Monte-CarloSimulationwithCrystalBallTorunasimulationusingCrystalBall?:SetupSpreadsheetBuildaspreadsheetthatwillcalculatetheperformaneemeasure(e.g.,profit)intermsoftheinputs(randomornot).Forrandominputs,justenteranynumber.DefineAssumptions——i.e.,randomvariablesDefinewhichcellsarerandom,andwhatdistributiontheyshouldfollow.DefineForecast—i.e.,outputorperformaneemeasureDefinewhichcell(s)youareinterestedinforecasting(typicallytheperformaneemeasure,e.g.,profit).ChooseNumberofTrialsSelectthenumberoftrials.IfyouwouldlaterliketogeneratetheSensitivityAnalysischart,choose“SensitivityAnalysis”underOptionsinRunPreferences.RunSimulationbuttononRunthesimulation.Ifyouwouldliketochangeparametersandre-runthesimulation,youshould“reset”thesimulation(clickonthe“ResetSimulationorintheRunmenu)first.ViewResultsTheforecastwindowshowingtheresultsofthesimulationappearsautomaticallyafter(orduring)thesimulation.Manydifferentresultsareavailable(frequencychart,cumulativechart,statistics,percentiles,sensitivityanalysis,andtrendchart).Theresultscanbecopiedintotheworksheet.AssumptionsForecastPreferencesSimulationSimulationWindowChartWaltonBookstoreSimulationwithCrystalBallRecalltheWaltonBookstoreexample:ItisAugust,andtheymustdecidehowmanyofnextyear'snaturecalendarstoorder.Eachcalendarcoststhebookstore$7.50andissoldfor$10.AfterFebruary,allunsoldcalendarsarereturnedtothepublisherforarefundof$2.50percalendar.SupposeWaltonpredictsdemandwillbesomewherebetween100and300(discreteuniform).Demand=d~Uniform[100,300]OrderQuantity=Q(decisionvariable)RevenueCostRefundProfit=$10*Min(Q,d)=$7.50*Q二$2.50*Max(Q-I,0)=Revenue-Cost+RefundStep#1(SetupSpreadsheet)ABCDEF1SimulationofWalton'sBookstore23Data4UnitCost=$7.505UnitPrice=$10.006UnitRefund=$2.5078DemandDistribution(Uniform)9Minimum=10010Maximum=3001112DecisionVariable13OrderQuantity=2001415Simulation16DemandRevenueCostRefundProfit17200$2,000.00$1,500.00$0.00$500.00BCDEF15Simulation16DemandRevenueCostRefundProfit17200=C5*MIN(C13,B17)=C4*C13=C6*MAX(C13-B17,0)=C17-D17+E17WaltonBookstoreSimulationwithCrystalBallStep#2(DefineAssumptions—i.e.,randomvariables)Selectthecellthatcontainstherandomvariable(B17)—colorcode(blue):B16Demand17200andclickonthe“DefineAssumptions”buttonintooHberCCeHimenu):IE»疋"《1訐険Lm固Selecttypeofdistribution:CeHBl7:DistfibubionGaHefyCuikoffliQK斗CanedIBinomialGcomcbK；lIllliiLiiiiMiNi-.DliMoreProvideparametersofdistributions:CeHB17:UnitaimDiitlriibuli口m1MJ.D015D0D200.00250.DO30D0D荷StaticrDymarnicd=-sqfTrials：|&0DPStopilSpedfiedPreclsianisfieadhedConfidenceLevel：|95.00%PStopIICalculallomErrorOccurs“mJCancelStep#5(RunSimulation)Clickonthe“StartSimulation”buttonintoolbar(orRunintheRunmenu):▲qliilB!⑥□髦鶴夕EB►血图更圏H占Step#6(ViewResults)Theresultsofthesimulationcanbeviewedinavarietyofdifferentways(frequencychart,cumulativechart,statistics,andpercentiles).ChoosedifferentoptionsundertheViewmenuintheforecastwindow.I直F口lif±C：dl£l：：PljDlri-|旦FaiiETCfixt：pEEtlri-IEdtPreleiaice^yiewHyi_H曲j50QTrialsFrequencyChart0OwtllersEdtPraleience^yiewHyiHelp500TrialsCumulativeChart0Outliers占三qpqottFA鱼urilwy000貧"-j,-,—2lj—,-1j(I2J5.