(DSSORA)isaninteractivemathematicalprogrammingsystemforoptimalresourceallocationdevelopedtosupportdecisionsofinvestment

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1 Jean-MichelThizy1,DanielE.Lane1,SavvasPissarides2&SurendraRawat1;3? 1FacultyofAdministration,UniversityofOttawa,OttawaONK1N6N5,Canada, InteractiveMultipleCriteriaOptimizationfor CapitalBudgetinginaCanadian 3StentorResearchCentreInc.,160ElginSt.,Ottawa,Ontario,K1G3J4Canada. 2BellCanada,160ElginSt.,Ottawa,Ontario,K1G3J4Canada, TelecommunicationsCompany (DSSORA)isaninteractivemathematicalprogrammingsystemforoptimalresourceallocationdevelopedtosupportdecisionsofinvestment incapitalintensivetelecommunicationsprojects.thesystemstrivesto Abstract.DecisionSupportSystemforOptimalResourceAllocation maximizecorporategoalswhilerespectingnancialconstraintssuchas researchconductedwhileattheuniversityofottawa, cess(ahp)isusedforquanticationofqualitativemanagerialjudgment pendenciesorsynergiesamongprojects.theanalyticalhierarchypro- inregardtotherelativevalueofprojectsthroughatwostageprocess.an theavailabilityofcapitalfunds,institutionalrequirementsandvariedde- managementandtheimplementationofprojectportfolioswithsignicantlyconsistentresults.theexibility,userfriendlinessandquicktimecientsofwhicharedeterminedbytheahp.then,amodiedsimplex ofdssoraandcometorelyonitseciency-seekingcapabilities.dss ORAhasbeentestedbyseveralgroupsofmanagersresponsibleforthe userscanbuildgradualcondenceintheconstraintcheckingmechanism algorithmproposessomeratesoffundingsubstitution.userschoosethe amountofsubstitutionorcanoverridethesubstitutionsproposed.thus, initialresourceallocationisfoundbyalinearprogram,theobjectiveco- responseofdssoramakeitaneectivenegotiationtoolinagroupsetting. 1TheCapitalBudgetingProcess Whilecapitalbudgetingconstitutesaclassicalresourceallocationproblem,its exercisebycorporateplannersisregulatedbyinstitutionalprocedurestoensure Keywords.Interactivemultiplecriteriadecisionmaking,optimization, etc.forexample,determiningthetotalamountofcapitaltobeallocated,what accountability,respectorganizationalstructures,safeguardminorityinterests, capitalbudgeting,telecommunications,mathematicalprogramming activitiesshouldbeconsideredforfunding,whichcriteriaarecompatiblewiththe?researchsupportedbybellcanada,nsercoperatinggrantsogp and OGP ,andAUCCGoingGlobalProgram

2 muchbeforethedecisionmodelleadingtoacapitalallocationisdened. directionofthermareallstepsthatrequirecarefuljudgmentanddeliberation measureofthecostsandbenetsofeachprojectandtheiruncertainty.systematicmethodsforcapitalbudgetinghavebeenactivelyinvestigatedbypubligram(mop)fortheannualcapitalbudgetingexerciseofacanadiantelecommunicationscompany.ithasbeenusedbyafunctionalgroupofthecompanywhich utilitiessuchastelecommunicationscompanies(salo,1989;hoadley,1993).the decisionsupportsystemdescribedherecentersaroundamultipleobjectivepro- isresponsibleforthemanagementofaportfolioofprograms4.theseprograms Theadequatedesignofananalyticalmodeltomeettheserequirementsis challenging:capitalbudgetingmodelsareoftenhinderedbyapooreconomic constructofmathematicaloptimization. resourcesamongallfunctionalgroupsoftherm.eachprogramcoordinatesa allyusethenarrowertermproject,reservingthetermprogramtothefamiliar catetheseresourcestoindividualprojectsparticipatingintheprogram.hence, inagreementwithmostoftheliteratureoncapitalbudgeting,wewillgener- arepresentedtothecompany'scentralcapitalbudgetingcommitteeallocating coherentsetofprojectsmeetingacommonsetofobjectives.giventheresources awardedtoaparticularprogram,themethodproposedcaninturnhelpallo- oforganizationalandoperationalconstraints,suchasprojectinterdependencies.thecommitteemakesdecisionsthatmaybecontestedbysomefunctional groups'managers.legitimateconcernspromptthecommitteetoreconsiderthe cordingtotherequestsofthefunctionalgroups.thereforetheprojectsarepri- oritized,usingexplicitcriteriathatreectthecompany'smission.currently, judgmentbasedupontheknowledge,inuenceandexperienceofeachmember inthebudgetingcommittee.thedecision-makersmustalsoconsideranumber theevaluationofeachprojectwithrespecttoeachcriterioninvolveshuman LimitedresourcespreventtheCommitteefromfundingalltheprojectsactributionsoftheprojectstothesecriteriaandthenatureofprojectdependencies. Theappealmechanismprovidesevidenceofthecomplexityandtheuncertainty existingintheactualbudgetingdecisionprocess.muchofthedicultycomes fromqualitativeandsubjectiveviewsofthecompany'smissionandtheroleof theprojectstoaccomplishthismission. allocationbymodifyingtherulesusedtodenethecompany'scriteria,theconnativecapitalprojectstoachievethem.itcanbeusedeitherbythecommittee quicklyintheeventthatresourcesrequestedarenotfullyallocated. orbydierentunitmanagerstopreparetheirfundingrequestortorespond evaluationofthemissionandgoalsofthecompanyandthesuitabilityofalter- 4Itispreciselysuchprogramplanningthatleadtotherstuseoflinearprogramming Ourdecisionsupportsystemaimsatformingamoreexplicit,quantitative (Dantzig,1963),originallycalledProgramminginalinearstructure.

