmansandDekker(2001),VisanddeKoster(2003),Steenkenetal.(2004),Vaccaetal.(2007),andStahlbockandVoß(2008).AsignificantamountofpapersdealingwiththeapplicationofORmethodsaddressestheplanningoftheseasidetransshipmentoperations.Fig.1showsimportantrelationsofthestrategicplanningandtheoperationsplanningattheseasidearea,theyard,andthelandsidearea.
Oneissueofseasideoperationsplanningistheassignmentofquayspaceandservicetimetovesselsthathavetobeunloadedandloadedataterminal.Thisproblemiscommonlyreferredtoastheberthallocationproblem(BAP).Thetransshipmentofcon-tainersbetweenavesselandthequayisgenerallyperformedbyspecializedcranes,whicharemountedonrailtracksalongsidethequay.Theassignmentofthesequaycranes(QCs)tovesselsandthedeterminationofworkplansforthecranesaddressestwofurtherproblems,namelythequaycraneassignmentproblem(QCAP)andthequaycraneschedulingproblem(QCSP).Solutionstotheseproblemsmustrespecttheberthlayoutandtheusedequipment,whereastheyimpacttheyardoperationsandtheworkforceplanning,seeFig.1.
*Correspondingauthor.Tel.:
+493455523425;fax:
+493455527198.
E-mailaddresses:
christian.bierwirth@wiwi.uni-halle.de(C.Bierwirth),frank.meisel@wiwi.uni-halle.de(F.Meisel).
Duetothevarietyoftechnicalequipmentsandterminallay-outs,researchhasproducedamultitudeofoptimizationmodelsfortheBAP,theQCAP,andtheQCSP.Moreover,atrendtowardsanintegratedsolutionoftheseproblemsisobservedintherecentliterature.Thelargenumberofavailablemodelsandproposedsolutionmethodspreventsaneasychoiceofasuitableapproachinaspecificsituation.ToprovideasupportinmodelingproblemcharacteristicsandinsuggestingapplicablealgorithmsthispaperdevelopsclassificationschemesforBAPs,QCSPs,andintegratedapproaches.
Thepaperisorganizedasfollows.InSection2thefocusedoper-ationalplanningproblemsaredescribedindetailagainsttheback-groundofdifferentterminalpropertiesandobjectives.AliteraturesurveyofBAPandQCAPformulationsispresentedinSection3whichisderivedfromanewclassificationschemefortheseprob-lems.Accordingly,aclassificationschemeandaliteraturesurveyarepresentedforQCSPformulationsinSection4.Sincefutureadvancesinthefieldareexpectedfromintegratedsolutionap-proaches,Section5providesaliteraturereviewofthestate-of-the-artintegrationconcepts.ThepaperissummarizedinSection6.
2.Planningofseasideoperations
2.1.Berthallocationproblem
IntheBAPwearegiventheberthlayoutofaCTtogetherwithasetofvesselsthathavetobeservedwithintheplanninghorizon.Foreachvesseladditionaldatalikethevessel’slengthincludingclearance,itsdraft,theexpectedtimeofarrival,andtheprojected
0377-2217/$-seefrontmatter2009ElsevierB.V.Allrightsreserved.doi:
10.1016/j.ejor.2009.05.031
Fig.1.Planningproblemsincontainerterminals.
handlingtimecanbegiven.Allvesselsmustbemooredwithintheboundariesofthequay.Theyarenotallowedtooccupythesamequayspaceatatime.Theproblemistoassignaberthingpositionandaberthingtimetoeachvessel,suchthatagivenobjectivefunctionisoptimized.AnexampleforthegraphicalrepresentationofaberthplanwithfivevesselsisshowninFig.2a.BerthplanninghasbeenshowntobeanNP-hardproblembyrelatingittothesetpartitioningproblem(Lim,1998),thesinglemachineschedulingproblemwithreleasedates(HansenandOguz,2003),andthetwodimensionalcuttingstockproblem(Imaietal.,2005).
