Simulation of a Container Terminal Through a Discrete Event Approach Literatur

Association for European Transport and contributors 20091 SIMULATION OF A CONTAINER TERMINALTHROUGH A DISCRETE EVENT APPROACH: LITERATURE REVIEW AND GUIDELINES FOR APPLICATION Armando Carten, Stefano de Luca Department of Civil Engineering University of Salerno 1INTRODUCTION Designandprojectappraisalofcontainerterminalsmaybecarriedout throughtwomainapproaches:optimizationorsimulation.Althoughthe approaches based on optimization models allow a more elegant and compact formulationoftheproblem,simulationmodelsaremainlybasedondiscrete eventsimulation(DES)modelsandhelptoachieveseveralaims:overcome mathematicallimitationsofoptimizationapproaches,supportandmake computer-generatedstrategies/policiesmoreunderstandable,andsupport decision makers in daily decision processes through a what if approach. SeveralapplicationsofDESmodelshavebeenproposedandsimulation results confirm that such an approach is quite effective at simulating container terminal operations. Most of the contributions in the literature develop object-orientedsimulationmodelsandpursueamacroscopicapproachwhich gatherselementaryhandlingactivities(e.g.usingcranes,reachstackers, shuttles) into a few macro-activities (e.g. unloading vessels: crane-dock-reach stacker-shuttle-yard),simulatethemovementofanaggregationof containersandthereforedonottakeintoaccounttheeffectsofcontainer types(e.g.20vs40,fullvsempty),theincidenceofdifferenthandling activitiesthatmayseemsimilarbutshowdifferenttimedurationand variability/dispersion (e.g. crane unloading a container to dock or to a shuttle) andthedifferenceswithinthesamehandlingactivity(e.g. stacking/loading/unloadingtimewithrespecttothetiernumber).Such contributionsprimarilyfocusonmodellingarchitecture,onsoftware implementationissuesandonsimulatingdesign/realscenarios.Activity durationisoftenassumedtobedeterministic,andthosefewauthorsthat estimatespecificstochastichandlingequipmentmodelsdonotclearlystate howtheywerecalibrated,whatdatawereusedandwhattheparameter valuesare.Finally,nooneinvestigatestheeffectsofdifferentmodelling hypotheses on the simulation of container terminal performances. The focus of this paper is on the effects that different hypotheses on handling equipment modelscalibration mayhaveonthesimulation(discreteevent)of containerterminalperformances.Sucheffectscouldnotbenegligibleand shouldbeinvestigatedwithrespecttodifferentplanninghorizons,suchas strategicortactical.Theaimistoproposetoanalysts,modellersand practitionersasortofaguidelineusefultopointoutthestrengthsor weaknesses of different approaches. Drawing on the model architecture proposed in a previous contribution by the sameauthors(Carten,CantarellaanddeLuca,2005),adiscreteevent simulation model is developed and applied to the Salerno Container Terminal in order to deal with the following issues: Association for European Transport and contributors 20092 analysis of the effects of different estimation approaches (sample mean andrandomvariableestimations)onestimatingwholeterminal performance,henceoncontainerterminalplanningstrategies.In particular,analysesweremadefordifferenttimehorizons:long-term planning interventions/investments, medium/short period, short-term or real-time applications. Analysis of the effects of different hypotheses on the level of aggregation of elementary activities (undifferentiated vs. container type model). Thepaperisdividedintofoursections.Inthefirstsection(section2)anin depthliteraturesurveyisproposed.Theaimistogobackoveraboutthirty yearofcontainerterminalsimulationmodels,tohighlightweaknessespoints of the existing approaches to handling equipment activities simulation, and to propose a synthetic but complete outline of the models calibrated and of their parameters.Insection3abriefdescriptionofthediscreteeventsimulation modelisreported.Insection4resultsfrommodelapplicationareproposed while the main conclusions are drawn in section 5. 2Literature review Theexistingliteraturereportsapproachestoeithermanagingacontainer terminalasasystem and tryingtosimulate allelements ormanagingasub-setofactivities(simultaneouslyorsequentiallyfollowingapredefined hierarchy). The main contributions seek to maximize overall terminal efficiency ortheefficiencyofaspecificsub-area(oractivity)insidetheterminal.The mostwidelyfollowedapproachesarebasedondeterministicoptimization methods,althoughrecentlyastochasticoptimizationmodelwasproposed (Murty et al., 2005). Such approaches schematize container terminal activities throughsinglequeuemodelsorthroughanetworkofqueues.Followinga stochastic approach, both modelling solutions may lead to analytical problems and/or unsatisfactory results if the probability distribution of activities involved does not belong to the Erlang family (Nilse and Abdus-Samad, 1977; Ramani, 1996).Moreover,theresultingnetworkcouldbeverycomplicatedand theoretical solution might not be easy to obtain. Insuchacontext,aneffectiveandchallengingalternativeapproachfor container terminal system analysis may be represented by discrete simulation. Simulationcanhelptoachievevariousaims:overcomemathematical limitationsofoptimizationapproaches,allowamoredetailedandrealistic representationofterminalcharacteristics,supportdecisionmakersindaily decisionprocessesthroughassessmentofwhatifscenariosandmake computer-generated strategies/policies more understandable. Simulationisnotanewmethodologyinportoperations.Severalworkshave beenpresentedsincethe1980s,mostofthemconcerningportoperations management.Manyoftheproposedmodelsdonotfocusonthedetails regardingthemodelset-up,itscalibrationanditsvalidation;butonthe application and/or the simulation of design scenarios. Moreover, although the estimation of handling activity models should be one of the main issues of all containerterminalapplications,thisproblemdoesnotseemtobetreatedin depthinmostapplications.Whilemanycontributionsdonotpresentany informationonhandlingactivitymodelsused,theremainingcontributions Association for European Transport and contributors 20093 carry out very simple approaches (deterministic) and/or give scant information ontheestimationapproachadopted,theexperimentaldataused,the parameters estimated and on parameter values. Theaimofouranalysisistwofold:(i)toproposeanextensivereviewofthe maincontributionsintheliterature,(ii)tofocusontheapproaches,models and parameters used to model handling activities. StartingfromthepioneeringworkofCollier(1980)investigatingtheroleof simulation as an aid to the study of a port as a system, the 1980s saw several worksimplementingthefirstsimulation-basedmodels.InAgerschouetal. (1983),Tugcu(1983)proposedasimulationmodelfortheportofIstanbul, dealingwithberthassignmentandunloadingoperations.Vesselarrivalis simulatedthroughPoissondistribution,whereasempiricaldistributionsare usedfortheremainingactivities.ElSheikhetal.