3 Budgeting Wenowfocusonamathematicalformulationofamultipleobjectiveprogram 2AMultipleObjectiveProgrammingSystemforCapital forcapitalbudgeting. 2.1ReviewofPreviousModels gramtosolveacapitalbudgetingproblem: Linearprogrammingwasappliedtocapitalbudgetingfromitsinception;there existsavastnumberofanalysesofcapitalbudgetingbylinearprogramming.we 1984;Crum,1981;Dean,1951;Wilkes,1983). shouldconsultmonographssuchas(bierman,1988;bromwich,1979;clark, brieyreviewlandmarkanalysesformop;forextensivebibliographies,readers Charnes,CooperandMiller(1959)werethersttoformulatealinearpro- maxnxj=1cjxj subjectto aijistheamountofresourceirequiredbyprojectj, where: cjisthenetpresentvalueofprojectj, 0xj1forj=1;...;n nxj=1aijxjbifori=1;...;m xjisthefractionofprojectjaccepted, biisthetotalamountofresourceiavailable, nisthenumberofprojectscompetingintheallocation, misthenumberofresourcesconsideredintheallocation. threebasicsetsofgoals:maximizationofnetpresentvalue,cashowbudgeting conventionalgoalprogrammingtechniques. proposinganinteractivemultiplegoalprogrammingmethodbasedonamutual preferencefunctionortrade-osamongcompetingobjectives,assuperiorto andsuccessiveinterplaybetweenadecision-makerandananalyst.spronkviewed hismethod,whichdoesnotrequireexplicitrepresentationofthedecision-maker's Deckro,Spahr,andHerbert(1985)presentedanon-lineargoalprogramwith Spronk(1981)extendedtheuseofgoalprogrammingincapitalbudgetingby andcontrolofrisk.

4 designedtosupportcollectivecapitalbudgetingdecisions. DecisionSupportSystemforOptimalResourceAllocation(DSSORA)isaninteractivemultipleobjectiveprogrammingsystemforecientresourceallocation 2.2TheMultipleObjectiveProgramofDSSORA fundingofeveryprojectislimitedbyupperandlowerbounds.ourprecise orsynergiesamongprojects:forexample,someprojectscannotbeimplemented unlessatleastacertainportionofanotherprojectisimplemented.finally,the fortheplanningperiod.constraintscanalsobeusedtorepresentdependencies inequalities,themostimportantofwhichisthecapitalfundsconstraintthat Otherconstraintsincludeoverallshorttermnancialimpactoftheportfolio suchasthemaximumlevelofacceptabledepreciationexpenseforeachproject representsthetotalavailabilityofcapitalthatmaybeallocatedtoallprojects. Theallocationofresourcestotheprojectsismadesubjecttoanumberof formulationis: EcientfMissionsatisfaction(x1;...;xn)g AvailabilityofCapital: subjectto: nxj=1xjc (1) Employeesforimplementation:nXj=1ejxjE DepreciationLimit:nXj=1djxjD (3) (4) (2) tionofthecorporatemissionviaamulti-valuedfunctionfin(1)thatcanbe wherexjmeasurestheleveloffundingofprojectj.dssoraassessessatisfac- Softwareandotherexpenses:nXj=1sjxjS Dependencies&Synergies:nXj=1aijxjbifori=1;...;r(6) Bounds:ljxjujforj=1;...;n(7) (5) ciationallowed.inasimilarway,ejrepresentsthenumberofemployeesneeded representsthedepreciationconstraint,wherethecoecientsdjarethenumber ofdollarsdepreciatedperdollarallocatedanddisthetotalamountofdepre- protection,savingsandstrategicimportance,themselvesimplicitlyknownfunctionsoftheallocation.inequality(2)representsthecapitalconstraint,inwhich Cdenotesthetotalbudgettobeallocatedamongthenprojects.Inequality(3) improvedbyincreasingcorporatecriteriasuchasrevenuegeneration,revenue

