Email marekiiasaacat Abstract Rational decisionmaking requires governance of attainable tradeoffs between con64258icting goals uncertainties and risks which in turn demands both novel modeling methods and appropriate modeling technology The paper de ID: 27785
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1042JOURNAL OF COMPUTERS, VOL. 4, NO. 10, OCTOBER 2009 © 2009 ACADEMY PUBLISHER theproblem;formulateamodeloftheproblem;solvethemodel;testthesolution;andimplementthesolution.Theshortcomingsofsuchanapproacharediscussedinmanyotherpublications,seee.g.,[4]and[7]formoredetails,andhavebeenthemaindrivingforcefordevelopingmethodsofmodelanalysisthatbetterservetheneedsofdecisionmakers.Thebasicfunctionofamodel-basedDecisionSupportSystem(DSS,illustratedinFig.1)istosupporttheuserinndingvaluesforhis/herdecisionvariablesthatwillresultinasolutionoftheproblemthatbesttshis/herpreferences.Acountlessnumberofactualapplicationsshowsthattomeetsuchrequirementsawell-organizedmodelanalysisphaseofthemodelingprocessiscomposedofseveralstages,seee.g.,[4],eachservingdifferentneeds.Thus,notonlyaredifferentformsoftypicallyusedforthesameproblem,butalsodifferentinstancesofeachoftheseformsaredeneduponanalysesofpreviouslyobtainedsolutions.Theanalysisofthemodelinstanceiscomposedofasequenceofsteps,eachofwhichconsistsof:1.Selectionofthetypeofanalysis,andthedenitionofthecorrespondingpreferentialstructure,whichtakesdifferentformsfordifferentmethodsofmodelanalysis,e.g.,for:Classicalsimulation,itiscomposedofgivenvaluesofinputvariables;Softsimulation,itisdenedbydesiredvaluesofdecisionsandbyameasureofthedistancebetweentheactualanddesiredvaluesofdecisions;Singlecriterionoptimization,itisdenedbyase-lectedgoalfunctionandbyoptionaladditionalcon-straintsfortheother(thanthatselectedasthegoalfunction)outcomevariables;Multicriteriamodelanalysis,itisdenedbyanachievementscalarizingfunction,whichrepresentsthetrade-offsbetweenthecriteriausedfortheeval-uationofsolutions.2.Selectionofasuitablesolver,andspecicationofparametersthatwillbepassedtoasolver.3.Generationofacomputationaltaskrepresentingamathematicalprogrammingproblem,thesolutionofwhichbesttstheuserpreferences.4.Monitoringtheprogressofthecomputationaltask,es-peciallyifitrequiresasubstantialamountofcomputingresources.5.Translationoftheresultstoauser-friendlyform.6.Documentingandlingtheresults,andoptionalcom-mentsoftheuser.Variousspecicationsofthepreferentialstructuresup-portdiversiedanalysesofdecisionsproblemaimedat:Suggestingdecisionsforreachingspeciedgoals;Analysesoftrade-offsbetweenconictinggoals;andEvaluationsofconsequencesofdecisionsspeciedbytheuser.ThersttwotypesofanalysesaregoalorientedandarediscussedinSectionIII.Now,webrieycommentonthethirdone,whichfocusesontheanalysisofalternatives.Forlargeproblemsitisdifculttospecifyvaluesofdecisionvariableswithoutapriorknowledgeoffeasiblealternatives,butsuchalternativesolutionsareprovidedbythegoal-orientedmodelanalysis,anduserstypicallyareinterestedinexaminingconsequencesofvariousmodi-cationsofsuchalternatives.Afrequentproblemwithusingtheclassicalsimulationiscausedbyinfeasibilityofthemodieddecisions.Thesoftsimulationmethodsprovidethesamefunctionalitywithouttheriskofgettinginfeasiblesolutions.Severalgeneralizationsofthesoftsimulationareusefulforamorecomprehensivesimulation-typeanalysis.Webrieyoutlinethreeofthem.Therst,calledinversesim-ulation,providessimilarfunctionalityinthespaceofout-comevariables(i.e.theuserspeciesthedesiredvaluesofoutcomevariablesinsteadofthedecisionvariables).Thesecond,calledgeneralizedinversesimulationconsistsofacombinationoftheanalysisprovidedbythesoftandinversesimulations.Finally,thesoftlyconstrainedinversesimulationsupportstheanalysisoftrade-offsbetweengoals(speciedinamoregeneralformasintheinversesimulation)andviolationsofaselectedsetofconstraints(whichareforthispurposetreatedassoftconstraints).However,allthese(andother)generalizationsofthesoftsimulationareinfactspecicapplicationsofthemulticriteriamodelanalysisdiscussedbelow.Amoredetaileddiscussionoftheseissuesisprovidedin[4].III.TOFFSBETWEENTTAINABLEOALSInreality,almostallactualdecisionproblemshavealarge(orinnite)numberofsolutions;theessenceofdecision-makingistoselectoneofthemthatoptimizesthepreferences.Solvingadecision-makingprob-lemasasinglecriterionoptimizationseemstobeveryattractivebecauseofferingauniquesolutionbasedonsolidmathematicalfoundationsisappealing,especiallyifoneconsidersthatanabundantchoice(evenamongdiscretealternatives)typicallycreatesproblems,suchasdissatisfactionorregret,see[8].However,assummarizedabove,thetraditionalORapproachesarebasedontheassumptionthatthebestsolutionofadecisionproblemistheonethatminimizesagivencriterion,e.g.,(2).Thisassumptionisapplicableonlytoaspecicclassofwellstructuredproblems;alreadyover50yearsagoSimon[9]demonstratedthatsuchanassumptioniswrongformostofactualdecisionmakingproblems.Recentstudies,seee.g.,[8],[10]conrmSimon'sresults.Mostdecisionproblemsrequireanactualanalysisofseveralcriteria,whicharetypicallyconicting,e.g.,cost,quality,performance,safety.Criteria(denotedbyaredenedbyselectedoutcomevariables)aretypicallyde-nedindifferentmeasurementunits.Itisusuallypossibletocomputeatleastagoodapproximationoftherangesofvaluesforeachcriterion. Basedonaproperanalysisoftrade-offsbetweencriteria,withoutaprioraggregationofcriteriaintoasingle-criteriongoalfunction. JOURNAL OF COMPUTERS, VOL. 4, NO. 10, OCTOBER 20091035 © 2009 ACADEMY PUBLISHER collectingthedata.Whilealsoforthistypeofproblemsitisstronglyadvisabletofollowprinciplesofstructuredmodeling,conformingtotheseprinciplesispracticallyamustformodel-basedsupportofanycomplexproblem.Westressthatthecomplexityischaracterizedprimarilynotbythesize,butratherbythestructureoftheproblemandbytherequirementsforthecorrespondingmodelingprocess.Here,weoutlinethemodelingprocessbasedontheStructuredModelingTechnology(SMT)[2].SMTisbasedontwosuccessfulparadigms:theStructuredMod-eling(SM)paradigmdevelopedbyGeoffrion[3],whichprovidesaprovenmethodologicalbackground,andtheObject-OrientedProgramming(OOP)paradigmwhich,combinedwithDBMS,XML,andtheWebtechnolo-gies,providesanefcientandrobustimplementationframework.SMTisusedthroughtheWebinterfandallpersistentelementsofthemodelingprocessaremaintainedbyaDBMS.ThustheWebandaDBMSprovideanintegratingframeworkforcollaborativeworkofinterdisciplinaryteamsthatuseSMTapplicationsforvariouselementsofthemodelingprocess.AdetailedpresentationofSMTcanbefoundin[2].HereweonlyoutlinebasicfeaturesofthreeSMTcom-ponents,notincludingtheanalysisoftrade-offsbetweenconictinggoals,whichisdiscussedinSectionIII.1)ModelSpecication:Modelspecicationisasym-bolicdenitionofthemodelcomposedofvariablesandalgebraicrelationsbetweenthem.Inordertoefcientlyhandlelargeandcomplexmodelsthespecicationex-ploitsthepowerofOOPcombinedwithcoreconceptsofSM,suchassets,relations,hierarchy,primitiveandcompoundentities.Primitiveentitieshaveattributesandfunctionscommonforthederivedtypes,namelyparam-eters,variables,andconstraints(representingparametricrelationsbetweenvariables),eachpossessingadditionalattributesspecicforeachofthem.Compoundentitiesarederivedfromthecorrespondingprimitiveentitiesandaccompanyingindexingstructures.2)Data:Dataforlargemodelscomesfromdifferentsources(alsoasresultsfromanalysesofvariousmodels),andlargersubsetsofdataaremaintainedbyteams.SMTexploitstheconceptofDataWarehouse(DW)forsupport-ingpersistencyandefciencyofdatahandling.Thelatterisachievedbydeningabasedataset,andsupportingincrementalmodicationsofthisset(whichallowsforavoidingduplicationsoflargeamountsofdataneededinmoretraditionalapproachesrequiringthestorageofcompletedatasetsevenwhenonlyasmallfractionofthedataismodied).ThedatastructuresofaDWaregeneratedautomati-callyfromthemodelspecication.Thisnotonlyassuresconsistencybetweenthedeclarationsoftheparametersinthemodelspecicationandthedatausedfortheirinstantiations,butalsosavessubstantialresourcesthatwouldotherwisehavebeenneededforpreparingandmaintainingdatastructuresforanycomplexmodel.3)Documentation:SMTexploitstheXMLcapabili-tiesforhandlingthedocumentation.InSMTanXMLdocumenttypeisdenedforenablingasingle-sourcesymbolicmodelspecicationthatcanbeusedforallrelevanttasksofthewholemodelingprocess.Thedoc-umentationofotherelementsofthemodelingprocessisdoneondifferentlevelsofdetail.Thebasicinformation(suchasdate,username,optionsrequestedforeachobjecttobeused)isautomaticallystoredintheDWbyeachSMTapplication.Additionally,auseraccessingaDBwithprivilegesfordatacreationormodicationisaskedtowritecomments,whicharelogged.B.ModelanalysisDevelopmentofapropermodelrepresentationoftherelationsbetweendecisionsandtheirconsequences(out-comes)isobviouslyakeynecessaryconditionforappro-priatesupportofrationaldecision-making.However,ithastobestressedthatthisisnotasufcientcondition:onealsoneedsapropersupportformodelanalysis.Boththeseelementscomplementeachother,andthequalityoftheweakeronedeterminesthequalityofthedecision-makingsupport.Modelanalysisisprobablytheleast-discussedelementofthemodelingprocess.Thisresultsfromthefocusthateachmodelingparadigmhasonaspecictypeofanalysis.However,theessenceofmodel-baseddecision-makingsupportispreciselytheopposite;namely,tosupportvariouswaysofmodelanalysis,andtoprovideefcienttoolsforevaluationsofvarioussolutions.Thetraditionalapproachtodecision-makingsupportistorepresentadecisionproblemasamathematicalprogrammingproblemintheform:=argminwhichprovidesoptimaldecisions.However,thisap-proachdoesnotworkforcomplexdecision-makingprob-lems.Themainreasonsforthatare:ThereisnouniquerepresentationofpreferencesThereisnouniquedenitionofthesetofadmissiblesolutions(becauseisdenedalsobytheboundsforvaluesofthecriterianotincludedinSensitivityanalysisrecommendedforpost-optimizationproblemanalysishasverylimitedapplicabilitytoactualcomplexproblems,seee.g.,[4];andLargeoptimizationproblemsusuallyhaveaninnitenumberofverydifferentsolutionswithalmostthesamevalueoftheoriginalgoalfunction,seee.g.,[4].Thus,optimizationinsupportingdecisionmakingforsolvingcomplexproblemshasaquitedifferentrolefromitsfunctioninsomeengineeringapplicationsorinveryearlyimplementationsofOperationalResearch(OR)forsolvingwell-structuredmilitaryorproductionplanningproblems.Thispointhasalreadybeenclearlymadee.g.,byAckoff[5],andbyChapman[6],whocharacterizedthetraditionalwayofusingORmethodsforsolvingprob-lemsascomposedofthefollowingvestages:describe 1034JOURNAL OF COMPUTERS, VOL. 4, NO. 10, OCTOBER 2009 © 2009 ACADEMY PUBLISHER ManagementofAttainableTradeoffsbetweenConictingGoalsMarekMakowskiInternationalInstituteforAppliedSystemsAnalysis,Schlossplatz1,A-2361Laxenburg,Austria.Email:marek@iiasa.ac.atAbstract—Rationaldecision-makingrequiresgovernanceofattainabletrade-offsbetweenconictinggoals,uncertaintiesandrisks,whichinturndemandsbothnovelmodelingmethodsandappropriatemodelingtechnology.Thepaperdealswithrecentdevelopmentsinappliedmodelingthathavebeenmotivatedbytherequirementsformodel-basedsupportofsolvingcomplexproblems.Itstartswithpre-sentingnovelmodelingtechnologyandintegratedmethodsofintegratedmodelanalysisaimedatsupportingdecision-makersindiversiedwaysofanalysisoftheunderlyingdecisionproblem.Then,multicriteriaanalysisisdiscussedinmoredetailwithafocusonanextensionofthereferencepointoptimization,whichsupportsaneffectiveanalysisoftrade-offsbetweenconictingcriteriaaimingatanal-ysisofattainablegoals.Next,newapproachestocopingwithendogenousuncertaintyandcatastrophicrisksarecharacterized,followedbyasummaryofissuesrelatedtotransparencyandpublicunderstanding.IndexTerms—multicriteriaoptimization,decision-makingsupport,uncertainty,risk,structuredmodeling,modelingsystemsandlanguages,modelmanagement,databaseman-agementsystems.I.INTRODUCTIONEverybodydealswithconictinggoals,uncertainties,anddiverserisksallthetime.Inmostcaseswemanageevencomplexproblemsbysuccessfullymakingdecisionsbasedonexperienceandintuition.Considerdrivingacar,forexample.Eachdrivercontrolsacarsubconsciouslyapplyingquitecomplexprinciplesofadaptivecontrol,typicallywithoutevenunderstandingthedynamicsofthecar.Moreover,inacongestedtrafceachdriverconstantlymonitorsthebehaviorofotherdriversandeveryfewsecondssubconsciouslypredictstheirbehavior,assessingtheriskrelatedtovariouscombinationsofthepredictedbehavior.Giventhecomplexityofthiseverydayactivity,itisamazinghowwell(measurede.g.,bythefrequencyofmistakesthatleadtoaccidents)theproblemofcontrollingcarsissolvedbydriverswithverydiversi-edbackgroundsandexperience.Ifeverydrivercandothis,thenoneshouldaskwhyformalmethodsmayhelpsolvingproblemsthatseemtobesimpler.Thesimplestanswertothisquestionmayresultfromamorecarefulconsiderationofdiverseapproachesto Thispaperisbasedon“RationalGovernanceofConictingGoals,UncertaintiesandRisks,”byM.Makowski,whichappearedintheProceedingsofthe2007IEEEInternationalConferenceonSystems,Man,andCybernetics,Montreal,Canada,October2007.2007IControlengineerscouldsolvedifferentialequationstooptimizethewaytheydriveacar,buttheydonotneedtodoso.analysisofrelationsbetweendecisionsandtheirconse-quences.Itiscommonlyknownthataccidentsdohappen.However,everybodywhodriveseitherevaluatesautilityofdrivinghigherthanadisutilityofanunlikelyaccident,ordoesnotevenmakesuchakindofanalysis.Analysisofcatastrophicrisks(i.e.,relatedtorareeventswithhighconsequences)isactuallyadifcultproblem,whichisbeyondthescopeofthispaper.Yet,severalkeyproblemsrelatedtoanalysisoftrade-offsbetweenconictinggoalscanbeillustratedbyevenverysimpledeterministicprob-lems,e.g.,achoicefromasetofdiscretealternatives.Amorecompletejusticationoftheneedforrationalmanagementofconictinggoals,uncertaintiesandriskscomesfromdiverseapplicationsofscience-basedsupportforsolvingcomplexproblemsinpolicy-making,industry,andmanagement.Whileitispossibletoaccumulateenoughknowledgeandexperiencetosolvediverseprob-lems,oftenevenwithoutunderstandingalltheunderlyingmechanisms,inmanyotherdecision-makingsituationsmathematicalmodelsandadequatemethodsofmodel-basedproblemanalysisarenecessaryforndingand/orjustifyingrationaldecisions.Suchsituationsarecharac-terizedbyatleastoneofthefollowingissues:Complexrelationsbetweenthedecisionsandthecorre-spondingoutcomes(measuresofconsequencesoftheirimplementations).Difculttoassesstrade-offsbetweenattainablegoals(preferredvaluesofoutcomes).Uncertaintiesandrisksrelatedtothedecision-makingsituation.Theneedsforsupportingthetransparencyofthedecision-makingprocessandenhancingpublicunder-standingofproblemsandtheconsideredsolutions.Rationalgovernanceofconictinggoals,uncertaintiesandrisksrequiresconcertedhandlingofallpertinentelementsofthedecision-makingprocess.Anumberofmethodshasbeendevelopedfordealingwitheachoftheissueslistedabove.Thecraftofdecision-makingsupportconsistsofadoptinganappropriateapproachtoeachelementofthedecision-makingprocesswhilerememberingthatthestrengthofachainisdeterminedbyitsweakestlink.Theremainingpartofthepaperisorganizedasfollows.ThenextSectionpresentsthecharacteristicsofmodels,andofmodelingprocessesaimedatdecision-makingsupportforcomplexproblems.SectionIIIdealswithmulticriteriaanalysisoftrade-offsbetweenconicting