(1987)developeda simulation model for the ship-to-berth allocation problem; the phenomenon is modelledasasequenceofqueues,andvesselinterarrivalandservicetime aremodelledthroughexponentialdistributionfunctions.Inthesameyear, ParkandNoh(1987)usedaMonteCarlotypesimulationapproachtoplan portcapacity,ComerandTaborga(1987)developedoneofthefirstport simulationsoftwares(PORTSIM),andChungetal.(1988)proposeda methodologybasedonagraphicsimulationsystemtosimulatetheuseof bufferspacetoincreasetheuseofhandlingequipmentandreducetotal container loading time. Inthe1990smucheffortwasspentonsimulatingterminalcontainers:the numberofapplicationsbasedonsimulationincreased,terminalswere modelledmorerealisticallythroughdisaggregationofthemainoperationsin several elementary activities, and much more attention was laid on real case studies. The focus of most contributions was on developing practical tools to simulateterminaloperations,onsoftwareissuesand/oronmodelvalidation. Lessattentionwasfocusedonmodellinghandlingactivitiesand/ormodel details. Kondratowicz(1990),withinageneralmethodformodelling seaportand inlandterminalsinintermodal freighttransportationsystems,proposedan object-orientedmodel,TRANSNODE, tosimulatedifferentapplication scenarios. Silberholz et al. (1991) described a simulation program that models thetransferofcontainerizedcargotoandfromships,Moscaetal.(1992) usedsimulationtoascertaintheefficiencyofanautomaticflatarsystem servicingarail-mountedcrane,andHassan(1993)gaveanoverviewofa computer simulation program used as a decision support tool to evaluate and improve port activities. Lai and Lam (1994) examined strategies for allocation of yard equipment for a large container yard in Hong-Kong. In the same year, Hayuth et al. (1994) used a discrete event simulation to build a port simulator, butthemainemphasiswasonsoftwareandonhardwareproblems.Key issuesoftheapplicationofmodelling andsimulationwerediscussedin Tolujev et al. (1996) and Merkutyev et al. (1998), both contributions proposing anapplicationtotheRigaHarbourContainer Terminal.Gambardellaetal. (1998)proposedadiscreteeventsimulationmodel(basedonprocess-orientedparadigm)tosimulatevesselloading/unloading.Themodelwas appliedtotheItaliancontainerterminalofLaSpezia(Italy),withscant information on the data used and on the characteristics of the equipment used intheapplication.ThesamecasestudywasanalyzedbyMastrolillietal. Association for European Transport and contributors 20094 (1998),usingamodelsimilartothatproposedinGambardellaetal.(1998) andproposingacalibrationandavalidationprocedureofsimulator parameters.Meansandstandarddeviationsareestimatedforquaycrane, yardcraneandstraddlecarrierservicetime,whereasspeedofcranesand traveltimeofshuttletrailersareassumeddeterministic,aswellasvessel arrival and truck arrival. Nevins et al. (1998) developed PORTSIM, a seaport simulation model able to animate and visualize seaport processes and in the sameyearBruzzoneandSignorile(1998)developedasoftwaretoolto support terminal operators in making strategic decisions. The main emphasis wasonoptimizingcontainerplacementinaterminal;ageneticalgorithm approachwasadopted,asimple applicationproposed,yetnodetailscanbe found on the performance functions used. The same authors (Bruzzone et al. 1999) investigated the effectiveness and benefits of a simulation approach as a decision support system for complex container terminals. InterestingmodellingdetailswereproposedbyKohetal.(1994),Holgun-Vera and Walton (1996) and Ramani (1996). Koh et al. (1994) developed an object-orientedapproachusingMODSIMsimulationsoftware.Theproposed modelreliesonexperimentaldata,averagevaluesareusedforhandling equipment,whereasWeibulldistributionseemsto fitcranecycletimebetter. Holgun-VeraandWaltonproposedasimulationmodelbasedonthenext eventapproach.Themodeliscalibratedonexperimentaldataandtwo approachesarecarriedout:adeterministiconebasedonempirical distributionandastochasticone.Gantrycrane,yardcraneandcrane movements are simulated through a random variable made up by systematic andarandomcomponent.Whilethesystematiccomponentsareestimated usingmultipleregression,thecorrespondingrandompartsarenotclearly introduced.Ramani(1996)designedanddevelopedaninteractivecomputer simulation model to support the logistics planning of container operations. The model provides estimates for port performance indicators. Since the end of the 1990s, the most important ports in the world have been modelledthroughdiscreteeventsimulationmodels,andgreaterinterestis showninthecalibrationofhandlingactivitiesmodels.YunandChoi(1999) developanobject-orientedsimulationmodelusingSIMPLE++languageand apply it to analyse the container terminal system used in Pusan. The system is analyzed as a whole (gates, yards and berths), deterministic and stochastic distributionfunctionsareconsidered:deterministicfortrailerspeedandfor interarrivaltimeoftrailersandtractors;uniformforservicetimeat thegates; exponential for interarrival time of trailers, vessels and service time of cranes.ThesamecasestudyproposedbyChoiandYun(2000)followsanobject-orientedapproach,developingamodeltosimulatetwodifferentterminals located in Pusan. The simulation tool is generic and transferable to any other terminal; it is based on Visual C++ and gives accurate results once validated onhistoricaldata.Asregardsequipmentcharacteristics,averagesareused for cranes and trailer speed, whereas distribution functions are used for crane operationtime(Normaldistribution).Itisnotclearwhetherperformance characteristics were estimated. TaharandHussain(2000)dealwithberthoperationandcraneallocation problems. Their discrete event simulation model is based on data collected at theportofKelangandspecificanalysesarecarriedouttoidentifythe distribution functions for inter-arrival