A simulation-based decision model for

ContentslistsavailableatScienceDirectBuildingandEnvironmentjournalhomepage:www.elsevier.com/locate/buildenvAsimulation-baseddecisionmodelfordesigningcontractperiodinbuildingenergyperformancecontractingQianliDenga,LimaoZhanga,b,1,*,QingbinCuia,XianglinJiangcaDepartmentofCivil&EnvironmentalEngineering,UniversityofMaryland,CollegePark,MD20742-3021,USASchoolofCivilEngineering&Mechanics,HuazhongUniversityofScienceandTechnology,Wuhan,Hubei430074,PRChinacInstituteforFinancialStudies,FudanUniversity,HandanRoad220,Shanghai200433,PRChinabarticleinfoArticlehistory:Received24June2013Receivedinrevisedform5September2013Accepted7September2013Keywords:EnergyperformancecontractingContractperiodCostsavingsguaranteeUncertaintymodelingOptimizationabstractThispaperpresentsasimulation-baseddecisionmodelforcontractperioddeterminationinEnergyPerformanceContracting(EPC).ThemodelattemptstoassisttheEnergyServiceCompanies(ESCOs)onhowlongthecontractperiodshouldbetobalancethebiddingcompetitivenessandthepotentialrev-enueloss.Theuncertaintieswithintheenergyefficiencyinvestmentandtheenergycostsavingsasreturnareaddressedbystochasticprocesses,takingthemaintenanceandsavingsperformancevaria-tionsandtheenergypricefluctuationsintoaccount.Consideringboththecontractperiodandtheenergycostsavingsguarantee,aframeworkisproposedtoidentifytheprofitsharinginEPCforboththeownersandtheESCOs.Anoptimizationmodelisderivedaccordingly,andthebalancedlengthofthecontractperiodisthenreached.Finally,acampuscaseispresentedtoverifytheapplicabilityoftheproposedmodel.Themethodcanbeusedbyindustrypractitionersasadecisionsupporttoolforcontractperioddesign,andisworthpopularizinginotherperformance-basedprojects.PublishedbyElsevierLtd.1.IntroductionPerformance-basedcontracting,whichbuysperformancethroughanintegratedacquisitionandlogisticsprocessdeliveringimprovedcapabilitytoarangeofproductsandservices,isgrowinginpopularityaroundtheworld.Industrialsectors,suchascom-mercialshipping,publictransport,healthservices,andenergygeneration,adopttheperformance-basedcontractingframeworkscommonly.Followingthegeneralperformance-basedcontractingmode,EnergyPerformanceContracting(EPC)emergedinNorthAmericainthe1970safterthefirstoilcrisis[1],andshowsaremarkablegrowthtrendinrecentyears[2,3].EPCutilizesthefutureenergysavingsrevenuestorepaytheinitialenergyefficiencyinvestment.Duringthecontractperiod,theEnergyServiceCom-panies(ESCOs)getsharedprofitsfromtheregularsavingsofutilitybills,andthefacilityownersupgradetheagingandinefficientas-setswithoutcapitalinvestment[4].SinceEPChasencouragedtheESCOtodevelopmoredesirableenergyefficientsolutions,thewell-designedprovisions,suchasthecontractperiod,wouldgoastepfurthertounitetheownerandthe*Correspondingauthor.Tel.:þ12022854227.E-mailaddress:limao_zhang@hotmail.com(L.Zhang).1Ph.D.CandidateatHuazhongUniversityofScienceandTechnology,andVisitingScholaratUniversityofMaryland,CollegePark,USA.0360-1323/$eseefrontmatterPublishedbyElsevierLtd.http://dx.doi.org/10.1016/j.buildenv.2013.09.010ESCOforasharedprofitgoal[5].Withinthecontractperiod,theESCOtakescareoftheoperationandmaintenance(O&M)activitiesfortheenergyconservationmeasuresand,atthesametime,holdsthemajorpartoftheenergycostsavingsasreturn.Afterthecon-tractperiod,theESCOleavesandboththeO&Mcostandthesav-ingsrevenuewouldbeheldbytheowner.Duetothecomplexityindynamicprojectenvironments,thelengthofthecontractperiodhasasignificantimpactontherisksallocationandbenefitssharing.Theenergycostsavingsproducedbytheenergyprojectmustbesufficienttocoverallprojectrelatedcostsoverthecontractperiodfromboththeowner’sandtheESCO’sperspectives.Thus,thelengthofthecontractperioddeterminediscriticalforboththeownersandtheESCOsconcerningtheEPCsuccess.However,tradeoffsexistinthecontractperioddecision-makingofEPC.Ingeneral,theESCOsprefertosignacontractwithalongercontractingtermasmoreprofitcanbemadeovertime.Buttheownersarelikelytoshortenthecontractperiodtoareasonablelength,soastoguaranteetheirprojectrightsandinterestsafterthewell-equippedfacilitytransferred.Also,theESCOsneedtomakecompetitiveofferconcerningtheshortercontractperiodtowinthebidding.HowtodeterminethecontractingtermbecomesacriticalissueinthenegotiationsbetweentheownersandtheESCOs.Be-sides,thereareotherlimits.AccordingtotheEnergyPolicyAct[6],thewholecontractperiodofEPCshallnotexceed20yearstoallowlongerpaybackperiodsforretrofits,includingwindows,heating72Q.Dengetal./BuildingandEnvironment71(2014)71e80

