MACMESE-39

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Planning and control of logistics for offshore wind farms BERND SCHOLZ-REITER, MICHAEL LÜTJEN 1 , JENS HEGER, ANNE SCHWEIZER BIBA – Bremer Institut für Produktion und Logistik GmbH University of Bremen Hochschulring 20, 28359 Bremen GERMANY {bsr|ltj |heg|vir}@biba.uni-bremen.de, http://www.biba.uni-bremen.de 1 corresponding author Abstract: Construction and utilization of offshore wind farms will increase within the next years. So far the first German offshore wind farm was constructed and put into operation by “Alpha Ventus”. Experiences illustrate that bad weather conditions are the main cause for delays in transport, handling and installation of offshore wind farms. This can lead to extensive project delays of several months. The main objective of current logistical research activities is the robust design of planning and control methods for offshore installations. In this study, the basic conditions and existing disturbances of supply chains for offshore installations are analyzed. Based on these results, a planning and control concept will be introduced. Additionally, a mathematical model using mixed integer linear programming (MILP) is developed. It calculates the optimal installation schedule for offshore wind farms by observing different weather conditions. The model can be used to reduce vessel operation times in dependence on seasonal or up-to-date weather forecasts. Key-Words: - Maritime Logistics, Supply Chain, MILP, Installation Scheduling, Offshore Wind Farm 1 Introduction The supply of fossil energies as coal, oil and gas is naturally limited in Germany and the utilization of nuclear energy is politically restricted. On consequence, the utilization of regenerative energy supplies like water, sun and wind is publicly funded. After the installation of more than 20.000 wind turbines onshore in Germany until the end of the year 2009, the first German offshore wind farm “Alpha Ventus” was opened in April 2010. Other European countries such as England, Denmark or Sweden, own bigger experiences with the installation of wind farms, which were documented in reports published in [1,2,3]. Beside enormous technical challenges with the components of offshore wind turbines, the logistic is also demanded to develop efficient installation and material supply concepts for the offshore-wind farms. Up to 2020 the installation of more than 37,000 MW [4] is planned in Europe, what corresponds to an annual installation of more than 1,000 offshore-wind turbines. On account of this scale the establishment of standard processes for logistics is necessary. They should consider planning aspects as well as execution aspects and should allow an efficient schedule of restricted resources like e.g. installation vessels and port facilities. First, we present aspects of the installation of offshore wind turbines. We describe different installation scenarios and the resulting requirements for the installation vessels. In a further step, the challenges of the supply chain management are discussed and occurring problems analyzed. Besides, we look at the weather forecasts and examples of offshore planning systems, which try to deal with these. After that, we present our own concept of a planning system for the installation scheduling of offshore wind farms. Following the mathematical model is introduced and an exemplary optimal installation schedule is calculated. After all, we conclude and provide an outlook to our next activities. 