time of ships (Weibull distribution) and for Association for European Transport and contributors 20095 service time at berths (distribution not mentioned). The model is implemented in ARENA software and is validated on historical data. LegatoandMazza(2001)examinethevesselarrival-departureprocess, developingaqueuingnetworkmodelthroughanobject-orientedapproach implemented in VISUAL SLAM language. Since no detailed disaggregate data are available, a first order Erlang distribution is applied for those services with thesupposedlargervariance,ahigherorderisadoptedformoreregular servicesand, finally,atriangulardistribution isusedtoassignthe number of containers to cranes. SgouridisandAngelides(2002)developadiscreteeventmodeltosimulate theinboundcontainerhandlingproblem.Themodelisimplementedinan EXTENDsoftwarepackageandappliedtotheportofThessaloniki.Truck inter-arrivaltimesfollowanErlangdistribution,whereasmaximum,minimum ormostprobablevaluesareestimatedforspeedandactivitytimeof equipment involved. Developingamicroscopicsimulationmodel,Chinetal.(2002)evaluatethe effectiveness of automated guidance vehicles. The focus is on the application and no details are given either on the models or data used. ShabayekandYeung(2002)proposeadiscreteeventsimulationmodel employingthe WitnessprogramtoanalysetheperformanceofHongKongs KwaiChungcontainer.Althoughthemodelencompassesalltheoperations thatmayoccurinaterminal,thefocusisonvesselarrivalsandtheir distributionamongtheexistingbuffersandoperators.Whilearrivalsare simulatedthroughadistributionfunction(k-stageErlang),theremaining operationsareanalysedinaveryaggregatewayandaveragevaluesare considered (average handling capacity). Kiaetal.(2002)useaportsimulatordevelopedinTAYLORIIsoftwareto investigatetheeffectivenessoftwodifferentoperationalsystemsappliedto theterminalofMelbourne.Withtheemphasisonterminalcapacity,allthe activitiesthatoccurinsidetheterminalarenotexplicitlysimulatedbut aggregated in one variable represented by the vessels service time. Although no details are reported on the model structure, interesting statistical analyses arepresentedonvesselarrivalpatterns(exponentialdistributionforinter-arrival times) and on vessel service time (k-stage Erlang distribution). Parola and Sciomachen (2005) present a discrete event model to simulate the logistic chain of a system made by two ports, three possible destinations and connectionsbetweenthem(byroadand/orbyrail).Thesimulationis undertaken through WITNESS simulation software and the main emphasis is onvesselberthing,vesselloading/unloadingandgateoperations.Vessel interarrivalisrepresentedbyanexponentialdistributionfunction(estimated), crane working time and truck waiting time by a truncated normal distribution. It isnotclearwhethertheprobabilitydistributionswereestimatedorsimply taken from the literature. Bielli et al. (2006) develop a simulation tool in JAVA programminglanguagetosimulatetheportofCasablanca.Thefocusison thearchitectureandonsoftwareissues;handlingactivitiesarehypothesised as deterministic. BugaricandPetrovic(2007)simulateunloadingservicesofbulkcargo vessels.Theystresstherelevanceof astochasticapproach andschematize thesystemasathree-phasequeuingsystemwithdifferentnumbersof servers in each phase. A simulation tool is created in PASCAL programming Association for European Transport and contributors 20096 language,andallvariablesaregeneratedusingtheMonte-Carlomethod accordingtodistributionfunctionsobtainedfromanexistingriverterminal: normalforanchorageoperationsandforcraneunloadingtimes,exponential for inter-arrival of vessels. Corts et al. (2007) set out to simulate the whole freight transport process in theGuadalquivirriverestuary.Despiteadetaileddescriptionofoperations andthesoftwaremodulesimplemented,littleinformationonequipment characteristics and time duration is reported. Deterministic functions appear to havebeenusedforgantrycranes,exponentialforthetransfertimeindock assignmentwhileforvesselarrivaltimeanempiricaldistributionfunctionis used. LeeandCho(2007)proposeamodeltosimulatetheeffectivenessofa dynamic planning system for yard tractors utilizing real-time location systems technology.AutoMod11.1softwareisusedandstatisticalmodelsare proposed. Of the contributions introduced so far, as already pointed out, only ten papers give information on the handling equipment models used. Half of them adopt a stochasticapproachandshowestimatedparametervalues.Mostofthe contributionsdealwithvesselloading/unloadingoperations.Thereis substantialheterogeneityregardingthelevelofaggregationofactivities involved and how such activities are aggregated in a single macro-activity: El Sheikh (1987), Choi (2000), Kia et al. (2002) and Shabayek and Yeung (2002) analyse the entire time to load (unload) a vessel (vessel cycle time); Koh et al. (1994) and Bugavic and Petrovic (2007) investigate the crane cycle time (time neededto:lockontothecontainer,hoistandtraverse,lowerandlocate, unlock and return); crane loading time to/from a vessel is analysed by Tugcu (1983),Thiers(1998),YunandChoi(1999),Merkuryevaetal.(2000),KMI (2000), Parola and Sciomachen (2005), Bielli et al. (2006), and Lee and Cho (2007). As regards vessel cycle time, a stochastic approach is unanimously proposed. Inparticular,ElSheikh(1987),Kiaetal.(2002)andShabayekandYeung (2002) suggest using Erlang random variables whereas Choi (2000) proposes normalrandomvariablesfortwocranetypes(quay,yard).Asregardscrane cycletime,Kohetal.(1994)advisetheuseofaWeibullrandomvariable; BugavicandPetrovic(2007),forabulkcargoterminal,proposenormal random variables and report the estimated parameters.Withregardtocraneloading/unloadingtime,Tugcu(1983),Thiers(1998), KMI (2000) and Bielli et al. (2006) follow a deterministic approach, contrasting with the stochastic approach adopted by Yun and Choi (1999), Merkuryeva et al. (2000), Lee and Cho (2007), Parola and Sciomachen (2005). Yun and Choi (1999)proposetheexponentialdistributionfunctionbothforquaycraneand yard crane; Merkuryeva et al. (2000) propose the uniform distribution function for quay crane and a triangular distribution function for yard gantry crane; Lee andCho(2007)suggesttheexponentialdistributionfunctionforquaycrane andatriangulardistributionfunctionforyardgantrycraneoperationtime. ParolaandSciomachen(2005)estimatedanormalrandomvariablebutdo not report parameter values. With respect to crane speed, all propose deterministic and aggregate models whileonlyYunandChoi(1999),Choi(2000),KMI(2000)andLegatoetal. (2008) report the estimated mean values. Association for European Transport and contributors 20097 Withrespecttootherhandlingequipment,notmuchcanbefoundinthe literature:SgouridisandAngelides(2002)usedeterministicvaluesfora straddlecarrier,whereasMerkuryevaetal.