Theremaybefurtherconstraintsinvolvedinberthallocation,whichleadstoamultitudeofBAPformulations.Spatialconstraintsrestrictthefeasibleberthingpositionsofvesselsaccordingtoapresetpartitioningofthequayintoberths.AccordingtoImaietal.(2005)thefollowingcasesaredistinguished:
(a)Discretelayout:
Thequayispartitionedintoanumberofsections,calledberths.Onlyonevesselcanbeservedateachsingleberthatatime.Thepartitioningcaneitherfollowtheconstructionofthequay(Fig.3a)orisorgani-zationallyprescribedtoeasetheplanningproblem(Fig.3b).
(b)Continuouslayout:
Thereisnopartitioningofthequay,i.e.vesselscanberthatarbitrarypositionswithinthebound-ariesofthequay(Fig.3c).Foracontinuouslayout,berthplanningismorecomplicatedthanforadiscretelayoutattheadvantageofbetterutilizingquayspace.
(c)Hybridlayout:
Likeinthediscretecase,thequayisparti-tionedintoberths,butlargevesselsmayoccupymorethanoneberth(Fig.3d)whilesmallvesselsmayshareaberth
(Fig.3e).Anindentedberthresultsiftwoopposingberthsexist,whichcanbeusedtoservealargevesselfrombothsides(Fig.3f).
Incaseofdraftrestrictionsfurtherspatialconstraintsmusten-surethatvesselsareberthedatpositionsofsufficientwaterdepth.Toavoidenlargingthehandlingtime,containervesselsusuallystayattheassignedberthingpositionduringtheentireservice.Incontrast,vesselsareallowedtoberepositionedinnavalportsandgeneralcargoterminals,seee.g.Brownetal.(1994,1997)andLeeandChen(2008).
Temporalconstraintscanrestricttheberthingtimesandthedeparturetimesofvessels.AccordingtoImaietal.(2001)thefol-lowingcasesaredistinguished:
(a)Staticarrival:
Therearenoarrivaltimesgivenforthevesselsorarrivaltimesimposemerelyasoftconstraintontheber-thingtimes.Intheformercaseitisassumedthatvesselsalreadywaitattheportandcanberthimmediately.Inthelattercaseitisassumedthatavesselcanbespeededupatacertaincostinordertomeetaberthingtimeearlierthantheexpectedarrivaltime.
(b)Dynamicarrival:
Fixedarrivaltimesaregivenforthevessels,hence,vesselscannotberthbeforetheexpectedarrivaltime.
Inordertokeeplinerschedules,latestdeparturetimesofthevesselscanbeprescribedadditionally.Insomepapersduedatesareexpressedbyamaximumwaitingplushandlingtimeforaves-sel.Inthedynamiccase,theentireserviceofavesselmustbeexe-cutedwithintheresultingtimewindow.
Fig.2.Space-timerepresentationofaberthplan(a),assignmentofcranestovessels(b).
(a)(b)(c)
(d)(e)(f)
Fig.3.Berthandquayrelationship.
VesselhandlingtimesareassumeddeterministicinthevastmajorityofpublishedBAPmodels.Still,literaturedealswithvesselhandlingtimesindifferentways:
(a)Theyareknowninadvanceandconsideredunchangeable,i.e.theyarefixed.
(b)Theydependonthevessels’berthingpositions.
(c)Theydependonthenumberofcranesservingthevessels.(d)Theydependontheworkschedulesoftheassignedcranes.(e)Theyobeytocombinationsof(b),(c),and(d).
Thegeneralgoalofberthplanningistoprovidefastandreliableservicesofvessels.Thisisreflectedintheliteraturebyvariousobjectivefunctions.Modelstominimizethesumofthewaitingandhandlingtimesofvessels(i.e.theportstaytimes)clearlypre-vail.Furtherobjectivesare,forexample,theminimizationoftheworkloadofterminalresourcesandtheminimizationofthenum-berofvesselsrejectedtobeservedataterminal.Theperformanceofaberthplanisoftenmeasuredintermsofcostswhichallowstocombinedifferentgoalsinanoverallcostfunction.
2.2.Quaycraneassignmentproblem
IntheQCAPwearegivenafeasibleberthplanandasetofidenti-calQCs,whichareavailableforservice.Foreachvesselincludedintheberthplan,thevolumeofcontainerstobeloadedandunloadedisknownaswellasthemaximumnumberofcranesallowedtoserveitsimultaneously.Thecranesaresupposedtobelinedupalongsidethequay.Theycanbemovedtoeveryvesselbuttheyarenotabletopasseachother.Theproblemistoassigncra
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