2 Installation of offshore wind turbines The installation of offshore wind turbines (OWT) is influenced decisively by the weather. While foundation structures can still be installed with greater airflow conditions and wind force, nacelle and blades require still air. In particular, the assembly of the blades requires nearly calm state. The feasibility of a wind farm construction is very low concerning the servicing and repair operations. For example, it is estimated by 50% to 75% in a year for a wind farm close to Ireland [5]. This leads to an extreme stockpiling of material and resources in order to exploit good weather periods for intensive installation or servicing work. This concerns the components of OWTs, which must be held ready in the harbor or on the vessel, as well as personnel capacities, which are needed for the installation processes. In addition, vessel and handling capacities are bounded to the harbor. 2.1 Installation scenarios and vessel requirements The installation scheduling of offshore wind farms is dependent strongly on the current weather conditions on ADVANCES in MATHEMATICAL and COMPUTATIONAL METHODS ISSN: 1792-6114 242 ISBN: 978-960-474-243-1

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Planning and control of logistics for offshore wind farms BERND SCHOLZ-REITER, MICHAEL LTJEN1, JENS HEGER, ANNE SCHWEIZER BIBA Bremer Institut fr Produktion und Logistik GmbH University of Bremen Hochschulring 20, 28359 Bremen GERMANY {bsr|ltj|heg|vir}@biba.uni-bremen.de, http://www.biba.uni-bremen.de 1corresponding author Abstract:Constructionandutilizationofoffshorewindfarmswillincreasewithinthenextyears.Sofarthefirst German offshore wind farm was constructed and put into operation by Alpha Ventus. Experiences illustrate that bad weatherconditionsarethemaincausefordelaysintransport,handlingandinstallationofoffshorewindfarms.This can lead to extensive project delays of several months. The main objective of current logistical research activities is the robust design of planning and control methods for offshore installations. In this study, the basic conditions and existing disturbancesofsupplychainsforoffshoreinstallationsareanalyzed.Basedontheseresults,aplanningandcontrol conceptwillbeintroduced.Additionally,amathematicalmodelusingmixedintegerlinearprogramming(MILP)is developed.Itcalculatestheoptimalinstallationscheduleforoffshorewindfarmsbyobservingdifferentweather conditions. Themodelcan beused to reducevessel operation timesindependenceonseasonalorup-to-dateweather forecasts. Key-Words: - Maritime Logistics, Supply Chain, MILP, Installation Scheduling, Offshore Wind Farm 1 Introduction Thesupplyoffossilenergiesascoal,oilandgasis naturallylimitedinGermanyandtheutilizationof nuclearenergyispoliticallyrestricted.Onconsequence, the utilization of regenerative energy supplies like water, sun and wind is publicly funded. After the installation of morethan20.000windturbinesonshoreinGermany until the end of the year 2009, the first German offshore windfarmAlphaVentuswasopenedinApril2010. OtherEuropeancountriessuchasEngland,Denmarkor Sweden, own bigger experiences with the installation of windfarms,whichweredocumentedinreports publishedin[1,2,3].Besideenormoustechnical challengeswiththecomponentsofoffshorewind turbines,thelogisticisalsodemandedtodevelop efficient installation and material supply concepts for the offshore-wind farms. Up to 2020 the installation of more than37,000MW[4]isplannedinEurope,what corresponds to an annual installation of more than 1,000 offshore-windturbines.Onaccountofthisscalethe establishmentofstandardprocessesforlogisticsis necessary.Theyshouldconsiderplanningaspectsas wellasexecutionaspectsandshouldallowanefficient scheduleofrestrictedresourceslikee.g.installation vessels and port facilities. First,wepresentaspectsoftheinstallationofoffshore windturbines.Wedescribedifferentinstallation scenariosandtheresultingrequirementsforthe installationvessels.Inafurtherstep,thechallengesof thesupplychainmanagementarediscussedand occurringproblemsanalyzed.Besides,welookatthe weatherforecastsandexamplesofoffshoreplanning systems,whichtrytodealwiththese.Afterthat,we presentourownconceptofaplanningsystemforthe installationschedulingofoffshorewindfarms. Followingthemathematicalmodelisintroducedand an exemplaryoptimalinstallationscheduleiscalculated. Afterall,weconcludeandprovideanoutlooktoour next activities. 