&1)[|5&21|$127.19t313.G0*500.00►plnflnltyCertainty|lD0r00%q|infinity戲加切告三qpqott二血iillllll1卜.oro($245.61)($59,211mwuclnGy50537.2512$127.19*313.60$500.00|l0000TheresultscanbecopiedintoaworksheetorWorddocument(chooseCopyundertheEditmenuinthesimulationoutputwindow.ProjectManagement—GlobalOilUsingTrendChartstoFindtheImpactofOrderQuantityonPotentialProfitDefineseveralforecastcells(G14:G18)forseveralpossibleorderquantities(Q=100,150,200,250,300).Usethesamerandomorderquantityforeachtocomparethemmoreequally(i.e.,oneassumptioncellfordemand——C14—withtherestsetequaltoC14).ABCDEFG1SimulationofWalton'sBookstore23Data4UnitCost=$7.505UnitPrice=$10.006UhitRefund=$2.5078DemandDistribution(Uniform)9Minimum=10010Maximum=3001112Simulation13OrderQuantityDemandRevenueCostRefundHofit14100200$1,000.00$750.00$0.00$250.0015150200$1,500.00$1,125.00$0.00$375.0016200200$2,000.00$1,500.00$0.00$500.0017250200$2,000.00$1,875.00$125.00$250.0018300200$2,000.00$2,250.00$250.00$0.00BCDEFG12Simulation13OrderQuantityDemandRevenueCostRefundProfit14100200=$C$5*MIN(B14,C14)=$C$4*B14=$C$6*MAX(B14-C14,0)=D14-E14+F1415150=$C$14=$C$5*MIN(B15,C15)=$C$4*B15=$C$6*MAX(B15-C15,0)=D15-E15+F1516200=$C$14=$C$5*MIN(B16,C16)=$C$4*B16=$C$6*MAX(B16-C16,0)=D16-E16+F16仃250=$C$14=$C$5*MIN(B17,C17)=$C$4*B17=$C$6*MAX(B17-C17,0)=D17-E17+F1718300=$C$14=$C$5*MIN(B18,C18)=$C$4*B18=$C$6*MAX(B18-C18,0)=D18-E18+F18Afterrunningthesimulation,choose“OpenTrendChart”intheRunmenu.Thischartgives“certaintybands”fortheforecastceof>the)%me,theprojectdurationwillfallwithintheinnerband(lightblue),25%ofthetimewithinthe2ndband(red),50%ofthetimewithinthethirdband(green),and90%ofthetimewithintheoutsideband(darkblue).GlobalOilisplanningtomovetheircreditcardoperationtoDesMoines,IowafromtheirhomeofficeinDallas.ThemoveinvoIvesmanydifferentdivisionswithinthecompany.Realestatemustselectoneofthreeavailableofficesites.PersonnelhastodeterminewhichemployeesfromDallaswillmove,howmanynewemployeestohire,andwhowilltrainthem.Thesystemsgroupandtreasurer'sofficemustorganizethenewoperatingprocedureandmakefinancialarrangements.Thearchitectswillhavetodesigntheinteriorspace,andoverseeneededstructuralimprovements.Eachsiteisanexistingbuildingwithsufficientopenspace,butofficepartitions,computerfacilities,furnishings,andsoon,mustallbeprovided.Acomplicatingfactoristhatthereisaninterdependenceofactivities.Inotherwords,somepartsoftheprojectcannotbestarteduntilotherpartsarecompleted.Forexample,Globalcannotconstructtheinteriorofanofficebeforeithasbeendesigned.Neithercanithirenewemployeesuntilithasdetermineditspersonnelrequirements.Thenecessaryactivitiesandtheirnecessarypredecessors(duetointerdependence)arelistedbelow.Threeestimatesaremadeforthecompletiontimeofeachactivity—theminimumtime,mostlikelytime,andmaximumtime.ActivityDescriptionImmediatePredecessorTimeEstimates(days)MinimumMostLikelyMaximumASelectOfficeSite——212121BCreateOrg.&Fin.Plan——202530CDeterminePersonnelReq.B152030DDesignFacilityA,C202842EConstructFacilityD404866FSelectPersonneltoMoveC121212GHireNewEmployeesF202532HMoveKeyEmployeesF282828ITrainNewPersonnelE,G,H101524EndGlobalOilSimulationwithCrystalBallStep#1(SetupSpreadsheet)ABCDEFGHIJ1GlobalOilRelocationProject2ActivityTime(Triangular)3ImmediateMostStartActivityFinish4ActivityDescriptionPredecessorsMinimumLikelyMaximumTimeTimeTime5ASelectSite-212121021216BCreateOrg.