(2000)proposeatriangular distributionfunctionfortheforklift.Asregardsshuttleperformances(speed, traveltime,waitingtime),thefewmodelsexistingarehardtotransferto different case studies (due to the influence of path length, path winding, traffic vehiclecongestioninsidethe terminalandsoon).Hencetheyareomittedin this survey. A synopsis of the above analysis is presented in tables 1, 2 and 3. Foreachtypeofhandlingequipmentandforeachactivitysimulated, probability distribution and corresponding parameters are reported. Table 1 Survey of handling models: Gantry crane (GC) craneoperationtime Quay GCYun and Choi (1999) exponential mean = 0.50 (min) Lee and Cho (2007)mean = 1.00 (min) Merkuryeva et al. (2000)uniform min.=2.00 (min.) max=4.00 (min.) Bielli et al. (2006)deterministicmean = 1.50 (min) Yard GCYun and Choi (1999)exponentialmean = 1.00 (min) Merkuryeva et al. (2000) triangular 40 loading : mean = 6.00 (min) 40 unloading : mean = 4.00 (min) s.d. = 0.41 (min) Lee and Cho (2007) mean = 1.55 (min) s.d. = 0.08 (min) Bielli et al. (2006)deterministicmean = 1.50 (min) - Parola and Schiomachen (2005) normalnot reported Tugcu (1983)deterministicnot reported Thiers (1998)deterministicnot reported KMI (2000)deterministicnot reported cranecycle time -Koh et al. (1994)weibull bulk cargoBugavic and Petrovic (2007)normal mean = 5.00 (min) s.d. = 0.26 (min) vessel cycletime Quay GCChoi (2000)normal mean = 112.80 (min) s.d. = 5.60 (min) Yard GCChoi (2000)normal mean = 87.00 (min) s.d. = 13.89 (min) Entire loading operationEl Sheikh (1987)Erlang mean = 4.20 (day) K = 4.33 Entire unloading operationEl Sheikh (1987)Erlang mean = 7.57 (day) K = 10.77 -Kia et al. (2002)Erlang mean = 37.85 (hour) K = 4.00 - Shabayekand Yeung (2002) Erlang mean [9.6, 16.3] (hour) K= 117 cranespeed quay gantry craneYun, Choi (1999)deterministic45 (metres/min.) Legato et al. (2008)deterministic45 (metres/min.) KMI (2000)deterministic45 (metres/min.) hoist with full load KMI (2000)deterministic 55 (metres/min.) hoist without load130 (metres/min.) ship trolley 180 (metres/min.) store trolley75 (metres/min. yard gantry craneChoi (2000)deterministic134 (metres/min.) -Tugcu (1983)deterministic -Koh et al. (1994)deterministic -Thiers (1998)deterministic Association for European Transport and contributors 20098 Table 2 Survey of handling models: Straddle carrier (SC) Handling activityModel usedCharacteristic parametersReferences speeddeterministic inside yard: 110(met./min.) outside yard:250 (met./min.) Shouridis andAngelides (2002) shuttle loading/unloading time deterministic 0.60 (min.) spreader movementdeterministic0.30 (min.) turningdeterministic0.02 (min.) container spottingdeterministic1.00 (min.) Table 3 Survey of handling models: Forklift (FL) Handling activityModel usedCharacteristic parametersReferences loading/unloading timetriangular 20 loadingmean = 4.00 (min.) st. dev. = 0.41 (min.) 20 unloadingmean = 3.00 (min.) st. dev. = 0.41 (min.) Merkuryeva et al. (2000) 3MODEL Theproposedapproachschematizesacontainerterminal(CT)asadiscrete event system and models its functioning through a simulator. A discrete event systemcanbedefinedasaninteractingsetofentities/objectsthatevolves through different states as internal or external events happen. Entities/objects may be physical, conceptual (information flows) or mathematical, and can be residentortransient.Residententitiesremainpartofthesystemforlong intervalsoftime;transiententitiesenterintoanddepartfromthesystem several times. Entitiescanbecharacterizedbyparametersand/orvariables.Parameters definestatic(stationary)characteristicsthatneverchange,variablesdefine thestate(dynamiccharacteristics)ofeachentityandmaychangeovertime and can further be classified as deterministic or stochastic.InaCTentitiesrepresentthehandlingequipment,thecontainersandall those physical locations relevant to CT operations (dock, yard, gates, etc..).Handlingequipmentisaresidentandactiveentityandmaybe characterized by parameters, variables and an activity.Containers are transient and passive entities. Physical locations are resident and passive entities. As for containers, they may be characterized by parameters and variables. Apartfromtheabove-describedentitiesotherentitiescanbeconsidered. Such entities do not usually move containers but can control/manage entities thathandlecontainersandcanthuschangetheirattributes.Thechangein such attributes may be driven by simple heuristic rules (e.g. if there are more than four trucks waiting for a reach stacker, use one more reach stacker) or by sub-modelsthatchangeentityattributes,tryingtooptimizeoverallterminal performance in real time. Indiscreteeventmodellingthemodelisdefinedoncethecasestudyis defined and three main tasks should be carried out. [a]Identification of the terminals logical and functional architecture. [b]Demand characterization and estimation. [c]Supply characterization and calibration. Association for European Transport and contributors 20099 Case study In this paper the Salerno Container Terminal (SalCT) is analyzed. SalCT is a majorprivatecontainerterminaloperatorinsouthernItaly,andisbothsmall and very efficient: it handles close to 0.45 MTEUs per year in less than 10ha (100,000m2),whichamountsto45kTEUs/ha.TheSalernoContainer Terminal(SalCT)can bedividedintothreesubsystems: enter/exitportgates (land-side),containeryards,andberths(sea-side).Containerhandling equipment comprises storage cranes, loading/unloading cranes, yard tractors, trailersandreachstackers.Thebasicactivitiesoccursimultaneouslyand interactively, and can be grouped into four main operations: receiving (gate yard), delivery (yard gate), loading(yard berth) and unloading (berth yard). Model architecture Threedifferentmacro-activitiesweretakenintoaccount:import,exportand transhipment. Apart from vessel arrival and berthing (not relevant to our case study)andapartfromtruckarrival,allthetypicalactivitiesofacontainer