2Installation of offshore wind turbines Theinstallationofoffshorewindturbines(OWT)is influenceddecisivelybytheweather.Whilefoundation structurescanstillbeinstalledwithgreaterairflow conditionsandwindforce,nacelleandbladesrequire still air. In particular, the assembly of the blades requires nearlycalmstate.Thefeasibilityofawindfarm constructionisverylowconcerningtheservicingand repair operations. For example, it is estimated by 50% to 75% in a year for a wind farm close to Ireland [5]. This leads to an extreme stockpiling of material and resources inordertoexploitgoodweatherperiodsforintensive installationorservicingwork.Thisconcernsthe componentsofOWTs,whichmustbeheldreadyinthe harbororonthevessel,aswellaspersonnelcapacities, whichareneededfortheinstallationprocesses.In addition,vesselandhandlingcapacitiesareboundedto the harbor. 2.1Installationscenariosandvessel requirements Theinstallationschedulingofoffshorewindfarmsis dependent strongly on the current weather conditions on ADVANCES in MATHEMATICAL and COMPUTATIONAL METHODSISSN: 1792-6114 242 ISBN: 978-960-474-243-1sea.Accordingly,differentattemptsexistswhichoffer optionsforanoptimizedscheduling.Itcanbe distinguishedbetweenthreeinstallationscenarios ==[[4]. As shown in figure 1, the first option (a) includes thepreassemblyinaclosersituatedharbor.Becauseof theshortertransporttimetothewindfarm,quick reactions to weather changes are possible. Figure1:Installationscenarios:a)Thecomponents, producedbyamanufacturer(M)aretransportedto theassemblyport(P)andassembledthere.Theyare broughttotheconstructionatthewindfarm(WF) afterwards,b)thecomponentsaretransportedfrom manufacturer(M)neartothewindfarm(WF).A ferry traffic is used to transport the components over thelaststretchc)thecomponentsaredirectly transportedfrommanufacturer(M)tothe construction at the wind farm (WF) Thesecondoption(b)containstheassemblyatthe establishmentplace.Itoccursthroughso-called construction vessels or platforms, which are supplied by mostlysmallersuppliervesselswithsuitable components and material. Bythethirdoption(c),pre-installedsinglecomponents arebroughtdirectlybythesupplierassistingquick "Jack-up"vesselstotheconstructionsites.Theyare mountedtherebyintegratedvesselcranes.The"Jack-up"showsamobileliftingplatform,whichcanstand withthehelpoflowerablemainpillarsontheseabed. Therefore,thenecessarystabilityisguaranteedforthe assembly process. Figure 2 shows the concept of such an installationvessel,whichisdesignedtooperatein medium water depth of 30 to 40m. These vessels operate onitsownandtransportalsotheOWT-components.In comparison to other vessel types, they should be able to extendtheiroperationtimeby50percenttomorethan 260 days per year. Figure2:Offshoreinstallationvesselwithjack-ups (Beluga-Hochtief) Additionally,theywillbeabletooperatewithdifferent loadingsets.Dependingonprojectstatusandweather conditionthe loadingsetwill bevaried.Intimes of bad weather,theloadingsetwillconsistofsubstructures, whichcan be installedalsowithhigherwindforcesand waves.Goodweatherconditionswillincreasethe amount of nacelles and blades, which will be loaded. At themoment,theoffshorecompaniesplantoinstall substructuresinthedarkermonthsfromautumnto springandtoassemblethenacellesandbladesin summer.Becauseoftheseasonalweatherchanges,this shouldhelptogetahighutilizationfortheinstallation vessels.Theideaofthispaperistopresentamethod, whichallowsadynamicalinstallationplanningof shortertimeperiodsonthebasisofup-to-dateweather forecasts.Thismeansthatoptimizedloadingsets, installationsequencesandmaterialdemandswillbe calculated. 