5 perdollarallocatedandeisthetotalnumberofemployees;sjdenotesthe softwareandotherexpensesperdollarallocatedtoprojectjandsisthetotal budgetforsoftwareandotherexpenses.constraints(6)representdependencies andsynergiesbetweenprojects.finally,in(7),ujandljrepresenttheupper andlowerlimitsofallocationtoprojectj.foreaseofpresentation,themodel issummarizedas: wherex=(x1;...;xp)t,aisafullrowrankmpmatrix,bisanm-vectorand Fisamulti-valuedfunction.TheoperatorEseekstheecientregionspecied bytheprogram,althoughtheinteractiveproceduredescribedinparagraph2.4 EfF(x)g Ax=b s.t. x0 (10) (8) isdesignedformoreexibleexploration. (9) Step1:DecisionmakersmustchooseanumberofcriteriaimportanttotheCompany'smissionagree,acompromiseonagivencomparisoncanbeobtainedeitherbydiscussion,voteorbytakingthegeometricmeanofeverymember'scomparison. anoverallscaleofimportance.whenindividualsintheevaluationgroupdis- ThismeasurementresemblesthefamiliarMOPmethodofpointestimate valueofeachofitscoecients,calledpriority. criterion.theanalytichierarchyprocess(saaty,1980)isusedtoassessthe ofthemulti-valuedcriterionfunction:f=(fh(x))h=1;...;h,wherefhisalinear Aninitialallocationwillrstbeobtainedbycalculatinglinearapproximations 2.3TheAnalyticHierarchyProcess Step2:Therelativeimportanceofeachpairofcriteriaismeasuredinordertoobtain Step3:AssessthevalueofeachofthecoecientsofFh,i.e.therelativeimpactof (thesimilaritywillberenedinstep4oftheprocedure.) that:phh=1h=1;thesecanbeusedtoreducethecriterionfunctiontothe linearobjective:maxhxh=1hfh(x1;x2;...;xn) weightedsumsthatdenesnonnegativemultipliershforh=1;...;hsuch Step4:Theoverallpriorityofeachprojectisobtainedastheinnerproductofthe andp4. Considerforexampletheallocationofresourcestofourprojects,P1,P2,P3 vectorsobtainedinstep2andstep3(forthisproject). eachpairofprojectsoneachcriterionh,byaseriesofpairwisecomparisons analogoustothoseofstep2.

6 Step1:Supposethatthecapitalbudgetingdecisiongroupchosethecriteria:revenue B,CandD).ThecorrespondinghierarchyisdisplayedinFig.1. generation,revenueprotection,savingsandstrategicimportance(labeleda, Mission Revenue Revenue Operational Strategic generation protection savings Importance (A) (B) (C) (D) Step2:Forthesakeofsimplicity,weassumethateverycomparisonwasmadeunanimouslybythedecision-makinggroup.Thefollowingisthecomparisonmatrixforthecriteria(forinstance,thesecondcoecient:5signiesthatthe Fig.1.AHPhierarchyforselectionoftelecommunicationsprojects criterionbisvaluedasmoreimportantthana): Project A1535 Project Project Project P1 B1=511=31 P2 P3 P4 C1=3313 A0:558 B0:096 C0:249 D0:0961CA