terminalwereexplicitlysimulated.ThearchitectureisproposedinFigure1, moredetailsmaybefoundin(Cartenetal.,2005;CartenanddeLuca, 2009). GATE YARDRoadNetworkRail NetworkRoadNetworkBERTHEXPORT YARDLOADc.m.1GATE INUNLOADEMPTY YARDRail Br. Acc.m.13ConsolidationDestinationc.m.16c.m.15c.m.6c.m.5c.t.S-CTranship.Loadc.t.RS-Sc.t.B-RSFirmc.m.10c.t.B-RSc.m.4c.t.B-CBufferNOYESc.t.RS-SEmptyYESNOc.m.8c.t.FL-Tc.t.S-FLTruckBr. Ac(empty)Shuttlec.m.3ShuttleNOYESc.m.2c.t.B-SShuttle c.m.9c.m.12NOYESc.t.RS-SVesselVesselc.m.0Br. Ac.c.t.T-RSWait Stor.c.t.RSWait Stor.YESNONOYESYESNOBUFFERStor. Wait c.m.7c.m.14TruckBr. Ac(full)c.m.11c.t.V-Cc.t.C-Bc.t.C-Vc.t.RS-BGATE OUTIMPORT YARDc.t.C-Tc.t.C-RRailYESNOStor.S-CStor.RS-CCust.Ac.Wait CustomsYESNOWaitTerminal containerGATE YARDRoadNetworkRail NetworkRoadNetworkBERTHEXPORT YARDLOADc.m.1GATE INUNLOADEMPTY YARDRail Br. Acc.m.13ConsolidationDestinationc.m.16c.m.15c.m.6c.m.5c.t.S-CTranship.Loadc.t.RS-Sc.t.B-RSFirmc.m.10c.t.B-RSc.m.4c.t.B-CBufferNOYESc.t.RS-SEmptyYESNOc.m.8c.t.FL-Tc.t.S-FLTruckBr. Ac(empty)Shuttlec.m.3ShuttleNOYESc.m.2c.t.B-SShuttle c.m.9c.m.12NOYESc.t.RS-SVesselVesselc.m.0Br. Ac.c.t.T-RSWait Stor.c.t.RSWait Stor.YESNONOYESYESNOBUFFERStor. Wait c.m.7c.m.14TruckBr. Ac(full)c.m.11c.t.V-Cc.t.C-Bc.t.C-Vc.t.RS-BGATE OUTIMPORT YARDc.t.C-Tc.t.C-RRailYESNOStor.S-CStor.RS-CCust.Ac.Wait CustomsYESNOWaitTerminal container Figure 1 Model architecture ID.ACTIVITY DESCRIPTIONID.ACTIVITY DESCRIPTION c.t. T-RSfrom Truck to Reach Stackerc.t. S-FLfrom Shuttle to Fork Lift c.t. RS-Sfrom Reach Stacker to Shuttlec.t. FL-Tfrom Forklift to Truck c.t. S-Cfrom Shuttle to Cranec.t. C-Rfrom Crane to Rail c.t. RS-Bfrom Reach Stacker to Berthc.t. C-Tfrom Crane to Truck c.t. RS-Cfrom Reach Stacker to Cranec.m.j j container movement (j[116]) c.t. B-Cfrom Berth to CraneBr. Ac.bureaucratic activities c.t. C-Vfrom Crane to VesselStor.storage c.t. V-Cfrom Vessel to CraneWaitcontainer waiting time c.t. C-Bfrom Crane to BerthCust. Ac.customer activities c.t. B-RSfrom Berth to Reach StackerRail Br. Ac.rail bureaucratic activities c.t. B-Sfrom Berth to ShuttleTruck Br. Ac.truck bureaucratic activities Association for European Transport and contributors 200910 Demand characterization Demandisrepresentedbysinglecontainers.Foreachmacro-operation (import,export,transhipment),thedemandflowswerecharacterizedover space,timeandtype.Asregardsspatialcharacterization,containerflows weresubdividedbyoriginanddestinationzoneandwerearrangedinorigin-destination matrices. In particular, for each operation macro-origin and macro-destinationzoneswereidentified,usuallycorrespondingtoquays,yards, gates. Different O-D matrices were estimated for each container type (20 feet vs.40feet,fullvs.empty,),eachdemandflowwascharacterizedbyits distributionovertime.(detailsinCartenetal.,2005;CartenanddeLuca, 2009). Supply characterization Asintroducedintheprevioussections,inacontainerterminalmacro-operations,operationsandhandlingactivitiesmaybedistinguished.Macro-operationsaresetupbyoperations;operationsaresetupbyelementary handling activities. In such a classification the different entities involved must be characterized by their geometrical characteristics (if physical points) and by thecorrespondingperformancesupplied(timedurationand/ortransport capacity). Storage capacity was estimated for quays and yards; averages and probability distribution functions were estimated for handling equipments time duration.Inthefollowingtables,resultsofestimation(samplemeansand probability function parameters) are reported for each handling equipment and foreachactivity.Detailsonthepursuedestimationmethodologiesand/or comments on estimation and calibration results may be found in Carten and de Luca, 2009). Handlingequipmentsinvolvedwere:mobileharbourcrane(MHC),gantry crane (GC), reach stacker (RS). MHCsoperatingintheSalernoContainerTerminalarethreeGottwaldHMK 260mountedonrubber-tyresandaremainlydevotedtoloading/unloading containersto/fromberthedvessels.Theresults,reportedintable6,concern loading activities from shuttle to vessel or from dock to vessel, and unloading activities from vessel to dock. The following container types were considered: undifferentiatedcontainers,20,40and20x20.SincemostSalerno ContainerTerminalloading/unloadingactivitiesconcernfullcontainers,the analysisismainlyfocusedonfullcontainers.Someresultsonempty containersareproposedonlyforactivitiesthatsystematicallyinvolveempty containers.Statisticalanalysisforundifferentiatedcontainersshowsthatthe Gammadistributionfunctionisalwaysstatisticallysignificant.Thesame randomvariableseemstobethebestapproximationforloadingand unloading activities that involve 20 and 40 (full or empty) containers. In table 7 means and standard deviations related to Gamma distribution are reported. Association for European Transport and contributors 200911 Table 6 MHC empirical results activity undifferentiated 20402 x 20 emptyfullemptyfullfull loading1.4260.6571.1020.3851.2570.4441.1210.3861.3320.4762.2140.926 unloading0.8710.2630.7680.2160.8560.221n.p.n.p.0.8670.2300.9710.366 loading from dock 1.3980.562n.p.n.p.1.3160.485n.p.n.p.1.4940.632n.p.n.p. loading from shuttle 1.4350.6781.1020.3851.1930.3871.1210.3861.2720.3892.2140.926 unloading to dock 0.8710.2630.7680.2160.8560.221n.p.n.p.0.8670.2300.9710.366 Table 7 MHC statistical results: parameters of Gamma distribution function activity undifferentiated 20402 x 20 emptyfullemptyfullfull loading1.3660.5141.0840.3871.2380.4051.1010.3401.2880.4022.0830.690 unloading0.8620.2140.6640.1390.8250.183n.p.n.p.0.8350.1880.9330.326 loading from dock 1.3890.441n.p.n.p.1.2520.407n.p.n.p.1.3720.485n.p.n.p. loading from shuttle 1.3500.5491.0840.3871.2270.4051.1010.3401.2440.3752.0830.690 unloading to dock 0.8620.2140.6640.1390.8250.183n.p.n.p.0.8350.1880.9330.326 GCs operating in the Salerno Container Terminal are four rubber-tyred gantry cranesusedbothformovement/storageofcontainersandforloadingof shuttles/trucks. This crane type usually consists of three separate movements forcontainertransportation.Thefirstmovementisperformedbythehoist, whichraisesandlowersthecontainer.Thesecondisthetrolleygear,which allowsthehoisttobepositioneddirectlyabovethecontainerforplacement. Thethirdisthegantry,whichallowstheentirecranetobemovedalongthe working