2.2Challengesinplanningofoffshoresupply chains Regardingtheoffshorematerialdemand,thewhole supply chain must be flexibly organized in order to a fast reactiontodisturbances.Especiallybyfineweathers, massive material requirements are needed in a short time thatmustbemappedintothesupplychain.Onthis occasion, inventory stock, production and delivery times must be synchronized, so that the installation of the wind farmisnotdelayedbymaterialshortages.Themain challengeisthecorrectdeterminationoftheinventory targetsintheharbor.Underinclusionoftherestricted harborfacilitiesandeconomicconsiderations,the inventorytargetsmustbedefinedinawaythata continuous supply with OWT-components is guaranteed. a)b)c)Source: BVG AssociatesADVANCES in MATHEMATICAL and COMPUTATIONAL METHODSISSN: 1792-6114 243 ISBN: 978-960-474-243-1Outgoingfromtheinventorytargetsintheharbor,the whole supply chain can be organized with concepts from theautomobileindustry.Thesupplychainsinthe automobile industry are state of the art and very efficient and flexible. Especially for the growing number of OWT-installations inthenext10years,itwillbenecessarytogetwell functioningsupplychains,whichallowsaline productionofwindfarms.Thehighprocess transparence,whichise.g.knownfromtheautomobile industry,willbealsoimportantfortheoffshore assembly.Processdisturbancesintransportor manufacturing lead to high subsequent costs, because the installationvesselhastoreturntotheharbor.Toavoid process disturbances, all aspects, which are able to affect thesupplychain,mustbeanalyzedatfirst.Infigure3, thematerialflowprocessfromtheproductionuptothe offshoreinstallationisillustratedandtherespective possible disturbance variables are identified. Figure3:Thematerialflowprocessandits disturbance variables in the supply chain for the installation of offshore wind farms Betweenproductionandoffshoreinstallation,itexists the shore-based transport, handling at the harbor and the sea-basedtransport.Thedisturbancescanreachfrom capacityproblemsoverqualityproblemstodifferent trafficandweatherconditions.Asaresult,wehaveto deal with delays in the supply chain. In order to increase thetransparenceandtheapplicationofrobustplanning andcontrolmethodswehavetouseinformation technologies for tracking and tracing. 2.3Weather forecasts Inordertoincludeweatherconditionsintothe installationplanningofoffshorewindturbines,weather forecastsareessential.Weatherpredictionsand numericalweatherforecastscanbecalculatedwith differentmodels.Reliableweatherpredictionsare mostlyprovidedforaperiodofapprox.14days.With theassistanceofensemblessuchpredictionsare validatedwhileintheso-calledmainrunthereal weatherdataareillustratedandeasilyvarieddataare processed in other runs of it. If the runs are very similar, it is very likely that the prediction is reliable [6]. Beyond that,seasonalweatherforecastsexist.Theyareapplied long-termandarevalidforlongerperiodse.g.months. Such forecasts are based on historical data and give ideas such as average wind speeds, temperatures and rain falls in this periods. Based on these long-term forecasts, it can bepredictedthatinwintertheprobabilityofdayswith goodweatherconditionsissignificantlylessthanin summer.Therefore,themasterplanoftheoffshore companiesistoinstallthesub-structuresinthedarker monthsandthetop-structureslikee.g.tower,nacelles and blades in the summer time. However, experiences of windfarminstallationsshowthatthisisnotthateasy. Anintegratedplanningoftheinstallationofsub-and top-structuresbyconsideringshorttimeforecastsis necessaryinordertogetanoptimalutilizationofthe vessels as limited and expensive resources. 