数据、模型与决策（第12版）课件 第14章 仿真

SimulationChapter14Copyright©2016PearsonEducation,Inc.TheMonteCarloProcessComputerSimulationwithExcelSpreadsheetsSimulationofaQueuingSystemContinuousProbabilityDistributionsStatisticalAnalysisofSimulationResultsCrystalBallVerificationoftheSimulationModelAreasofSimulationApplicationChapterTopicsCopyright©2016PearsonEducation,Inc.Analoguesimulationreplacesaphysicalsystemwithananalogousphysicalsystemthatiseasiertomanipulate.Incomputermathematicalsimulationasystemisreplacedwithamathematicalmodelthatisanalyzedwiththecomputer.Simulationoffersameansofanalyzingverycomplexsystemsthatcannotbeanalyzedusingtheothermanagementsciencetechniquesinthetext.OverviewCopyright©2016PearsonEducation,Inc.Alargeproportionoftheapplicationsofsimulationsareforprobabilisticmodels.TheMonteCarlotechniqueisdefinedasatechniqueforselectingnumbersrandomly

fromaprobabilitydistributionforuseinatrial(computerrun)ofasimulationmodel.Thebasicprinciplebehindtheprocessisthesameasintheoperationofgamblingdevicesincasinos(suchasthoseinMonteCarlo,Monaco).MonteCarloProcessCopyright©2016PearsonEducation,Inc.Table14.1ProbabilitydistributionofdemandforlaptopPCsIntheMonteCarloprocess,valuesforarandomvariablearegeneratedbysamplingfromaprobabilitydistribution.Example:ComputerWorlddemanddataforlaptopssellingfor$4,300overaperiodof100weeks.MonteCarloProcessUseofRandomNumbers(1of10)Copyright©2016PearsonEducation,Inc.ThepurposeoftheMonteCarloprocessistogeneratetherandomvariable,demand,bysamplingfromtheprobabilitydistributionP(x).Thepartitionedroulettewheelreplicatestheprobabilitydistributionfordemandifthevaluesofdemandoccurinarandommanner.Thesegmentatwhichthewheelstopsindicatesdemandforoneweek.MonteCarloProcessUseofRandomNumbers(2of10)Copyright©2016PearsonEducation,Inc.Figure14.1AroulettewheelfordemandMonteCarloProcessUseofRandomNumbers(3of10)Copyright©2016PearsonEducation,Inc.Figure14.2NumberedroulettewheelMonteCarloProcessUseofRandomNumbers(4of10) Whenthewheelisspun,theactualdemandforPCsisdeterminedbyanumberatrimofthewheel.Copyright©2016PearsonEducation,Inc.Table14.2GeneratingdemandfromrandomnumbersMonteCarloProcessUseofRandomNumbers(5of10)Copyright©2016PearsonEducation,Inc.Selectanumberfromarandomnumbertable:Table14.3AtableofdelightfullyrandomnumbersMonteCarloProcessUseofRandomNumbers(6of10)Copyright©2016PearsonEducation,Inc.Repeatingtheselectionofrandomnumberssimulatesdemandforaperiodoftime.Thenextslideshowsdemandfor15consecutiveweeksasdrawnfromtherandomnumbertable.Estimatedaveragedemand=31/15=2.07laptopPCsperweek.Estimatedaveragerevenue=$133,300/15=$8,886.67.MonteCarloProcessUseofRandomNumbers(7of10)Copyright©2016PearsonEducation,Inc.MonteCarloProcessUseofRandomNumbers(8of10)Table14.4Randomlygenerateddemandfor15weeksCopyright©2016PearsonEducation,Inc.Averagedemandcouldhavebeencalculatedanalytically:MonteCarloProcessUseofRandomNumbers(9of10)Copyright©2016PearsonEducation,Inc.Themoreperiodssimulated,themoreaccuratetheresults.Simulationresultswillnotequalanalyticalresultsunlessenoughtrialshavebeenconductedtoreachsteadystate.Itisoftendifficultto