area.Theanalysescarriedoutconcernloadingandunloadingtotheshuttle/truck, and loading and unloading to the stack (sometimes called pile). Each activity wasanalyzeddistinguishingundifferentiatedcontainersfrom20and40 containers.Moreover,loadingtimefromstackisreported,further distinguishing the tier. The analysis is focused on full containers, since these activitiesarethemostfrequentintheSalernoContainerTerminal.Finally, averages and standard deviations were estimated for trolley speed and crane speed.Asregardsundifferentiatedcontainers,theGammadistribution functionprovedthebestsolutionforallanalysedactivities.Similarresults wereachievedonanalysingactivitiesforeachcontainertypeandeachtier number. In tables 10 and 11 means and standard deviations are reported for each activity. Association for European Transport and contributors 200912 Table 8 GC empirical results (minutes) activity undifferentiated 2040 fullfull loading (from shuttle)0.8880.352n.a.n.a.n.a.n.a. unloading (to shuttle)1.3310.4341.3030.4601.3670.402 loading (from stack)0.7690.3800.7580.2830.7740.422 unloading (to stack)0.7600.309n.a.n.a.n.a.n.a. loading (from stack) - tier 11.0250.4311.0190.3481.0310.509 loading (from stack) - tier 20.7130.2700.7060.1880.7210.340 loading (from stack) - tier 30.6720.2900.6580.1690.6830.361 loading (from stack) - tier 40.6250.3740.6180.2360.6360.401 loading (from stack) - tier 50.6140.3760.6050.2610.6230.415 unloading (to stack) - tier 11.1010.236n.a.n.a.n.a.n.a. unloading (to stack) - tier 20.7530.339n.a.n.a.n.a.n.a. unloading (to stack) - tier 30.699 0.312 n.a.n.a.n.a.n.a. unloading (to stack) - tier 40.647 0.309 n.a.n.a.n.a.n.a. unloading (to stack) - tier 50.640 0.307 n.a.n.a.n.a.n.a. activity undifferentiated 2040 fullfull trolley speed (with container) 12.6636.41613.2434.14212.5086.902 free trolley speed 49.07630.202 ---- crane speed12.9165.515n.a.n.a.n.a.n.a. Table 10 GC statistical results: parameters of Gamma distribution function activity undifferentiated 2040 fullfull loading (from stack)0.7520.4060.7410.3110.7690.457 unloading (to stack)0.7660.352n.a.n.a.n.a.n.a. loading (from stack) - tier 11.0220.4491.0110.3531.0600.561 loading (from stack) - tier 20.6870.2500.6580.2220.7120.256 loading (from stack) - tier 30.6680.3230.6590.2460.6730.383 loading (from stack) - tier 40.5920.3250.5830.2610.6060.390 loading (from stack) - tier 50.5710.3550.5600.2800.5840.399 unloading (to stack) - tier 11.0970.231n.a.n.a.n.a.n.a. unloading (to stack) - tier 20.7030.308n.a.n.a.n.a.n.a. unloading (to stack) - tier 30.6710.256n.a.n.a.n.a.n.a. unloading (to stack) - tier 40.6380.245n.a.n.a.n.a.n.a. unloading (to stack) - tier 50.6130.240n.a.n.a.n.a.n.a. activity undifferentiated 2040 fullfull trolley speed (with container) 11.6534.59712.7404.27511.2034.530 free trolley speed 46.60929.892 ---- crane speed 11.4984.586 n.a.n.a.n.a.n.a. Association for European Transport and contributors 200913 TheRSsoperatingintheSalernoContainerTerminalareelevenandare equippedwithatwin-liftspreaderabletomovetwofull20containers.They areusedbothtotransportcontainersinshortdistancesveryquicklyandto pile/storage them in various rows. Theanalysescarriedoutconcern:loadingtoshuttle/truck,unloadingfrom shuttle/truckandstacking.Eachactivitywasanalyzeddistinguishing undifferentiatedcontainersfrom20and40containers.Moreover,stacking wasanalyzeddistinguishingthetiernumber.Theanalysisisfocusedonfull containers since in Salerno Container Terminal the main activities are related to full containers. For the stacking time, the time duration for each tier, up to five, was computed, but it was not possible to distinguish containers typology. For the mentioned activities Gamma random variable fits the data better due tobestvaluesofthevalidationtest.Intable13,theresultsareshowed.As regards RSs speed, the authors suggest to estimate the time duration of these activities directly. Table 12 RS empirical results activity undifferentiated 2040 fullfull loading to shuttle/truck0.3570.2500.3440.2050.3650.272 unloading from shuttle/truck0.2150.1140.1530.0550.2360.119 stacking time0.2880.157n.a.n.a.n.a.n.a. stacking time - tier 10.2010.062n.a.n.a.n.a.n.a. stacking time - tier 20.1860.077n.a.n.a.n.a.n.a. stacking time - tier 30.2380.098n.a.n.a.n.a.n.a. stacking time - tier 40.3550.148n.a.n.a.n.a.n.a. stacking time - tier 50.5420.164n.a.n.a.n.a.n.a. Table 13 RS statistical results: parameters of Gamma distribution functionactivity undifferentiated 2040 fullfull loading to shuttle/truck0.3070.1700.3040.1550.3110.188 unloading from shuttle/truck0.1860.0740.1440.0560.2000.087 stacking time0.2600.146n.a.n.a.n.a.n.a. stacking time - tier 10.1850.056n.a.n.a.n.a.n.a. stacking time - tier 20.1670.071n.a.n.a.n.a.n.a. stacking time - tier 30.2120.086n.a.n.a.n.a.n.a. stacking time - tier 40.3340.118n.a.n.a.n.a.n.a. stacking time - tier 50.5420.140n.a.n.a.n.a.n.a. Association for European Transport and contributors 200914 4SIMULATION RESULTS To plan investments for a container terminal several project scenarios need to becomparedthroughperformanceindicatorestimation.Theseindicators couldbeglobal,ifreferringtothecontainerterminalasawhole(aggregate indicators), or local if referring to a single container (disaggregate indicators). Globalindicatorsaregenerallyusedtoevaluatethebenefitsoflong-term investments;whilelocalindicatorsareusedtoevaluatethebenefitsof medium/short-term investment and for real time applications. Totesttheapplicabilityofthemodelarchitectureproposedforallthecited kindsofapplication,theimplementedmodelwasvalidatedwithrespectto performanceindicatorscoherentwiththosemeasuredbytheterminal monitoring office and summarized above: global performance indicators terminaloperationtime:dailytimerequiredtobringallterminal activities to a close; local performance indicators handling equipment indicators; ovessel loading and/or unloading time; oquay/yard crane idle time; oshuttle waiting time; oshuttle transfer time; oreach stacker stacking time; oreach stacker idle time; ogate in/out waiting time; container indicator; ocontainer operation time: time required to move a container with handlingequipment(e.g.,timespentmovingacontainerfrom quay to vessel or from shuttle to stack). Startingfromthemodelarchitectureproposedintheprevioussection,four differentmodelsbasedonfourdifferenthandlingequipmentmodels,were implemented: Sample Mean Undifferentiated (SMU) model.Samplemeanvaluesareusedtoestimatehandlingequipmenttime duration and there is no distinction between containers type. Sample Mean Container Type (SMCT) models. Samplemeanvaluesareusedtoestimatehandlingequipmenttime durationandcontainerstypeareexplicitlytakenintoaccount:20full and/or empty; 40 full and/or empty; 2 x 20 full. Random Variable Undifferentiated (RVU) model. The time associated to each single activity is the realization of a random variable,handlingequipmentstimedurationismodeledasarandom variable and there is no distinction between containers type. Random Variable Container Type (RVCT) models.Handling equipment time duration is modeled as a random variable and containerstypeareexplicitlytakenintoaccount:20fulland/orempty; 40 full and/or empty; 2 x 20 full. The discrete event simulation model was developed in Witness software, the simulationswerecarriedoutonIntelCore2CPU2.00GHz,2.00GBRAM, the values used for calibration are obtained by determining the average of 25 simulations. Association for European Transport and contributors 200915 In the following tables and figures analyses on computational time (table 14), absolutepercentageerror(table14),cumulativeabsolutepercentageerror variationarereported(figure2).Infigure3and4asensitivityanalysisis proposed. The results in terms of simulation time point out that random variable models requireacomputationaltimemuchgreaterthansamplemeanones.The former require about 20 minutes, the latter are below one minute. Resultsintermsofglobalindicatorsshowanaverageabsolutepercentage errorofmorethan10%fortheSMUhandlingmodel,whereasinusingthe RVU handling model the percentage estimation error is lower than 5%. Using theContainerTypemodels,resultsintermsofglobalindicatorsshowan averageabsolutepercentage errorofabout 9% forthesamplemeanmodel, whereas in using the random variable model the percentage estimation error is about 3%. The use of sample mean handling models does not produce very good results in terms of local indicators; average percentage estimation errors exceed 13% for handling equipment indicators and are about 30% for container indicators.Resultsobtainedusingrandomvariablehandlingmodelsaresignificant: averageabsolutepercentageerrorsforhandlingequipmentindicatorsare morethan6%withtheRVUhandlingmodel,andabout3%withRVCT handlingmodels.Withrespecttocontainerindicators,whenonlyusingthe RVCT handling models the absolute percentage estimation error is acceptable (>11%); in all other cases the estimation errors are about 30%. Table 14 Average absolute percentage estimation error: estimation sample handling model simulation time (minutes) absolute percentage estimation error global indicators local indicators handling equipment containers SMU0.5010.1%13.2%30.8% SMCT0.608.9%11.0%29.3% SRVU18.704.6%6.5%28.5% RVCT21.302.6%3.0%11.2% Infigure2cumulativeabsolutepercentageestimationerrorvariationis reported. With respect to the global indicator the results described above are confirmed;formorethan80%ofthebusinessdaysimulated,theabsolute percentageerrorislowerthan10%.Regardingthehandlingequipment indicators,thegreatvariabilityofthephenomenonobservedproduces absolute estimation errors for sample mean estimations lower than 10% only for25%ofthehandlingequipmentsimulated,whileforrandomvariable estimations the absolute estimation error is always lower than 10% and for the RVCTthisvalueislowerthan5%for75%ofthehandlingequipment simulated. Iftheaimofthesimulationistoestimatecontainermovement,theonly suitable handling model is the RVCT one: only for this model is the absolute estimation error of the container operation time lower than 10% for 45% of the observations,andlowerthan15%forover60%oftheobservations.By contrast,forover80%oftheobservationstheabsoluteestimationerroris Association for European Transport and contributors 200916 lowerthan30%.Ascanbeseeninfigure2,theothermodels(SMU,SMCT andRVU)produceunacceptable absoluteestimationerrors forthepurposes of the simulation. 0%20%40%60%80%100%0% 20% 40% 60% 80% 100%Percentage of business daysAbsolute percentage estimation error Terminal operation timeSMU / SMCT RVU RVCT0%20%40%60%80%100%0% 20% 40% 60% 80% 100%Percentage of handling equipmentsAbsolute percentage estimation errorHandling equipment indicatorsSMU / SMCT RVU RVCT Figure2Cumulateabsolutepercentageestimationerror:terminaland handling equipment 0%20%40%60%80%100%0% 20% 40% 60% 80% 100%Percentage of containersAbsolute percentage estimation error Container operation timeSMU / SMCT RVU RVCT Figure 3 Cumulate absolute percentage estimation error: containers Toevaluatethemodelssensitivity,thepercentageperformanceindicators variationswithrespecttotheinputvariablespercentagevariations(e.g., percentagevariationinequipmentnumberorequipmentperformance)were estimated.Infigures3and4somerepresentativeresultsobtainedwiththe RVCThandlingmodelsestimatedarereported(resultsrelatedtotheother performance indicators are analogous).IntheSalernocontainerterminaltherearecriticalactivities:thegate-in procedure and vessel loading time. With respect to gate-in activity (figure 3), thetruckwaitingtime(queuewaitingtimeplusservicetime)percentage variation was estimated with respect to the service time percentage variation; thesimulationresultsshowanexpecteddecreasedbenefiteffect;in particular,-10% ofservicetimeproducesabout-35% oftruckwaitingtime;- Association for European Transport and contributors 200917 20%ofservicetimeproducesabout-55%ofwaitingtimewhile-30%of service time produces more than -70% of waiting time. -80%-60%-40%-20%0%-80% -60% -40% -20% 0%GATE IN waiting time % variationGATE IN service time % var. Figure 3 An example of the models sensitivity: gate-in waiting time variation measured against gate-in service time variation With respect to vessel loading time (figure 4), one of the critical points of the Salerno terminal is the low arrival frequency of the shuttles near the vessels. Hence a crane number increase does not produce a great reduction in terms ofvesselloadingtime.Instead,ashuttlelagtimereductionproducesa significant vessel loading time variation (e.g., -30% of shuttle lag time produce about-30%ofvesselloadingtime).Thisphenomenonoccurstillcrane capacity is reached; then only a combined increase of crane number with the shuttle lag time could