2.4Examplesofplanningsystemsconsidering the weather relations A suitable planning model for the installation of offshore equipmentshasnotbeenintroducedintheliteratureup to now. The topical software solutions are aimed only on theoperationofwindfarmsorequipments.TheITSIT serviceSalzgitterGmbHownswithWindPLANTa software,whichservesforthetechnicaloperationof windfarmsandownsanexpansionmoduleforthe weather-conditionedmaintenanceplanning.Another manufacturerofcorrespondingoperatingsoftware is the BTCBusinessTechnologyConsultingAG.WithBTC windfarmcentreitdisposesaproductsolutionthat supportsthetechnicalmanagerinexecutionand documentationofthenecessarymaintenanceand servicing measures [7]. Finally, it can be noticed that no logisticalorientedsoftwaresolutioncouldbeidentified fortheassemblyofoffshorewindturbines,whichtakes theweathereffectsintoconsideration.Theintroduced researchapproachesoffervaluableapproachesforthe developmentofspecificoffshoresolutions.However, theyarenottransferableonaccountoftherestrictions specific for application. supply chain for installation of offshore wind parks-street- and space conditions-load security delay-storage capacity-out-of-stock situations-search timetime delay-weather conditions-missing material & components-staff capacity-loss of time-delayed supply-delayed production-search time in temporary storeproduction-incorrect fixation-bad weather conditions-restowingtransportharborhandlingtransportoffshore installationADVANCES in MATHEMATICAL and COMPUTATIONAL METHODSISSN: 1792-6114 244 ISBN: 978-960-474-243-13Conceptofaplanningsystemforthe installationschedulingofoffshorewind farms The objective of a planning system for the installation of offshorewindfarmsistoreducetheconstructiontime, whichisproportionaltotheinstallationcosts.The capacitiesofvessels,harborfacilitiesandstaffhaveto becharteredfortheplannedprojecttimeandeach additionaldayleadstoextracosts.Therefore,the conceptoftheplanningsystemconcentratesonthe offshoreactivitiesbydevelopingaMILPplanning model,whichcontainstransportandinstallation processes,differentweatherconditionsandan installation vessel as resources (figure 4). Additionally,inthenearfuturevesselswillbecomethe bottleneckinthewindfarminstallationprocess[4]. Therefore, it is important to optimize especially this part of the supply chain. Figure 4: Concept of planning system for coordination of onshore and offshore activities TheMILPplanningmodelcanbeusedforstochastic optimization.Withthehelpofthestochastic optimizationtheuncertainweatherconditionscanbe considered.Fortheuncertaindatalikelihood distributionsareacceptedasinputsforthelinear optimizationmodel.Thusexpectationsoftheobjective functioncanbeoptimized[8].Therefore,thestochastic programmingisused,forinstance,bytheplanningin telecommunicationnetworksandfinancialinvestments as well as in the supply chain management [9]. Aftercalculatinganoptimalinstallationschedule, suitabletargetinventoriescanbecalculatedforthe wholesupplychainbyusingdeliverytimes.Occurring materialshortageswillbeconsideredbyrolling planning.Dependingontheactualinventoriesnew installation will be calculated. 4 MILP for vessel planning Asmentionedabovewedevelopedamathematical modelusingMILPtocalculateoptimalinstallation schedules for the vessels. Installation vessels are already thebottleneckinwindfarminstallationprocessesand theyprobablywillstay.Theirutilizationshouldbeas highaspossibleandtheyshouldbeusedinthemost efficientway.Thegeneralobjectiveistominimizethe building time for a wind farm. The developed model can not only be used for exact short-term planning, it is also applicabletosimulationrunscalculatingproject durationsregardingdifferentweatherseasonsinlong-term planning. 4.1Properties of the mathematical model The following properties of the installation processes are considered in model: 1.One installation vessel for the installation of one wind farm 2.Selectionofaloadingsetattheharbor(how manysub-structuresandhowmanytop-structures can be loaded) 3.Vesselloadingtimeandtraveltimefromthe harbor to the wind farm and back 4.Building time for a sub-structure / top-structure 5.Weather conditions are modeled in three types a.good weather: substructures and top-structures can be built b.mediumweatherconditions:only substructures can be built c.bad weather conditions: nothing can be built The input parameters for our model are shown in table 1. Input parameters