systemreplacements,wallinsulation,site-basedgeneration,advancedenergysavingstechnologies,andotherretrofits.StatesandlocalauthoritieshavealsoissuedlegislationontheEPCdura-tion.Forinstance,themaximumenergyperformancecontractperiodforNewJerseyis10years,NorthCarolina,12years,Mary-land,15years,andFlorida,20years.Therefore,thecontractperiodinEPCshouldbeneithertoolongnortooshortaccordingtotheestimation.Owingtotheabsenceofauniversallyacceptedstandard,howtodeterminethelengthofthecontractperiodonawinewinbasishasnotbeenagreeduponintheEPCmarket.Toalargeextent,thefutureO&Mcost,theunknownenergyconservationmeasureper-formance,andthefluctuatedenergyprice,areconsideredasthemainuncertaintiesthataffecttheprojectsuccessinEPC.Asaresult,mismatchesbetweentheestimatedandtheobservedprojectper-formancecommonlyariseinindustrialpractice[5].Inthispaper,theuncertaintieswithintheenergyperformanceduringthecon-tractperiodofEPCaremodeledintwoseparatestochasticpro-cesses,namelytheannualenergysavingsamountandtheenergyprice.Aframeworkconcerningthesharedenergysavingsrevenuesisproposed,andtheowners’andtheESCOs’profitsarethenderivedrespectivelyduringthecontractperiod.AnoptimizationmodelforthecontractperioddesigninEPCisstructuredtoaddressthepotentialrisksonawinewinbasis.Asimulation-baseddecisionapproachwithquantitativeanalysisisthendevelopedtodeterminehowlongthecontractperiodshouldbeinordertobalancetheprofitexpectationsforboththeownersandtheESCOs.Thispaperisorganizedasfollows:therelatedstudiesonthedeterminationofthecontractlengtharereviewedinSection2.Section3modelstheuncertaintiesinenergysavingsperformanceonasimulationbasis,withtheenergyefficiencyinvestment,theenergysavingsinstabilityandtheenergypricefluctuationtakenintoaccount.InSection4,adecisionmodelwithquantitativeanalysisisdevelopedtodeterminehowlongthecontractperiodshouldexactlybe.InSection5,acampuscaseisusedtoverifytheapplicabilityoftheproposedapproachforthecontractperioddetermination.Finally,theconclusionsaredrawninSection6.2.LiteraturereviewInrecentyears,performance-basedcontractingframeworkshavebecomemoreandmorepopularinsocialwelfareprograms[7],publichealth[8],public-privatepartnership(PPP)[9,10],andenergysectors[11].AsanalternativefinancingmechanismauthorizedbytheUnitedStatesCongress,EPCisclassifiedasoneoftheperformance-basedcontractingformswhichfocusesondevelopingstrategicperformancemetricsanddirectlyrelatingcontractingpaymentthroughincentivized,long-termcontractswithspecificandmeasurablelevelsofoperationalperformance[12].Thus,EPCisintendedtoacceleratetheinvestmentincost-effectiveenergyconservationmeasuresofexistingbuildings[13].AsatypicalEPC,theESCOsprovideturnkeyservicesincludinginvestigating,designing,financing,andrenovatingthoseagingandinefficientassetswithmultipleenergyconservationmeasures[14].Duringthecontractperiod,theESCOsguaranteethattheim-provementscouldgeneratesufficientenergycostsavingstopayfortheprojectinvestment.Afterthecontractperiod,theremainingcostsavingsareattributedtotheowners.BasedontheperformanceguaranteesofferedbytheESCOs,technicalrisksaretransferredfromtheownerstotheESCOs.TheESCO’sremunerationisbasedonthedemonstratedenergyperformance.Essentially,theESCOswillnotreceivepaymentunlesstheprojectdeliverstheenergycostsavingsasexpected.Ingeneral,manychallengesandproblemshavebeenencoun-teredwhichaffectsatisfiedperformanceachievementduetotheuncertaintiesandunforeseenrisksoveralongcontractperiod,typicallymorethan10years.AccordingtoGhoshetal.[15],theambiguityregardingrealizationofestimatedsavingswasrankedasoneofthehighestmarketbarriersfortheadoptionofEPCintheprivatebuildingsector.HowtodeterminethecontractingtermbecomesacriticalissueinthenegotiationsbetweentheownersandtheESCOs,whichmightaffectthepromotionanddevelopmentoftheEPCintheenergysavingmarket[13].Duetothelimitedpreviousresearch,identifyingthedecision-makingprocessofthecontractlengthinotherperformance-basedcontractinggivessomereferences.AccordingtoZhangandAbouRizk[16],acontractperiodisdefinedasthetimespanwhichincludesaconstructionperiodandanoperationperiod,duringwhichthecontractorhastherighttocommerciallyoperatethefacilityorservice,beforeitistransferredbacktotheownerorgovernment[17].Thecontractperiodisvitaltothesuccess,sinceitdirectlyaffectstheinterestsandrisksofboththeinvolvedparties.Areasonablelengthofthecontractperiodcanhelptoalleviatethefinancialriskforboththecontractorandtheowner,sothattheycouldreachtheirexpectedinvestmentreturnswithintheoperationperiod.YuandLam[18]indicatedthatthedeterminationofthecontractlengthisacom-plexproblem,duetothenatureoftheproblem,suchassubjectivity,non-linearity,andmulti-criteria.Forsimplicity,thecontractperiodispresettoafixedlengthinsomeearlycases,particularlyingovernment-investedprojects.Forinstance,thefirsteightDesign-Build-Finance-Operate(DBFO)roadsintheUnitedKingdom[19]andthefiveBuild-Operate-Transfer(BOT)tunnelprojectsinHongKong[20]allhada30-yeargovernment-presetcontractperiod,eventhoughthephysicallength,designcapacity,trafficdemand,constructiontimeandconstructioncosts,arequitedifferentforeachproject[21].However,thetraditionalpracticeoffixingtheconcessioninadvancedoesnotgenerallyleadtoanefficientso-lutionduetothepotentialfinancial,economic,andsocialproblemswithoutsufficientjustification[22].Failuresortherenegotiationofconcessioncontractsfrequentlyoccurredovertheoperationalperiodintheaboveprojects.Tosolvethisproblem,scholarsadoptedvariousresearchmethods,suchasthenetpresentvalue(NPV),thepaybackperiod[23],theNPV-at-riskmethod[24],NPV-basedconcessionmodels,bargaining-gametheory,andsimulationtechniques[18].Asoneofthecommonlyusedinvestmentevaluationmethods,theNPV-at-riskmethod[24]isformedbythecombinationoftheweightedaveragecostofcapitalanddualrisk-returnmethods.ComparedwiththetraditionalNPVmethod,theNPV-at-riskmethodrequirestheprobabilitydistributionsofvariables,whereasthosearehardtoevaluateinreality.Hence,thismethodisusefulinassistingrela-tivelysimpledecision-makingintheinvestmentevaluationforprivatelyfinancedinfrastructureprojects.Actually,theuncertainfactorsaremostlikelytoaltertheprojectperformanceandfuturecashflowwithinthecontractperiod[25].Toaddresstheinevitableuncertainties,thesimulationmodelingapproachprovidesapowerfultoolforstochasticmodelingprocessandriskallocationinuncertainenvironments[26,27].Simulationistheimitationoftheoperationofareal-worldprocessorsystemovertime,andcanbeusedtomeasureandevaluateconstructionandeconomicun-certaintiesandrisks[28].Inthepast10years,thesimulationtechniqueshaveextendedfromcomputersciencetodecision-makingandoptimizationinconstructionfields[29,30].ShenandWu[31]proposedaMonteCarlosimulationapproachfortheconcessionperioddeterminationofaBOTproject,withthestim-ulatedvaluesofriskfactorsconsidered,suchasNPV,capitalin-vestment,tollprice,anddiscountrate.Ngetal.[32]alsodevelopedasimulationmodeltoassistthepublicpartnertodeterminetheoptimalcontractperiod,withtheuncertainparameters,suchasthecost,operationrevenue,andincome.Zhang[18]proposedawineQ.Dengetal./BuildingandEnvironment71(2014)71e8073