7 Step3:Nextarethematricesofcomparisonsoftheprojectsundereachcriterion: P11175 A:P1P2P3P4 P21175 P41=51=5311CA P31=71=711=3 B:P1P2P3P4 P21=3111=9 P11351=5 C:P1P2P3P4 P41=31=71=311CA P25157 P311=513 P111=513 projectsyieldonecolumnofthefollowingmatrix: FollowingthemethodofStep2,foreachcriterion,comparisonsbetween P31=5111=9 P459911CA P11571 D:P1P2P3P4 P21=5131=3 P413711CA P31=71=311=7 Step4:BymultiplyingthismatrixbythevectorofmultipliersfoundinStep2, P40:1020:0620:6770:3871CA P30:0500:1530:0580:052 P20:4240:6320:0660:121 P10:4240:1530:1990:440 constraints(2)-(7)toproduceaninitialallocationofresources: Ṫheprioritiesarethenusedasobjectivecoecientsofalinearprogramwith P10:34 max0:34x1+0:33x2+0:06x3+0:27x4 P20:33 P30:06 P40:271CA overallallocationof$180million,andadependencyconstraint(6): Givenindividualbounds(7)displayedinTable1,thecapitalallocationobtained bylinearprogrammingiscontainedinitslastcolumn. TheconstraintsoftheexampleincludeonlyCapitalAvailability(2)withan 0:5x1+x380:

8 Table1.Allocationconstraints(therightmostthreecolumnsdisplay$million) ProjectPrioritiesDependencyLowerUpperInitial P2 P LimitLimitAllocation TheInteractiveAllocation P3 P Dependencyrighthandside:80 Capitalavailable:$180million Theallocationdelineatedpreviouslymayneedfurtherrenementorsensitivity 45 constraints. leavesagreatleewaytodecision-makerswhileenforcingthebudgetorother analysis.totheseends,thedecisionsystemoersaninteractiveprocedurethat proposed.thereforeuserscanproposetheirownsolutions,buildgradualcondenceintheconstraintcheckingmechanismofthesimplexmethod,andcometo algorithmproposessomeratesoffundingsubstitution.then,usersdecideinteractivelywhatamountofsubstitutionispreferable,andcanoverridetherates notresorttoaninteractiveoptimizationinthespaceofcriterionmultipliers analyticalformofeachcriterioncouldbeelusive.thus,thedecisionsystemdoes asclassicalmopmethodspropose,butallowsuserstoassesstheirpreferences directlyinthespaceofbudgetallocations.ateachstep,amodiedsimplex Infact,itwasfoundthatnotonlythevaluesofthepriorities,buteventhe relyoftheeciency-seekingcapabilitiespatternedafter(georion,1972;zionts, 1976). partitionedasx=(xn;xb),wherexnisthesubvectorofnonbasicvariablesand xbisthesubvectorofbasicvariables.correspondingly,aispartitionedasa= [NjB],whereNconsistsofthenonbasiccolumnsofAandBconsistsofthebasic columns.hence: MultiplyingbothsidesbyB?1yields: Considertheprecedingformulation(8){(10).Letthecurrentsolutionxbe whichisequivalentto:xb=b?1b?b?1nxn: B?1NxN+IxB=B?1b; NxN+BxB=b: ofdecreaseinthebasicvariablexbicausedbyaunitincrementinthenon-basic DenethematrixY=B?1N.Eachofitscomponentsyijdescribestheamount

9 Step0:Settheiterationcountertat0.Selectaninitialsolution(e.g.fromtheinitial allocation,eachoftheprecedingquantitiesreceivesasuperscriptt. vectors.atthet-thiterationofthefollowingalgorithmforinteractiveresource variablexnj.hence,itscolumnsy1;y2;...;yp?mcanbeusedtodenetrade-o Step2:Eitherselectaproperamountoftrade-oxtNjforsomej2[1;...;p?m], Step1:ForeverynonbasicvariablextNj,j2[1;...;p?m],atrade-ovectorytjis calculatedandpresentedtousers. using:min linearprogram):xob=(bo)?1(bo?noxon): i:ytij>0xtbi andlet: ytijxtnjmax?xtn;max x'b=xtb?ytjxtnj; x'nk=xtnkfork6=j; x'nj=xtnj+xtnj; i:ytij<0xtbi ytik; Step3:If,forsomeindexq2[1;...;m],x'Bq=0,thenlet orterminatewithsolutionxt. xt+1=(e1;...;ek?1;ep?m+q;ek+1;...;ep?m+q?1;ek;ep?m+q+1;...;en)x'; Forexample,attheoptimumofthelinearprogramdisplayedinTable1,part Sett=t+1andgotoStep1. elseletxt+1=x'. and(bt+1)?1=(e1;...;ek?1;k;ek+1;...;en)(bt)?1; k=(?y1k=yqk;?y2k=yqk;...;1=yqk;...;?ym?1=yqk;?ym=yqk) oftherowsofthematrix?ycorrespondingtotheoriginalvariablesx1;x2;x3; characterizedbythedirectionoftherstcolumn,inanamountxtn1=5.the allocationtoprojectp1decreasesby5,theallocationstoprojectsp2andp3 Toillustratetheuseoftheprecedingmatrix,supposeuserschooseatrade-o P40:00:00:01:01CA: P30:51:00:00:0 P20:5?1:?1:?1: P1?1:0:00:00:0 (11)