Number of wind turbine installations12 Vessel loading time8 Vessel travel time to/from wind farm4 Sub-structure installation time24 Top-structure installation time48 Medium weather start timesArrayofweather start times Medium weather durationsArrayofweather condition durations Bad weather start timesArrayofweather start times Bad weather durationsArrayofweather condition durations Table 1: Input Parameter Themodelcanbeeasilyextendedespeciallyformore detailedinstallationstepsandcomponents.Justthe same,withweathertypes,whichcanbeadjustedtothe installation steps. OnshoreOffshoreMaterial supply planning systemMILP planning systemOptimal installation scheduleWeatherconditionstarget inventoryRessources(trucks, storages,plants etc.)Transport and manufacturingprocessescurrent inventoryRessources(vessels, harbourfacilities etc.)Transport and installationprocessesADVANCES in MATHEMATICAL and COMPUTATIONAL METHODSISSN: 1792-6114 245 ISBN: 978-960-474-243-1 Figure 5: Sequence of installation steps Infigure5thesequenceoftheinstallationstepsis depicted. At first, the vessel loading set is selected. The installationshipscanhandlewithseveralfixloading sets because each set requires their own superstructures on ship. Currently the model supports two loading sets: thefirstcontains4sub-structuresand2top-structures andthesecondcontains2sub-structuresand4top-structures. After the loaded vessel is arrived at the wind farm, the installation processes can begin, if the weather conditions allow it. Each installation process is indexed, which allows the solver to check at the beginning of the top-structureinstallationprocess,ifthereisat leastone sub-structure available. To do this, the model combines thetypicalmulti-periodicproductionformulation(e.g. [10])withthetypical continuous-timerepresentation of ajob-shop(e.g.[11]).Themulti-periodicformulation setsthecurrentstorageleveltothestoragelevelfrom thelastperiodplustheproductionminusthedemand. Theadvantageofthismodeltechniqueisthatthe discretestoragelevelisknownateachperiod.The disadvantage is, that there is always a discrete time slot and for example production amounts can only be set for a whole period (ts : storage; tp : production; td : demand; t: period): t t 1 t 1 t 1s s p d = + (1) Thejob-shopformulationismoreflexiblewith,for example,starttimes,becausethemodelonlydefines that the start time of production x, starts after production x-1 plus the duration of the production (pt): i 1 ix x pt+ + (2) Themodelalsocheckstheavailabilityofrequired structuresonshipforeachproductionstep.Installation timesarenon-overlappingwithweatherconditions. Onlysub-structurescanbebuiltduringmedium weather. 4.2Complexity and Solver runtime The planning problem belongs to the NP-hard problems, but since the planningmodel considers only one vessel, realisticscenarioscanbecalculatedinacceptabletime. SCIP[12]wasabletocalculateanoptimalsolutionfor the example provided in 4.3 in less than one minute on a standardofficecomputer.However,addingmorewind turbines or weather types leads to a much longer solving time or makes the model unsolvable. On the other hand, modeloptimization[13]couldincreasethesenumbers again. 4.3Planning and scheduling example Sinceweatherforecastsareonlyvalidanduseablefora shorttimehorizon,theSolver(e.g.SCIPorCPlex) should solve the mathematical model each time the vessel arrives at the harbor and needs to be loaded. This way the currentweatherconditionscanbeintegratedintothe planning most reliable. To optimize the supply chain and make sure that parts of the wind turbines are ready for the vessel,longerplanninghorizonsshouldbeconsidered. Anexampleofonewindfarmwith12turbinesis provided here. Additionally to the data presented in table 1 weather periods have been added randomly. Periods are usually1-3dayslongandmightbeoverlapping.The probabilityofmediumweatherandbadweatherare approximately33%each.Thatmeans,thateach condition,goodweather,mediumweatherandbad weather, equally occur. A Gantt chart of the example data ispresentedinfigure6.Loadingsetscorrespondtothe number of sub- and top-structures. 