winconcessionperioddeterminationmethodology,inwhichBOTprojectswereaddressedasaprincipal-agentmaximizationprob-lem.Bothdeterministicandsimulation-basedmethodsarepro-videdtodeterminetheconcessionperiod.YuandLam[33]developedadecisionsupportsystemforthedeterminationofconcessionperiodlengthintransportationprojectunderBOTcontract,withtheimpactofinfluentialfactorstakenintoaccount.Ingeneral,thedeterminationofthecontractperiodlengthisregardedasacomplicatedproblemincorporatingvariousinfluen-tialfactorslikethefluctuationoffuturemarkets.Eachmethodhasitsprosandcons,withregardtothedifferentpurposesofapplication.Movingtheexistingresearchforward,theuncertaintiesunder-lyingtheinfluentialfactorsarecloselyrelatedtothecontractperioddetermination,andfurtheraffectthefinalprofitachievementamongparticipatingparties.InregardtoEPC,itischaracterizedasalong-termacquisitionofenergyefficiencyperformanceservices,associatedwiththeannualenergyefficiencyinvestmentandtheguaranteedenergycostsavings.Tobespecific,ESCOswouldreimbursetheownersifthereisashortfallintheactualenergysavingscomparedwiththeguaranteedsavings,andsharetheexcessrevenueatapredefinedpercentageifexceedstheguaran-teedsavings.Accordingly,thoseaddedprofitsharingspecificationsincreasethecomplexityandchallengeindeterminingabalancedcontractperiod.Theaforementioneddeterminationmethodscanprovidevaluablereferencesforapossiblewayofsolvingthecon-tractperiodprobleminEPC,however,fewstudieshaveinvesti-gatedtheproblemonthedeterminationofthecontractperiodlengthinEPC.Incurrentcases,thecontractperiodsinEPCaremostlydeterminedbasedonempiricalestimation,ratherthanquantitativeanalysis.Thus,theoutcomesmightdiffersignificantlyfromtheverifiedperformance[18].Inordertoconductareason-ablecontractperiodinEPC,theinvestmentmechanismofEPCisaddressedinthisresearch,withthecontractperiodandtheenergycostsavingsguaranteetakenintoaccount.Theuncertaintiesun-derlyingtheinfluentialfactorsaresimulatedstochasticallyovertime,andthenanalyzedandincorporatedintothedeterminationofthecontractlengthinordertodecomposetheperformanceun-certainties.Finally,adecisionmethodwithdetailedstep-by-stepprocedureisdevelopedtocalculatehowlongthewinewincon-tractperiodshouldbeinEPC,providingaquantitativebasisforthecontractnegotiationbetweentheownersandESCOs.3.EnergyperformancesimulationEnergyperformanceestimationplaysanessentialroleinthesuccessofanEPCprojectforeithertheownerortheESCO.Severalfactorsareinvolvedwhichaffecttherealenergyperformance,includingtheenergyefficiencyinvestment,energysavingsamount,aswellastheenergymarketprices.Incurrentindustrialpractices,mostenergyperformanceestimationsaredeterministiconthebasisofexperience,regardlessoftheinfluenceofthepotentialuncertaintieswithintheaforementionedfactors.Thus,inthissec-tion,thestochasticenergyperformanceestimationmodelispro-posedusingthesimulationtechniques,withthedrifttrendsandthepotentialvolatilitiesforboththeenergyefficiencyinvestmentandtheenergycostsavingstakenintoconsideration.3.1.EnergyefficiencyinvestmentThelargeenergysavingspotentialsetthestageforaconsider-ableincreaseinenergyefficiencyinvestmentsoveryears.SincetheESCOsareresponsibleforobtainingprojectfinanceinmostEPCcases,theenergyefficiencyinvestmentwouldbeconsideredasaninternalallocationoffunds.Toolowaninvestmentmightnotyieldadequatefuturecashflowthatwouldbeusedtopayfortheprojectinvestmentdebt,whiletoohighaninvestmentmightreachthemaximumenergysavingslimitandnottakegoodadvantageofeverydollarinvested.Consideringtheirreversiblenatureofenergyefficiencyinvestments,acost-effectivewayforinvestmentdecision-makingisneededinthedesignstageoftheenergyeffi-ciencytechnologiesselection.Asaresult,theenergyperformancecontractingmightbeacomplexcontractualarrangementbetweentheownersandtheESCOs.AccordingtothemeasurementandverificationpracticeoftheESCOs,theenergysavingsachievedwithinthetermofthecontractareeitherreportedonayearlybasisorcalculatedasanannualaverage[34].Typically,performance-basedprojectinvestmentcouldbedividedintotwoparts.Acapitalcostbudgetisusedforthefundingtopayofflong-termdebtandtheacquisitionoffixedassetsandwhererepaymenttypicallyextendsbeyondoneoperatingperiod.Incontrast,operatingcostsarethosegeneralexpensesthatareincurredoverthecourseofoneoperatingperiod,suchassal-ariesorsupplybills.InEPC,therepaymentofthebankdebtcouldbeconsideredasthecapitalcost,whereaspayingsalariesoftheO&MengineerscouldbeconsideredastheO&Mcosts,asseeninEq.(1).Herein,Nrepresentstheeconomiclifetimeofthewholeenergyefficiencysystems.Fromtheenergyefficiencyprojectperspective,theinvestmentisdenotedbyI(t),wheret¼0,1,.,N;thecapitalcostisdenotedbyICthatoccursatyear0;andtheO&McostisdenotedbyIOM(t),wheret¼1,2,.,N.󰀁IðtÞ¼It¼0ICOMðtÞt¼1;2;.;N(1)ThehighercapitalcostsICaremorelikelytoresultinthehigherO&McostIOM.Astimegoesby,thedeteriorationandthefailureofenergyefficiencymeasuresmightcausetheO&Mcostincreasing.Thus,theinnerrelationsbetweenICandIOMarerepresentedbyEq.(2).IOMðtÞ¼dtÀ1HðtÞIC;t¼1;2;.;N(2)wheredistheO&Mcostcoefficientandd>1.{H(t):t¼0,1,.,N}isastochasticprocessthatH(t)standsfortheO&Mcostcoefficient.GeometricBrownianmotion(GBM)process,whichfocusesonthepercentagechanges,arecommonlyusedinuncertaintymodelingwhichsharestherandomandstatisticalnatureofthemotions[35].Hereweassume{H(t):t¼0,1,.,N}followsGBMwithnodrifteffect,asshowninEqs.(3)and(4).dHtisanincrementalchangeduringashortperioddt;dWH(t)istheBrownianmotiondWðtÞ¼3pffiffiffiffiffithatHHdt,where3HwN(0,1).{sH(t):t¼1,2,.,N}isthevolatilityparameterofthesavingsquantity,andH0istheinitialvalueoftheunittimeenergysavingscoefficient.dHt¼sHtHtdWHðtÞ;t¼1;2;.;N(3)s2Ht¼H0eÀHt2tþspffiHt3Ht;t¼1;2;.;N(4)3.2.EnergycostsavingsTheenergycostsavings,regardedasprojectreturns,aretiedtotheenergyefficiencyinvestments.Beforeintroducingthesimula-tionmodel,twoassumptionshavebeenmadeastheprerequisites:1)Variationsoftheannualenergycostsavingsaremainlyattrib-utedbytheenergysavingsamountandtheenergyprice.Thoughotherriskfactors,suchastheweatherconditions,thevariedhumanoperations,therandomoccupancies,andthegovernmentmacro-74Q.Dengetal./BuildingandEnvironment71(2014)71e80