10 eachincreaseby2:5.theallocationtoprojectp4staysthesame.therefore afterdecreasingthefundingofprojectp3by5,theallocationisgivenby(12). standpoint(itenablesdecisionmakerstoreducetheresourcesallocated)and 57:5 32:5 fromatheoreticalone:userscanavoidthepervasiveassumptionthattheirutilityfunctionmustbepseudoconcave,underwhichlargerallocationsarealways preferredtosmallerones(zionts,1976). ofpurelyreducingresourcesforaprojectmaybeusefulbothfromapractical decreasetheallocationtoproject2.unlikelyatrstbrush,suchadecision Thethirdcolumnofthematrix(11).indicatesthatitisfeasibletosimply 451CA requirements,allowabledepreciationexpense,softwareandotherexpenses,manpowerneedsandrelationshipsbetweenprojects.amongthemodulessupporting directlytheinteractiveresourceallocation: {amoduleforprojectvalueassessmentimplementstheahpmethodologyto availabilitiesandprojectrequirements,e.g.,bystoringinformationaboutcapital 1992).Financialinformationmodulesaredesignedtomonitorcapitalresource 3ComputerImplementation mentedasasmalllibraryofobjectswrittenformicrosoftwindows(pissarides, nancialinformationmanagementandresourceallocation.eachmoduleisimple- DSSORAprovidesadecisionsupportenvironmentthatcomprisesmodulesfor- Fig.2representsthemutualrelationshipsbetweenthemodulesofDSSORA {amoduleofbudgetreallocationallowsuserstoexplorealternativefunding {anoptimizingmoduleusesthemtodetermineaninitialallocationbylinear programming,and calculateprioritiesforeachproject, whicharedescribedinmoredetailnext. 3.1ProjectValueAssessment byproposingsomesubstitutions,oneofwhichtobeselectedbydecision ThismoduleimplementstheAHPmethodologyonahierarchyformedbyatop makers. projects,asdescribedinsect.2.3andfig.1. levelcomprisingcriteriaforthecorporatemissionandabottomlevelforthe

11 Project requirements Project evaluation Resource availability Initial resource allocation limits.usersmustthencompareeachcriterionwitheachoftheotherones, ria,ithasbeenfoundthatvekeptthenumberofcomparisonswithintolerable corporatemission.althoughthereisnotheoreticallimitonthenumberofcrite- Usersarerstaskedtoinputatmostvenamesofcriteriacharacterizingthe Comparisonsofmissioncriteria Fig.2.DSSORAmodulediagram choosingoneofthefollowingcharacterizations: Interactive {Equal resource {ModeratelyMoreImportant allocation

12 TheinterfaceusedforthecomparisonsisshowninFig.3.Usersarerequiredto llintheboxeswithappropriatesymbols.whenallthecomparisonsaremade, therightmostcolumnoffig.3. thesystempresentsuserswithavectorofprioritiesforthecriteriadepictedin {StronglyMoreImportant {AbsolutelyMoreImportant {VeryStronglyMoreImportant Forthesecondlevelofthehierarchy,usersmustcompareeachpairofprojects,as Comparisonsofprojects followingthesameprocedureasforcriterioncomparisons.attheendofthe comparisonsforagivencriterion,thesystempresentsuserswiththeproject showninfig.4.theprojectsarecomparedpairwiseaccordingtoeachcriterion, Fig.3.Projectvalueassessment:missioncriteria;projects. prioritiesaccordingtothecurrentcriteriontogetherwithaninconsistencyratio (Saaty,1980).Ifthisratioistoohigh,userscangobackandcomparethepairsof projectsagain.whenalltheprojectsarecomparedaccordingtoallcriteria,the systempresentsuserswiththeoverallprojectandcriterionprioritiestogether withtheoverallinconsistencyratio.again,iftheratioistoohigh,userscan revisethecomparisonsinordertoobtainabetterratio.