4.4Simulationswithstochasticweather conditions TheMILPcanbeusedforsimulationrunsconsidering stochastic weather conditions. One might be interested inestimatesofthebuildingtimeofawholewindfarm: goodestimates,whichcanbeusedforsupplychain optimizationslater,canbecalculatedbysimulating differentweatherconditionsandtheir(partlyfaulty) forecasts.TheMILPissolvedexactlyforeachweather andforecastcombination.Moreover,ifenough simulationsrunsareperformed,significantstatistical results can be gathered. 5 Conclusion Thiscontributionintroducestothecurrentstatusofthe offshore-windenergyinGermanyandindicatesthe problemswhichexistwithintheoffshoresupplychain. Themaincauseforextensiveprojectdelaysarebad weather conditions. Accordingly, a concept of a planning systemforthecoordinationofonshoreandoffshore activities is depicted. The core of this planning system weather med. badstructureinstallation 1.1 1.2 1.3 1.n 2.1 vessel (travel + loading) 1 1 2Start: Vessel is loaded 1sttour and leaves the harborVessel arrives andinstallation processesof sub- or top-structurescan startNo installation duringbad weatherVessel returns and isloaded for 2nd tourADVANCES in MATHEMATICAL and COMPUTATIONAL METHODSISSN: 1792-6114 246 ISBN: 978-960-474-243-1 Figure 6: Gantt Chart of the example for an optimal installation schedule isaMILPwhichcalculatesoptimalinstallation schedules by observing different weather conditions and vesselloadingsets.Basedonthismodel,seasonaland up-to-dateweatherforecastscanbeconsideredand statisticalsignificantresultscanbegathered.Thenext workingstepsincludethedevelopmentofasimulation model, which contains the material flow of offshore and onshore processes. Also, the planning and control of the onshorematerialsupplyshouldbeimprovedbyusing autonomous control methods. References: [1] ResearchatAlphaVentus(RAVE),Interaktive Offshore-WindenergieKartevonEuropa, http://rave.iset.uni-kassel.de, 21.08.2010. [2] I.Bishop,C.Stock,Usingcollaborativevirtual environmentstoplanwindenergyinstallations, Renewable Energy, Vol. 35, No. 10, 2010,pp. 2348-2355. [3] G.Gerdes,A.Tiedemann,S.Zeelenberg,"Case Study:EuropeanOffshoreWindFarms", http://www.offshore-power.net/, 18.08.2010. [4] EuropeanWindEnergyAsscociation,Oceansof Opportunity-EWEAOffshoreReport2009, EWEA, 2009. [5] S.Breton,G.Moe,Status,plansandtechnologies foroffshorewindturbinesinEuropeandNorth America, Renewable Energy, Vol. 34, No. 3, 2009, pp. 646-654. [6]J.Hinnethal,G.Clauss,RobustPareto-optimum routingofshipsutilisingdeterministicand ensembleweatherforecasts,ShipsandOffshore Structures, Vol. 5, No. 2, 2010. [7]T. Luhmann, Steuerung von Offshore-Windparks DasintegrierteLeitsystemfrAlphaVentus, http://www.btc-ag.com, 17.08.2010. [8]P.Kall, J. Mayer, StochasticLinear Programming, Springer, 2005. [9] S.Sen.Stochasticprogramming:Computatinal issuesandchallenges.In:S.GassandC.Harris, editors,EncyclopediaofOR/MS.Kluwer Academic Publishers, 2001. [10]N. V.Sahinidis,I. E.Grossmann,Reformulation ofthemultiperiodmilpmodelforcapacity expansionofchemicalprocesses,Operations Research, Vol. 40, 1992, pp. 127144. [11]B.Scholz-Reiter,J.Heger,T.Hildebrandt, AnalysisandComparisonofDispatchingRule-BasedSchedulinginDualResourceConstrained Shop-FloorScenarios,MachineLearningand Systems Engineering, 2010, (accepted, to appear). [12]T.Achterberg,ConstraintIntegerProgramming, TU Berlin, Thesis, 2006. [13]J.C.-H.Pan,J.-S.Chen.Mixedbinaryinteger programmingformulationsforthereentrantjob shopschedulingproblem.Computers& OperationsResearch,Vol.32No.5,2005,pp. 11971212. weekmed. weatherbad weathertop-structuresub-structureloading set 1loading set 27 8 9 10 1 2 3 4 5 6ADVANCES in MATHEMATICAL and COMPUTATIONAL METHODSISSN: 1792-6114 247 ISBN: 978-960-474-243-1