Fig.1.Proposedframeworkofthecontractperioddecisionmodel.

controlpolicymightaffecttheannualcostsavingsrevenue,inthisstudy,theyaretakenascontrolledandcorrectedthroughthemeasurementandverificationprocess;and2)Thefutureenergysavingsamountispositivelycorrelatedtotheprojectinitialin-vestment.Boththevariationoftheenergyconservationperfor-manceandthefluctuationsofenergymarketpriceareconsideredinthismodel.Thediscrete-timestochasticprocessoftheannualenergycostsavingsisdenotedby{R(t):t¼0,1,.,N},whichisalsotheannualprojectrevenue.Since{R(t):t¼0,1,.,N}iscomprisedoftheselectedmajorfactors,namelytheannualenergysavingsamount{Q(t):t¼0,1,.,N}andtheannualenergymarketprice{PE(t):t¼0,1,.,N},Eq.(5)isderivedaccordingly.decreasinggraduallyduetotheageinganddeteriorationsoftheenergyconservationmeasures.󰀁QðtÞ¼0ICKðtÞt¼0½lnðNÀtÞÀ1󰀃t¼1;2;.;N(6)RðtÞ¼QðtÞPEðtÞt¼0;1;2;.;N(5)wheretheenergycostsavingsR(t)equalstotheamountofenergysavedQ(t),multipliedbytheenergymarketpricePE(t)foraspecificyeart.Asaresult,simulationoftheenergycostsavingsevolutionprocess{R(t):t¼0,1,.,N}couldbederivedfromthesimulationsoftheenergysavingsamountevolutionprocess{Q(t):t¼0,1,.,N}andtheenergypriceevolutionprocess{PE(t):t¼0,1,.,N}.3.2.1.EnergysavingsamountDifferentenergyefficiencyinvestmentswouldresultincorre-spondinglydifferentenergysavingsamounts.Beforesigningthecontract,system-designengineersevaluatetheenergyefficiencyconditionsfortheselectedbuildingsanddrafttheenergyconser-vationmeasurementplan.Then,investmentschemesareestab-lishedaccordingly.Generally,commoditieswithhigherpricesareexpectedtoprovidegreaterutilityvalueorbetterperformance.Asaresult,thehigherenergyefficiencyinvestment,especiallythecapitalinvestmentIC,isexpectedtogivethehigherenergysavingsamountQasareturn,andviceversa.Here,theannualenergysavingsamountismodeledasEq.(6)indicates.Twoassumptionsareinvolvedinthisenergysavingsamountmodel:1)Thecapitalinvestmentwouldpositivelyaffectthevolumeofenergysavedintheoperationperiod;2)Theannualenergysavingsamountiswhere{Q(t):t¼0,1,2,.,N}standsfortheevolutionaryprocessofenergysavingsamount;ICstandsforthecapitalcost;K(t)standsfortheenergysavingsamountcoefficientthat{K(t):t¼0,1,.,N}evolvesovertimeasarisk-neutralprocess.Wealsoassume{K(t):t¼0,1,.,N}followsGBMwithoutdrifteffect,asseeninEqs.(7)and(8),wheredKtisanincrementalchangeinthetotalenergysavingsquantityduringashortpperioddt;dWK(t)istheBrownianffiffiffiffiffimotionthatdWKðtÞ¼3Kdt,3KwN(0,1).where{sK(t):t¼1,2,.,N}isthevolatilityparametersofthesavingsquantity,andK0istheinitialvalueoftheunittimeenergysavingscoefficient.dKt¼sKtKtdWKðtÞ;Às2Kt2t¼1;2;.;N(7)Kt¼K0epffitþsKt3Kt;t¼1;2;.;N(8)3.2.2.EnergypriceSimilartogeneralcommodityprices,theenergypricesfluctuaterandomlyinmarkets.Sincemanycountriesaroundtheworldinitiatetoswitchthepowerindustryfromacentralizedoperationalapproachtoacompetitiveone,theenergypricingbeginstobesetthroughbidsandoffersfollowingthesupplyanddemandprinci-ples.Takingtheelectricpowersupplyasanexample,thepublicserviceisgraduallyreplacedbythecompetitivemarket,whichisamoreefficientmechanismfortheenergysupplywithhighreli-abilityandlowcost.InUnitedStates,energymarketsarealsodrivenprimarilybythefundamentaleconomicinteractionsofsupplyanddemand(EIA,2009).Therefore,uncertaintiesandQ.Dengetal./BuildingandEnvironment71(2014)71e8075

randomnessexistintheenergypricemodeling.CortazarandSchwartz[36]proposedanearlyoilpricingmodelthatwasbasedonGBMasacomponentofanexercisetopriceanaturalresourceinvestment.Sezgenetal.[37]alsousedthemodifiedGBMtodescribetheelectricitypricingevolutionprocess.Duetothesto-chasticnatureofenergyprices,thisstudyalsoadoptsGBMtodescribetheevolutionprocesswithinthetermofthecontract.Eq.(9)representstheenergymarketprice{PE(t):t¼0,1,.,N}thatevolvesasarisk-neutralprocess.PE0istheinitialvalueoftheen-ergymarketprice.Eq.(10)isderivedfromEq.(9),andEq.(11)isderivedfromEq.(10).dPEt¼aEtPEtdtþsEtPEtdWPðtÞ;t¼1;2;.;N(9) dlnPEt¼aEtÀs2!Et2dtþsEtdWPðtÞ;t¼1;2;.;N(10)󰀄s2󰀅EtPEtÀ2tþspEt3PffitEt¼PE0ea;t¼1;2;.;N(11)wheredPEtstandsfortheincrementalchangeintheenergypricewithinashortperiodofdt;dWP(t)isaBrownianmotiondWpffiffiffiffiffithatPðtÞ¼3Pdt,where3PwN(0,1).DuetothecharacteristicsofGBM,Eq.(11)isusedforthesamplepathsimulationoftheenergyprice{PE(t):t¼0,1,.,N}.InputsofEq.(11)aretheinitialenergypriceatyear0,PE0,theannualpricedrifteffect,aEt,andtheannualpricevolatilityeffect,sEt.Both{aE(t):t¼1,2,.,N}and{sE(t):t¼1,2,.,N}arederivedstatisticallybaseduponthehistoricalrecordofpastenergyprices.DifferentstochasticmodelscouldalsobeenappliedtotheevolutionprocessesofaE(t)andsE(t)accordingtothespecificeconomicenvironment.4.AdecisionmodelforcontractperioddeterminationBasedontheenergyperformanceestimation,howtoobtainareasonableanddesirablecontractlengthhasbeenraisedasatradeoffquestion.Duringtheperiod,thegeneratedNPVisneededtosatisfytherequirementsofboththeownersandtheESCOs.TheESCOsprefertosignacontractwithalongercontractperiod,whiletheownersaremorelikelytoshortenthecontractlengthsoastoguaranteetheirowninterest.Thus,thedevelopedcontractperioddeterminationmodelisnotmeanttoachievethehighestprofitforeitherparticipant,theownerortheESCO,ratheritismeanttoachieveabalancebetweenthetwoextremeswithinthesamedecision-makingprocess.Therefore,adecisionsupportmodelforthecontractperioddesignisdevelopedinvolvingboththeownersandtheESCOs’consideration.ThecontractlengthisthenselectedafterbalancingtheinterestsofboththeownersandtheESCOs.4.1.FrameworkAgeneralframeworkforthecontractperioddeterminationmodelisshowninFig.1.Accordingly,theprofitNPVestimationprocessisdividedintothreesequentialsteps:1)savingsperfor-mancesimulation(Section3);2)contractspecification;and3)energysavingsprofitsharing(Section4.2).ForStepI,theenergysavingsperformanceestimationisfromthegeneralEPCperspec-tive.Uncertaintieswithintheenergyefficiencyinvestment,theenergysavingsamountandtheenergypricesareinvolved.ForStepII,thecontractdesignismadethroughthenegotiationsoftheownersandtheESCOs,includingtheperformance-basedcontractperiodandtheannualcostsavingsguarantee.Thosespecificationssomehowensurethesavingsaresufficienttopayforthefullcostofthelong-termprojectfinancing.BasedonStepIandII,StepIIIβSt−GβFig.2.DivisionsoftheannualenergycostsavingsbetweentheownersandtheESCOs.