13 algorithmwaseasedbyimplementingitasanobjectforanintegratedmanipulationofthesimplextableau,performingthefollowingfunctions: determinesaninitialallocationofresourcestoprojects.designingasimplex 3.2InitialResourceAllocation Theprioritiesareusedasobjectivefunctioncoecientsofalinearprogramthat Fig.4.Projectvalueassessment:projects. 3.3InteractiveResourceAllocation Themoduleforinteractiveallocationdisplaysthecurrentallocationinaneasy {keeptrackofalltheelementsinthetableau, inordertoobtainamoredesirableallocation,ordirectlytoswapsomeresources format.itallowsuserstochangesomeoftheinputsfromthepreviousmodules {keeptrackofthesizeofthetableau, betweenprojectswithoutviolatingtheconstraints.foreachproject,theinteractiveanalysisdisplaysinformationonobjectivecoecientsoftheoriginallinear program,itsmodiedvaluesandcorrespondingallocations,asshowninfig.5 {currentobjectivecoecient, {performpivotoperations. anditemizedbelow: {originalobjectivecoecientdeterminedbyahpanalysis,

14 Forsensitivityanalysisoftheresources,themodulealsodisplaysthefollowing {ascrollbartochangetheobjectivecoecient, {originalallocationdeterminedbylinearprogramming, {currentallocation, {ascrollbartochangetheallocation. Fig.5.Userinterfaceforinteractiveresourceallocationbysensitivityanalysis informationrelativetoeachconstraint: Themoduleoersfouroptionstochangetheallocationofresources: {currentrighthandsidevalue {originalrighthandsidevalue {ascrollbartoallowthechangeoftherighthandsidevalue, {originalvalueofthelefthandsidedeterminedbylinearprogramming, {currentvalueofthelefthandside. \Optimize"onthescreen,whichacceptsthenewdataasinputtothesimplex algorithmcontainedinthemoduledescribedpreviouslyanddisplaysthenew {changeofobjectivefunctioncoecients, {computer-assistedchangeoffundingallocation,and {unassistedchangeoffundingallocation. {changeofamountsofresources(therighthandsideoftheconstraints), Inthersttwooptions,theallocationismodiedbyselectingthemenuitem

15 allocationsbothnumericallyandonscrollbars.thereforeuserscanperform sensitivityanalysisonboththeobjectivecoecientsandtheconstraintright handsidevaluesbydraggingthescrollbarcursorsineitherdirection.infig.5, foranewobjectivefunction asalgebraicfunctions.inthelastoption,i.e.unassistedchange,theycansimply bylinearprogramming:inparticular,theyneednotexpressthemissioncriteria theallocationbecomes: Thelasttwooptions,illustratedinFig.6,allowuserstoby-passre-optimization max0:31x1+0:31x2+0:06x3+0:32x4; changetheallocationofresourcestotheprojectsbychangingthepositionof thecursorsonthescrollbars,usingthemouse.eachcursoronthescrollbars canmoveuntiloneoftheconstraintsisviolated.forexample,userscanachieve amoredesirablesolutionbydecreasingtheallocationtoprojectp2from30to x1=50;x2=25;x3=55;x4=50: Ofcourse,thenewsolutionmaynotbeoptimalwithrespecttotheobjective 26andincreasingtheallocationtoProjectP4from45to47.Inthisunassisted change,anyarbitraryallocationwillbepossiblewithintheconstraintsspecied. coecientsdisplayedbytheinterface. Fig.6.Userinterfaceforinteractiveresourceallocation:computer-assistedtrade-os