further improve loading performance. -100.0%-80.0%-60.0%-40.0%-20.0%0.0%0% 20% 40% 60% 80% 100%Vessel loading time % var.Shuttle / Crane number % var.Crane numb. % var. Shuttle lag time % var. Shuttle lag time% var. + 50%crane numb. Figure 4 An example of the models sensitivity: vessel loading time variation measured against shuttle/crane number variation Association for European Transport and contributors 200918 5CONCLUSIONS Inliteraturenumerouseffortsmaybefoundinthefieldofsimulationofa containerterminal,mostoftheexistingpapersareonlyfocusedonthe applicationand/oronthecomparisonofdesignscenariosanddonotpay great attention on the model set-up, its calibration and its validation. If on the onehand,manycontributionsdonotpresentanyinformationonequipment handlingmodelsused,theremainingcontributionscarryoutverysimple approaches(deterministic)and/orgivescantyinformation:ontheestimation approach pursued, on experimental data used, on parameters estimated and on parameters value. Moreover, no one investigates the effects that different hypothesesonhandlingequipmentmodelscalibrationmayhaveonthe simulationofcontainerterminalperformances.Sucheffectscouldnotbe negligibleandshouldbeinvestigatedwithrespecttodifferentplanning horizons, such as strategic or tactical.In this paper a discrete event simulation model was proposed and applied to theSalernocontainerterminalinordertoaddresssomeoftheopenissues introducedabove.Theaimwastosuggesttoanalysts,modellersand practitionersasortofaguidelinesusefultopointoutthestrengthsor weaknesses of different approaches. Guidelines were presented through: (a)a preliminary in depth literature survey; (b)thedescriptionofthedevelopeddiscreteeventmodels,withparticular attentiontoestimationresultsofhandlingactivitymodelsforthree handlingequipment(mobileharbourcranes,gantrycranes,reach stackers)andfordifferentcontainertype(undifferentiated,20feet,40 feet, empty, full.); (c)thesimulationoftheeffectsofdifferenthypothesesregarding(i)the approachtoestimatehandlingactivitiestimeduration(samplemeanvs randomvariableestimation),(ii)thelevelofaggregationofhandling activities (e.g. vessel loading vs explicit simulation of elementary activities sequence), (iii) the segmentation of container type. Literaturereviewallowedacomprehensionofwhathasbedoneinthelast twentyfiveyearsincontainerterminalsimulationfieldandgavedetailed informationonapproachespursued,softwareused,modelscalibratedand corresponding parameters. Among the contributions proposed only ten papers give information on the handling equipment models used. Half of them adopt a stochasticapproachandshowestimatedparametervalues.Mostofthe contributionsdealwithvesselloading/unloadingoperations.Thereis substantialheterogeneityregardingthelevelofaggregationofactivities involved and how such activities are aggregated in a single macro-activity. As regardsvesselcycletime,astochasticapproachisunanimouslyproposed. With regard to crane loading/unloading time both deterministic approach and stochasticonehavebeenpursued. Withrespecttocranespeed,allexistent papersproposedeterministicandaggregatemodels.Withrespecttoother handlingequipment,notmuchcanbefoundintheliterature;someone propose deterministic values for a straddle carrier, whereas other one propose atriangulardistributionfunctionfortheforklift.Asregardsshuttle performances (speed, travel time, waiting time ), few models exist and are Association for European Transport and contributors 200919 easilytransferabletodifferentcasestudies(duetotheinfluenceofpath length, path winding, traffic vehicle congestion inside the terminal and so on). Discrete event model description and calibration results enriched the existent stateofart,gavesomeinsightsonthebestcalibrationapproach(Moment, Maximum Likelihood), highlighted a family of distribution functions suitable to simulatehandlingequipmenttimedurationandallowedtodefinethebest performingdistributionfunctionsforeachhandlingequipmentandforeach containertype.Fromastatisticalpointofview,MaximumLikelihood estimationapproachseemedtobethemostperformingone,andNormal, Gamma and Weibull distribution functions turned out statistically significant to interprethandlingactivitiestimeduration.Inparticular,Gammarandom variableledtobettergoodnessfitforallhandlingactivitiesandforall containertypeinvolved.Thewholesetofdistributionfunctions(andoftheir parameters)allowedtoimplementdifferentsimulationmodelsasactivities level of aggregation changes and as container type changes. Theapplicationofdiscreteeventmodelallowedtodrawsomeoperational guidelinesonthebestapproachtosimulatehandlingequipmentactivities and/or on the best approach to simulate terminal performances with respect to different planning horizons. Ifthefocusistosimulatehandlingequipmenttimeduration,bothsample mean and random variable estimation can be pursued. Sample mean models couldbeusedforestimatinghandlingequipmentindicators,butgreater averageabsolutepercentageerrorsmustbeaccepted(11%to13%)with respecttorandomvariablehandlingmodelsthatallowabsolutepercentage errorvaryingfrom3%to6%.Ifthefocusistosimulatesinglecontainertrip time(containerindicators),onlytheRandomVariableContainerType handlingmodelscanbeused.Inthiscaseaverageabsolutepercentage estimation error is about 11%, while it is about 30% for the other approaches. Finally,differentplanninghorizons(strategicvstactical)wereinvestigated with respect to two different modelling hypotheses: sample means vs. random variablehandlingmodels.Instrategicplanninghorizon,sincetheaimisto simulatewholecontainerterminalperformancewithrespecttolonger simulationtimehorizon(forinstance365days),itisimportanttohavea simulation model efficient, easy to implement and realistic in the simulation of aggregateterminalperformanceindicators(e.g.terminaloperationtime).In suchacontextsamplemeanhandlingmodelsmaybeused,sincerealistic micro-simulationofsinglecontainersmovementdoesnotsensiblyimprove simulationresults.Intacticalplanninghorizons,benefitsfrommedium/short-terminvestmentsand/orbenefitsfromrealtimestrategiesshouldbe estimated.Inthiscontext,itisimportanttohaveasimulationmodelefficient and realistic in the simulation of single container movement. Obtained results showedthatonlytheuseofrandomvariablehandlingmodelsallows satisfactory simulation results. 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