displaystheenergyperformancesimulationfromboththeownersandtheESCOsperspectives.Theseparatedenergyefficiencyin-vestmentsandtheenergycostsavingsreturnscouldderivetheowner’sprofitNPVOandtheESCO’sprofitNPVErespectively.Optimizationmodelforthebalancedcontractperiodisthendevelopedaccordingly.4.2.SharedprojectprofitAsFig.1indicates,threestepsareneededforthesharedenergyefficiencyperformancecalculationfromboththeownersandtheESCOs’perspectives:thesharedenergyefficiencyinvestment,thesharedenergycostsavings,andthesharedprofitnetpresentvalue.4.2.1.SharedenergyefficiencyinvestmentDistinguishedfromthecapitalcostandtheO&Mcost,onthetimescale,theenergyefficiencyinvestmentcouldbetruncatedintotwoparts,thecontractperiodandafterthecontractperiod.Inmostcases,EPCsarefinanceddirectlywithESCOs.Asaresult,alltheenergyefficiencyinvestmentswithinthecontractperiodincludingboththecapitalcostandpartoftheO&McostsbelongtotheESCOs.Afterthecontractperiod,projectsaredeliveredbacktotheownersandtheremainingO&Mcostswouldbepaidbytheownersthemselves.Therefore,theenergyefficiencycostI(t)isdividedintotwoparts:owner’senergyefficiencyinvestmentIO(t),andESCO’senergyefficiencyinvestmentIE(t),asseeninEqs.(12)e(14).󰀁I0t¼0;1;.;nOðtÞ¼IðtÞt¼nþ1;nþ2;.;N(12)󰀁IEðtÞ¼IðtÞt¼0;1;.;n0t¼nþ1;nþ2;.;N(13)IðtÞ¼IOðtÞþIEðtÞt¼0;1;.;N(14)4.2.2.SharedenergycostsavingsTheachievedannualenergycostsavingswouldbevalidatedbytheaudit.Iftheverifiedsavingsarelessthantheguaranteedsav-ings,theESCOswouldpaytheshortfall.Iftheverifiedsavingsaremorethantheguaranteedsavings,theownersandtheESCOswouldsharetheexcess.Thoughtheformoftheenergysavingsguaranteesvaries,ingeneral,theguaranteeprovidesavehiclefortransferringrevenuerisksfromtheownerstotheESCOs.HereweuseGtodenotetheguaranteedannualenergycostsavings;aand1Àatodenotetheowner’sandtheESCO’srevenuesharewithinthesavingsguarantee;band1Àbtodenotetheowner’sandtheESCO’sexcessrevenuesharebeyondthesavingsguarantee.Tobespecific,threescenariosmightoccur,includingunder-performed76Q.Dengetal./BuildingandEnvironment71(2014)71e80