16 coecients(11). example,choosingthersttrade-oyieldsthenewallocationgivenby(12). generatedbythesystem,showninfig.6,thattransposesthematrixofreduced changetheallocationbypressingabuttononthescreen.thechangesarere- ofvalues,bothofwhichrepresentingtheallocationlevelstoeachproject.for ectedbythepositionofcursorsonthescrollbarsandthecorrespondingdisplay Eachtrade-oindicatesarateoffundingsubstitution.Userscandecideto Inanassistedchange,userscanselectoneallocationtrade-ofromalist problemathandbyexploringtheregionspeciedbytheconstraints.itdoes updatesthelistoftrade-os. oftherighthandsidevaluesbecomeszero,thesystemperformsapivotand inparticularneednotbepseudoconcave,aqualicationthatwouldrestrictthe notrequireanyanalyticexpressionoftheobjectiveorutilityfunctionwhich searchtoextremepointsonly. Thealgorithmisdesignedtohelpusersgetabetterunderstandingofthe Usersareallowedtoswitchtoadierenttrade-oatanytime.Whenone withdssoraconsistedofvemanagers.first,afunctionalgroupofsta 4FieldTrial AeldtrialwasconductedtotestwhetherDSSORAcouldsupportgroupdecisionsasrequiredbytheCompany'sbudgetingprocess.Twogroupsthatworked managersresponsibleforthefundingofaportfolioofveprogramslabeledp1, P2,P3,P4andP5(eachconsistingofnumerousprojects)hadtodeveloptheir fundingallocationrequestfortheprograms.thegroupheldamanagerialviewof eachprojectanditsroleintheportfolio,ratherthanatechnicalunderstanding ofitsfunctionsandvalueinthecorporatetelecommunicationsnetwork.consequently,itsmembersdieredfairlysubstantiallyintheirinitialevaluationofthsionaimedatdevelopingacommonunderstandingoftheroleoftheprojects Thiswasconrmedinourcase,asarstevaluativesessionsparkedadiscusparisonshaveintuitiveappeal,pinpointinginternalinconsistenciesofjudgment. responsibleforimplementationoftheseprogramsbeforetherequestcouldbe forwardedtothecontrolcommitteeresponsibleforfundingallocation. intable2.yet,consensuswasrequiredofthisrequestbythelinemanagers importanceofeachprogramtowardeachcorporatemissioncriterion,asshown adequacyofthemethod,theoutcomeofthesecondsessionofpairwiseevaluationswasthattheprioritiesofeachofthemanagersfortheprogramswereclose insatisfyingcorporatemissioncriteria,andofcriticalunderlyingassumptions underwhichallprojectshadtocompeteforfundingallocation.attestingtothe enoughtoreachaunanimousconsensusaboutthevalidityofthevaluesbased Saaty(1990)notedthatthehierarchicalrepresentationandthepairwisecom- ontheaverageinputofthegroup,displayedinthelastcolumnoftable2.the roleeachsessionofdssoratowardthisprogressiveconciliationisrepresented infig.7.

17 Fig.7.UsingDSSORAforconsensusbuilding

18 Project12345inputs P P P Table2.Projectimportanceassessmentresults P P Basedoninputs frommanager Basedon average aninteractiveresourceallocationwasnecessary. 5Conclusion managers.giventheconsensus,inneitherexperimentdidthemanagersfeelthat theimplementationoftheprojectswithinthecorporatetelecommunications network.consensuswasreachedinonesession,andtheresultingprojectevaluationsweresignicantlyclosetotheresultsobtainedbytherstgroupofsta ThesecondgroupusingDSSORAcomprisedlinemanagersresponsiblefor ApplyingDSSORAtoresourceallocationwithinafunctionalunitlimitsthe projectmanagers.beyondtheinteractivemopmethodology,theeldtrial provedthatthesystemwasaneectivenegotiationtoolinagroupsetting. numberofprojectsunderconsideration,withseveralensuingbenets: DSSORAhasbeentestedwithveryconsistentresultsbyseveralgroupsof CapitalbudgetingintheCompanyspansmanyunitsandassociatedprograms. ToadaptDSSORAtointer-unitbudgeting,currentresearchfocusesoneective decompositionandaggregationtechniques(liang,1994).acentralissueisthe {increasedlikelihoodofconsensusbuilding, {limitedinterferenceofexternalconstraintswiththeconsensualevaluations, {relativelyfewpairwisecomparisons, {familiarityofthemanagerswiththeprojects, formationofsubportfoliosofprogramsbalancingtworequirements: {possibleacceptanceofresultsasabaseforimplementation. projects. portfoliosofprograms,followedbyintra-programallocationtotheconstituting Inthissetting,resourceallocationcouldproceedalongseveraltiers:allocationto {easethecomparisonsofprojects, {circumscribeprojectsthatshareimportanttechnologicaloroperationaldependencies.

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