&Fin.Plan-202530025257CDeterminePersonnelReq.B1520302520458DDesignFacilityA,C2028424528739EConstructFacilityD404866734812110FSelectPersonneltoMoveC12121245125711GHireNewEmployeesF20253257258212HMoveKeyEmployeesF28282857288513ITrainNewPersonnelE,G,H1015241211513614115ProjectCompletionTime=136.00HIJ3StartActivityFinish4TimeTimeTime5021=H5+I56025=H6+I67=J620=H7+I78=MAX(J5,J7)28=H8+I89=J848=H9+I910=J712=H10+I1011=J1025=H11+I1112=J1028=H12+I1213=MAX(J9,J11,J12)15=H13+I131415ProjectCompletionTime==J13Step#2(DefineAssumptions—i.e.,randomvariables)Eachoftherandomactivitytimes(B,C,D,E,G,andI)isassumedtofollowthetriangulardistribution.Cell06:TrianqularDiftntznitionAesumptiDn|PlBk]-u2a.Min||=E622.5025QD27.50宙Static厂DynamicLikeliest|-F65曰30004Isd.od-Max|=G6HelpIGlobalOilSimulationwithCrystalBallStep#3(DefineForecast—i.e.,output)G一「HIJ15ProjectCompletionTime=136.00]CellJ15istheforecastcell:Step#4(ChooseNumberofTrials)500trialswererun.Inaddition.SensitivityAnalysiswasenabledintheOptionsoftheRunPreferencesdialoguebox.Thisallowsforthegenerationofsensitivityanalysisresultslater.Step#5(RunSimulation)Step#6(ViewResults)OFom-wl:rteiaGtCw*pl«ikNi1kw丄1基1Pre泌fliwiipl刨血1hw2CullURrsE#阳申严?!：阳SOITNnln1DCC1Ciimulnllv%C.tnunIICerlHinly抽1~1耳「%h|pInilntlyFgucncy9百co►IfjiriimityCertninly|100.(111%4pInllnllyUUllbRrS•WOAdditionalResultsAvailablewithCrystalBallSlidethetrianglesbelowthehistogramstodeterminetheprobabilitythattheoutput(projectduration)islessthanacertainvalue(e.g.,adeadline),greaterthanacertainvalue,orbetweenanytwovalues(byslidingbothtriangles).wceeaermine”e,rangetAlternatively,youcantypeinvaluesforthelowerboundorupperboundtodeterminetheprobability.Youcanalsotypeinaprobability(inthathasthatprobability.|OFom-wl:Pt祜itCmpkiikHi1me1.11莫1£*MitnRjfi匕阳3RjpdHp.GIB--【■I|x|SHOTNhIrFrRqnenc^i(^hnrtTrlHlnFrRqnenc^i(^hnil!2CHlIUnrs>冒黑豊EL13125DueCerlninly[TsTJfi—%153175165.C04[HaHmse-ncy963DOO*.mz==DOO120.N13125Cerlmnt^14250CwThereisa79%chaneetheprojectwillbecompletedwithin150days.Thereisa2.4%chaneethattheprojectwilltakemorethan160days.SensitivityChartChoose“OpenSensitivityChart”unimtheuRNotethatthischartisonlyavailableifyouselectedthe“SensitivityAnalysis”optionunderRunPreferences.Thischartgivesanindicationastowhichrandomvariables(activitytimes)havethegreatestimpactontheoutputcell(projectcompletiontime).VariabilityinactivityEhasthegreatestimpactonoverallprojectduration,followedbyactivityD,C,I,andB.VariabilityinactivityGhasalmostnoimpact.FittingaDistributionfit”cadasiributiontCrystalBallcanbeusedtoThefollowingdatahasbeencollectedfortheprevious100phonecallstoamail-orderhouse:ABCDEFGHI1PhoneData23ArrivalInterarrivalLengthofCallInterarrival「LengthofCall4Customer#(minutes)Time(minutes)Time(minutes)518.228.223.77Averages2.0044.516212.254.034.537312.270.024.048416.263.983.70Simulation249518.061.815.3810618.870.814.3611723.464.584.4112823.530.085.1413928.735.204.76141030.561.834.68151132.361.805.061611236.904.545.751711343.306.404.06181443.880.573.25191545.171.293.5799195194.020.284.2610096195.481.463.3710197195.870.384.4510298196.840.985.0610399197.810.975.20104100200.432.614.25GHI3InterarrivalLengthofCall4Time(minutes)5Averages=AVERAGE(D5:D104)=AVERAGE(E5:E104)(80rowshavebeenhidden)FittingDatatoaDistributionUsingCrystalBall?tofitdatatoadistributionSelectaspreadsheetcell.ChooseDefineAssumption.ClicktheFitbutton,thenselectthesourceofthefitteddata.ClicktheNextbutton,thenselectthedistributionstotrytofit.ClickOK.InterarrivalTimeCompaii^onChart■EMponentidlDistribiAionRate-0.0□InputDataJ•»!-•••=■•irmIr»«i«»iimu»-iiiq|Acceptil丨也IP1tt1CFii-SquareTest9.2000p-value0.5132Koknogorov-Smirnov0.049BAriderson-Dafling0.2750NextDistributionPrev,DistrrbutronServiceTime
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