(StG).ThestructureofthedetailedprojectcostandprofitsharingdivisionisdisplayedinFig.2.Obviously,therevenueuncertaintiesfromtheannualenergysavingsdirectlyaffecttheachievementoftheownerandtheESCO’srevenues.Eqs.(15)and(16)havedefinedtwostochasticprocess{RO(t):t¼0,1,.,N}and{RE(t):t¼0,1,.,N},whereRO(t)standsfortheowner’sannualrevenueandRE(t)standsfortheESCO’sannualrevenuefromEPC.Foraspecificyeart,theenergycostsavingsR(t)equalstotheowner’srevenueRO(t)plustheESCO’srevenueRE(t)asEq.(17)showsbelow.8<0t¼0ROðtÞ¼:aGþmax½0;bðStÀGÞ󰀃t¼1;2;.;n(15)Stt¼nþ1;nþ2;.;N8¼<0t¼0REðtÞ:StÀaGÀmax½0;bðStÀGÞ󰀃t¼1;2;.;n(16)0t¼nþ1;nþ2;.;NRðtÞ¼ROðtÞþREðtÞt¼0;1;.;N(17)4.2.3.SharedprofitNPVNPVanalysishasbeenwidelyusedtomeasuretheexcessorshortfallofcashflowsinpresentvaluetermsoncefinancingchargesaremet[38,39].SincetheownershipwouldbetransferredfromtheESCOstotheownersduringEPC,boththeowner’sandtheESCO’sprofitcouldbedividedintotwoparts,withinthecontractperiodandafterthecontractperiod.Inthefirststage,t¼0,1,.,n,theownerisnotinvolvedintheenergyefficiencyinvestmentandwouldreceivethecontractspecifiedsharingoftheenergycostsavings.Theowner’srevenueisdirectlytransferredtotheprofit.Whileinthesecondstaget¼nþ1,nþ2,.,N,theownerholdsalltheremainingenergycostsavingsrevenueaftertheESCOleavestheprojectaswellastheO&McostoccurredwiththegeneralprojectconditionNPV¼Paccordingly.ComparedNt¼0RðtÞÀIðtÞ=ð1þrpÞtwhererpstandsfortheexpectedprojectrateofreturn,theowner’sandtheESCO’sprojectprofitNPVsaredisplayedinEqs.(18)and(19).NPVXNRO¼OðtÞÀIOðtÞt¼0ð1þrOÞt¼XnaGþmax½0;bðStÀGÞ󰀃XNStÀIðtÞð1þr(18)t¼0OÞtþt¼nþ1ð1þrOÞtNPVXNRE¼EðtÞÀIEðtÞt¼0ð1þrEÞt¼XnStÀaGÀmax½0;bðStÀGÞ󰀃ÀIðtÞt¼0ð1þrEÞt(19)whereNPVOandNPVEstandsforthediscountednetpresentvalueoftheowner’sandtheESCO’sprofitinEPC,respectively;Nstandsforthelifetimeoftheenergyconservationsystemandnstandsforthecontractperiodoftheenergyperformance-basedproject;rOandrEstandfortheowner’sandtheESCO’sex-pectedrateofreturn,respectively.DuetothehigherrisksthattheESCOsentailcomparedwiththeowners,theESCOislikelytorequestahigherrateofreturntocoverthehigherprobabilityoflossesbroughtbyunderperformanceoftheenergycostsavingsguarantee,rE!rO.4.3.OptimizationTobalancetheprofitsharingaccordingtoboththeownersandtheESCOs’expectations,anoptimizationmodelisdesignedfortheESCOstodetermineanappropriatelengthofthecontractperiod.TheoptimizationmodelcouldnotonlyassisttheESCOsdesigntheenergysaving-basedcontract,butalsosupporttheownersinthebiddingselection.Duetotheharshlycompetitiveenvironment,multiplecompaniesusedtoparticipateinbiddingsforoneproject.TheEPCmarketsaremostlybuyers’marketssincetheownershavepurchasedadvantagesovertheESCOs.Asaresult,giveneachESCOparticipatedasabidderreceivingpositiveprofitNPVwithexpectedrateofreturn,theownerschoosethebestofferbidwhichmaxi-mizestheowner’sprofitNPV.Mathematically,themodelisintendedtofindtheappropriateenergyperformancecontractperiodninorderto:MaximizeNPVOSubjectto:NPVE!0(20)Asapopularfinancialtoolforinvestmentanalysis,differentNPVssuggestdifferentinvestmentdecisions.NPV>0meanstheproposedprojectwouldaddvaluetothefirmthatcouldbeaccepted.NPV<0meanstheproposedprojectwoulddeductvaluefromthefirmthatshouldberejected.NPV¼0meanstheprojectwouldneithergainnorlosevalueforthefirm.Inthiscase,theconstraintconditionisthattheESCO’sprofitNPVshouldnotbenegative,NPVE!0,whichguaranteestheESCOtoreceiveprofitwiththeexpectedrateofreturn.Atthesametime,theowner,astheleadingparty,wouldliketochoosethebestofferbidwiththemaximizedprofitNPVfromtheowner’sperspective.BoththeownersandtheESCOscanutilizethismodeltomakebetter-informeddecisionsontheenergyperformancecontractperiod.5.CaseapplicationThecasestudyisconductedinordertoverifytheapplicabilityoftheproposedframeworkforthecontractperioddesign.AccordingtoHopperetal.[4],municipals,universities,schools,hospitals(MUSH)andthefederalgovernmentaccountforabout80%ofthetotalEPCmarket,sincetheseorganizationsaretypicallystarvedforcapitalandmaintenancebudgets.AsoneofthemajorentitiesusingEPCtoobtainenergyefficiencyfacilityimprovements,inthisstudy,auniversitycaseischosentoshowhowtheproposedmethodforthecontractperioddesignwouldbeapplied.Sincethisisarealcasewithsignedcontract,theinvestmenthasalreadybeenmadeatthebeginningofEPC.First,ourproposedmodelisusedtocheckthefinancialreasonablenessoftheenergyefficiencyinvestment.Thenbasedontheanalysis,weanalyzethebalancedcontractperiodaccordingtothevariedcontractspecificationorexteriorvariablesfromboththeownersandtheESCOs’perspectives.Therelationsamongtheenergyefficiencyinvestment,thegeneratedenergycostsavings,andthespecifiedsavingsguaranteearetakenintoconsiderationaccordingly.Improvementsuggestionsarethengivenbasedonthesimulationresultsandtherelatedsensitivityanalysis.5.1.BackgroundMarylandhasinitiatedEPCsince1993withvariedkindsofprojects,suchasmunicipalofficebuildings,firestations,andwastewatertreatmentplants.Asaresult,therelativelymatureEPCmechanismshaveformedlocally.FortheselectedEPCcase,theUniversityofMarylandcampuscommunityadoptedEPCinordertoQ.Dengetal./BuildingandEnvironment71(2014)7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Table1Definitionsoftheparametersandnumericalvaluesforthecase.ParametersSymbolsValuesEconomiclifetimeoftheenergyN25yearsefficiencysystemCapitalcostoftheenergyefficiencyIC$20,668,991investmentDepreciationcoefficientd1.05InitialvalueoftheO&McostcoefficientH00.05VolatilityoftheO&McostcoefficientsH0.25InitialvalueoftheenergysavingsK00.004amountcoefficientVolatilityoftheenergysavingsamountsK0.01coefficientInitialvalueoftheenergypricePE0$26,025permillionBtuEnergypricedrifteffectaE0.0523EnergypricevolatilityeffectsE0.0856AnnualenergycostsavingsguaranteeG$3,000,000Owners’expectedrevenuesharewithina5%theguaranteeESCOs’expectedrevenuesharewithin1Àa95%theguaranteeOwners’excessrevenuesharebeyondb20%theguaranteeESCOs’excessrevenuesharebeyond1Àb80%theguaranteeOwners’expectedrateofreturnrO8%ESCOs’expectedrateofreturnrE15%developacarbon-neutralandresource-efficientcampusinfra-structure.BeforeEPC,about75%ofthebuildingsontheUniversityofMarylandareolderthan25yearswithanaverageageof40years.Since2009,multipleenergyconservationmeasuressuchaslightingupdating,waterconservation,buildingenvelope,buildingcontrols,andwindowreplacementshavebeenconducted.Thesignedcon-tractperiodis13yearsandabout22%ofenergyconsumptionreductionwouldbereachedforeachyear.Theestimatedenergyefficiencycapitalinvestmentis$20.67millionandtheannualcostsavingofthestartingyearis$1,904,343.DetailedinformationofthecaseparametersislistedinTable1.Allthevaluesusedherearedefinedasthegeneralformsofenergyefficiencymix.Inputscouldbeupdatedaccordingtothespecificenergyconservationmeasures.EconomiclifetimeoftheenergyefficiencysystemNareobtainedfromtheenergyefficiencyfacilitytechnicalreportsandthesystemengineers’subjectiveestimation.Thevaluesoftheparameters(d,IC,H0,sH)areusedforsimulatingtheenergyefficiencyinvestmentIand(IC,K0,sK)areusedforsimulatingtheenergysavingsamountQ.TosimulatethefutureenergypricePE,(PE0,aE,sE)arederivedbasedonthepast15-yearhistoricalenergypricerecordofMaryland[40].HereweassumeaEandsEareconstantinthemodelforcalculationsimplification.Otherparameters(G,a,1Àa,b,1Àb)areobtainedfromtheenergysavingsguaranteeincontractand(rO,rE)areobtainedbasedonthestakeholders’expectationandtheeconomicenvironment.5.2.ResultsanalysisDuetothecomplexityforobtainingtheanalyticalsolutionsfortheenergyperformanceestimations,MonteCarlosimulationisconductedinthiscasetoyieldthenumericalsolutionforthediscrete-timemodel.AsSection3indicates,theenergyefficiencyperformancecouldbedecomposedintotwoparts,theenergyef-ficiencyinvestmentandtheenergycostsavingsreturn.SamplepathsofthegeneraldevelopmenttrendaredisplayedinFig.3.Fortheenergyefficiencyinvestment,theinitialcapitalcost,whichoccursinyear0,takesasthebiggestinvestmentamountattheEPCstart.Then,theannualO&McostincreasesgraduallythroughtheFig.3.Samplepathoftheenergyefficiencyprojectperformance.

economiclifetimeoftheenergyefficiencysystemwithfluctuations.Fortheenergycostsavingsreturn,combinationsofthedecreasingtrendofenergysavingsamountandtheincreasingtrendofenergypricesaswellastheuncertaintiesbuildtheenergycostsavingsreturn.Thecostsavingsincreaseswithfluctuationsatthefirstseveralyearsoftheprojectlifetimeandthendecreasegraduallyuntilthesavingsperformancereacheszero.Duetothespecifiedcontractperiod,theownersandtheESCOsneedtodeveloptheirownenergyefficiencyinvestmentandsav-ingsreturnbasedontheprojectperformancerespectively.Takingtheoriginalcontractperiodn¼13yearsasanexample,whichhasbeenspecifiedinthecontract,theownershiptransferenceoccursfromtheESCOstotheownersattheendof13thyear.Accordingly,theenergyefficiencyinvestmentandtheenergycostsavingsreturnforboththeowners’andtheESCOs’partsaredividedintotwostagesrespectively.SamesimulationdatasetsasFig.3areusedinFig.4showingbelow.Theowners’energyefficiencyperformanceismainlyfocusedonthesecondstage,whiletheESCOs’ismainlyfocusedonthefirststage.SincetheESCOsleaveafterprojectde-liveryandtheremainingenergycostsavingsperformanceaswellastheO&Mcosthavebeenheldbytheowners.Whenwerepeatedtheabovesimulationprocessfor100,000times,theprofitNPVdistributionsofboththeownersandtheESCOsarederivedaccordingly.AsFig.5showsbelow,mostcasesoftheproposedEPCdosatisfytheexpectedrateofreturn(NPV>0)forthecontractperiodn¼13years,buttherearestillchancesthatcouldnotsatisfy(NPV<0).Inrealpractice,thoughtheESCOswouldliketosecuretheirprofitNPVspositivewiththeexpectedrateofreturn,thecompetitiveEPCmarketmightmakethemcompromiseonoccasion.Asaresult,theESCOshavetotakepartoftheriskstowinthebidding.ItisreasonabletoassumeboththeownersandtheESCOsjustkeeptheexpectedprofitNPVpositivewithcertainrateofreturnastheconstraints.InordertoanalyzetheexpectedprofitNPV,differentcontractperiodshavebeensetallthroughtheeconomiclifetimeoftheenergyefficiencysystems.Fig.6showstheinnerrelationsamongtheexpectedprojectprofitNPV,theowner’sexpectedprofitNPVandtheESCO’sexpectedprofitNPV.SincetheexpectedprojectprofitNPVonlyrelatestotheprojectprofitablenessitself,itisnotaffectedbyrevenuedivisionbetweentheownersandtheESCOs,Fig.6indicatestheexpectedprojectprofitNPVasaflatline.WhiletheESCO’sexpectedprofitNPVincreasemonotonically,theowner’sexpectedprofitNPVdecreasesmonotonicallyasthecontractperiodincreases.ThisfitstherealindustrysituationthattheESCOsalwaystrytonegotiateforalongercontractperiod,whiletheowners78Q.Dengetal./BuildingandEnvironment71(2014)71e80

Fig.4.Samplepathsofthesharedenergyefficiencyperformancewith13-yearcontractperiod.

struggletoavidthelongerterm.Therefore,theoptimizationmodelinSection4.3isimportanttogiveabasisforfindingthebalancedcontractperiod.AccordingtoFig.6,theoriginalcontractperiod(n¼13years)givesthepositiveexpectedprofitNPVsforboththeownersandtheESCOs(NPVO¼$16,462,759;NPVE¼$1,244,597).ThissatisfiesthemodelconstraintsthatNPVO>0andNPVE>0.Thus,todelivertheprojectattheendofthe13thyearisreasonableforthisEPCcase.However,therewouldbeamorecompetitivechoiceifsettingthecontractperiodasn¼12yearsbeforebidding.TheexpectedprofitNPVsforboththeownersandtheESCOsarealsopositive(NPVO¼$18,065,603;NPVE¼$536,116).Ontheonehand,this12-yearcontractperiodguaranteestheESCOsexpectedprofitthoughtheentireEPC.Ontheotherhand,the12-yearcontractperiodgiveslargerchancesfortheownerstowinthebidincompetition.Therefore,thecontractperiodn¼12yearswouldberecommendedinthiscasebasedonthepro-posedsimulation-baseddesignmodeliftheEPCwasstillreadyforbidding.Tosomeextent,theslightdeviationbetweentheoriginalcontractperiod(n¼13)andtheoptimizedcontractperiod(n¼12)indicatedthattheeffectivenessofmathematicalsimulationmodelingwasvalidatedwithinanacceptablerange.Furthermore,similarim-provementsanalysisonotherEPCscouldalsobeconductedthroughthemodelwithdifferentvaluesoftheparameters.5.3.DiscussionIfwegobeyondtheexistingcontractperioddesigningmodelandfocusonabroadersenseoftheparametersensitivities,severalparameterswouldpotentiallyaffectthebalancedlengthofthecontractperiod,suchasthecapitalcostoftheenergyefficiencyinvestmentIC,theannualenergycostsavingsguarantee(G,a,b),theowners’expectedrateofreturnrO,andtheESCOs’expectedrateofreturnrE.Controllingalltheotherparameters,ifwechangeoneoftheparametersinthecontract,thebalancedcontractperiodmightchangecorrespondingly.Table2displaysthedetailedsensitivityinformation.BasedonTable2,alltheparameterslisted,excepttheowners’expectedrateofreturnrO,wouldaffectthebalancedlengthofthecontractperiod.TheguaranteedannualcostsavingsGhaveanegativeeffectonthecontractperiod,whichmeansthehighertheannualsavingsguaranteed,theshorterthebalancedcontractperiodmightbe.Inthecontrast,otherparameters(IC,a,b,rE)havethepositiveeffect.Itiseasytoexplainintuitivelythateitherthemoreinvestmentmadeorthelessproportionalenergycostsavingsreturnwouldtakelongertimetoberepaidorrepaythecosts.Be-sides,theowners’excessrevenuesharebeyondtheguaranteebissensitivetothebalancedlengthofthecontractperiod.Asaresult,thoughthefactorbisoftenignoredorpaidlessattentioninnegotiation,itwouldbeoneofthecriticalfactorsinthecontractdesign.6.ConclusionsForatypicalEPC,thelengthofthecontractperiodisoneofthemostcriticalfactorsthataretighttoboththeownersandtheESCOs’projectprofitableness.However,tradeoffexistsintheFig.5.Histogramoftheowner’sandtheESCO’sprofitNPVwith13-yearcontractperiod.

Q.Dengetal./BuildingandEnvironment71(2014)71e8079

Fig.6.ProfitNPVfortheproject,theownersandtheESCOsofdifferentcontractperiods.

contractperioddeterminationthatwouldgoneithertoolongtolosebiddingcompetitivenessnortooshorttoincurlargeloanrisks.Sincethecontractperiodismostlydeterminedbyempiricalesti-mation,ratherthanquantitativeanalysis,mismatchesbetweentheestimatedenergysavingsandtheactualobservationscommonlyariseinindustrialpractice.Thispaperpresentsasystematicapproachforthewinewincontractperioddeterminationonaquantitativebasis,attemptingtoinformtheEnergyServiceCom-panies(ESCOs)howlongthecontractperiodshouldbemade.Asimulation-baseddecisionmodelisdevelopedtoaddresstheTable2Sensitivityanalysisoftherelatedparametersonthebalancedcontractperiod.ParameterPercentagechangeAdjustedvalueBalancedcontractperiodICÀ50%10,334,49610À20%16,535,19311020,668,99112þ20%24,802,78912þ50%31,003,48713GÀ20%2,400,00012À10%2,700,0001203,000,00012þ10%3,300,00011þ20%3,600,00011ParameterAdjustedvalueBalancedcontractperioda1%113%115%127%129%13b10%1015%1120%1225%1330%14rO4%126%128%1210%1212%12rE10%812%915%1218%1820%25potentialuncertaintiesexistinginboththeenergyefficiencyin-vestmentandtheenergyefficiencyreturns.Finally,themethodisappliedinauniversitycaseastochecktheproposedcontractperioddesignstrategies.Theresultsdemonstratethefeasibilityoftheproposedmethodanditsapplicationpotentials.Furtherworkcanexpandtootherkindsofperformance-basedprojectsencounteringsimilarsituationswheretradeoffsexistinthecontractperioddetermination,suchasPrivate-PublicPartner-ship,Building-Operate-Transfer,orprincipal-agentprojects.Theinitialinvestmentsofthoseperformance-basedprojectsaretypi-callypaidbackfromthefutureperformancewhereuncertaintiesmightexist.Toaddressthepotentialrisksforthecontractperioddeterminationturnsouttobeimportantwithvariousuncertainfactorsinvolved.Accordingly,thisproposedsystematicapproachforthedeterminationofthecontractperiodlengthwithaquanti-tativeanalysiscouldbeusedbyindustrypractitionersasadecisionsupporttooltoprovideguidelinesforcontractperioddesigninthoseprojects,andtoincreasethelikelihoodofsuccessfulperformance-basedprojectsunderuncertainenvironments.AcknowledgmentTheauthorswouldliketothankthecapitalprojectsdepartmentofUniversityofMarylandfortheirsupportandsharingoftheprojectinformation.Allresultsandconclusionspresentedherearethatoftheauthorsalone.References[1]BrownI.Europeanenergyperformancecontracting.EnergyPolicy1988;16:297e301.[2]HopperN,GoldmanC,GilliganD,SingerTE,BirrD.AsurveyoftheUSESCOIndustry:marketgrowthanddevelopmentfrom2000to2006;2007.[3]SatchwellA,GoldmanC,LarsenP,GilliganD,SingerT.AsurveyoftheUSESCOIndustry:marketgrowthanddevelopmentfrom2008to2011;2010.[4]HopperN,GoldmanC,McWilliamsJ,BirrD,McMordieK.Publicandinstitu-tionalmarketsforESCOservices:comparingprograms,practicesandperfor-mance.Berkeley,CA:ErnestOrlandoLawrenceBerkeleyNationalLaboratory;2005.[5]YikF,LeeW.Partnershipinbuildingenergyperformancecontracting.BuildResInform2004;32:235e43.[6]EnergyPolicyActof2005,Pub.L109-58,119Stat.594.[7]HeinrichCJ,ChoiY.Performance-basedcontractinginsocialwelfarepro-grams.AmRevPublicAdmin2007;37:409e35.[8]ChapinJ,FetterB.Performance-basedcontractinginWisconsinpublichealth:transformingState-Localrelations.MilbankQuarter2002;80:97e124.[9]GrunebergS,HughesW,AncellD.Riskunderperformance-basedcontractingintheUKconstructionsector.ConstructManageEcon2007;25:691e9.[10]HodgeGA,GreveC.Publiceprivatepartnerships:aninternationalperfor-mancereview.PublicAdminRev2007;67:545e58.[11]SteinbergerJK,vanNielJ,BourgD.Profitingfromnegawatts:reducingab-soluteconsumptionandemissionsthroughaperformance-basedenergyeconomy.EnergyPolicy2009;37:361e70.[12]TaylorK,ShaverM.Performance-basedcontracting.Fosteringaccountability:usingevidencetoguideandimprovechildwelfarepolicy;2010.p.291.[13]XuP,ChanEH-W,QianQK.Successfactorsofenergyperformancecontracting(EPC)forsustainablebuildingenergyefficiencyretrofit(BEER)ofhotelbuildingsinChina.EnergyPolicy2011;39:7389e98.[14]ICF,NAESCO.Introductiontoenergyperformancecontracting.ICFInterna-tional;2007.[15]GhoshS,Young-CorbettD,BhattacharjeeS.BarrierstotheuseofESPCintheprivatebuildingsector:perceptionoftheA/E/CCommune.In:47thASCannualinternationalconference.Omaha,NE2011.[16]ZhangX,AbouRizkSM.Determiningareasonableconcessionperiodforpri-vatesectorprovisionofpublicworksandservice.CanJCivilEng2006;33:622e31.[17]OzdoganmID,TalatBirgonulM.Adecisionsupportframeworkforprojectsponsorsintheplanningstageofbuild-operate-transfer(BOT)projects.ConstructManageEcon2000;18:343e53.[18]YuCY,LamKC.ADecisionSupportSystemforthedeterminationofconces-sionperiodlengthintransportationprojectunderBOTcontract.AutomatConstruct2013;31:114e27.[19]ZhangX.Pavingthewayforpubliceprivatepartnershipsininfrastructuredevelopment.JConstructEngManage2005;131:71e80.[20]ZhangX,KumaraswamyM.HongKongexperienceinmanagingBOTprojects.JConstructEngManage2001;127:154e62.80Q.Dengetal./BuildingandEnvironment71(2014)71e80

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