validateresultsofsimulation-thattruesteadystatehasbeenreachedandthatsimulationmodeltrulyreplicatesreality.Whenanalyticalanalysisisnotpossible,thereisnoanalyticalstandardofcomparison,thusmakingvalidationevenmoredifficult.MonteCarloProcessUseofRandomNumbers(10of10)Copyright©2016PearsonEducation,Inc.Assimulationmodelsgetmorecomplextheybecomeimpossibletoperformmanually.Insimulationmodeling,randomnumbersaregeneratedbyamathematicalprocessinsteadofaphysicalprocess(suchaswheelspinning).Randomnumbersaretypicallygeneratedonthecomputerusinganumericaltechniqueandthusarenottruerandomnumbersbutpseudorandomnumbers.ComputerSimulationwithExcelSpreadsheetsGeneratingRandomNumbers(1of2)Copyright©2016PearsonEducation,Inc.Artificiallycreatedrandomnumbersmusthavethefollowingcharacteristics:Therandomnumbersmustbeuniformlydistributed.Thenumericaltechniqueforgeneratingthenumbersmustbeefficient.Thesequenceofrandomnumbersshould

reflectnopattern.ComputerSimulationwithExcelSpreadsheetsGeneratingRandomNumbers(2of2)Copyright©2016PearsonEducation,Inc.Exhibit14.1SimulationwithExcelSpreadsheets(1of3)Copyright©2016PearsonEducation,Inc.Exhibit14.2SimulationwithExcelSpreadsheets(2of3)Enter=VLOOKUP(F6,Lookup,2)inG6andcopyittoG7:G20Enter=4300*G6inH6andcopyittoH7:H20=AVERAGE(G6:G20)GeneraterandomnumbersforcellsF6:F20withtheformula=RAND()inF6andcopyittoF7:F20Copyright©2016PearsonEducation,Inc.Exhibit14.3SimulationwithExcelSpreadsheets(3of3)Clickonthe“View”tab,thenon“FreezePanes”Spreadsheetis“frozen”atrow16toshowfirst10weeksandlast6Copyright©2016PearsonEducation,Inc.RevisedComputerWorldexample;ordersizeofonelaptopeachweek.ComputerSimulationwithExcelSpreadsheetsDecisionMakingwithSimulation(1of2)Exhibit14.4=1+MAX(G6-H6,0)isenteredinG7andcopiedtoG8:G105=VLOOKUP(F6,Lookup,2)isenteredinH6andcopiedtoH7:H105Shortagesarecomputedbyentering=MIN(G6-H6,0)inI6andcopyingtoI7:I105=G6*50isenteredincellL6andcopiedtoL7:l105Copyright©2016PearsonEducation,Inc.Ordersizeoftwolaptopseachweek.ComputerSimulationwithExcelSpreadsheetsDecisionMakingwithSimulation(2of2)Exhibit14.5NewformulafortwolaptopsorderedperweekCopyright©2016PearsonEducation,Inc.Table14.5Distributionofarrivalintervals

Table14.6DistributionofservicetimesSimulationofaQueuingSystemBurlinghamMillsExample(1of3)Copyright©2016PearsonEducation,Inc.Averagewaitingtime=12.5days/10batches =1.25daysperbatchAveragetimeinthesystem=24.5days/10batches =2.45daysperbatchSimulationofaQueuingSystemBurlinghamMillsExample(2of3)Copyright©2016PearsonEducation,Inc.SimulationofaQueuingSystemBurlinghamMillsExample(3of3)Caveats:Resultsmaybeviewedwithskepticism.Tentrialsdonotensuresteady-stateresults.Startingconditionscanaffectsimulationresults.Ifnobatchesareinthesystematthestart,thesimulationmustrununtilitreplicatesnormaloperatingsystem.Ifthesystemstartswithitemsalreadyinthesystem,thesimulationmustbeginwithitemsinthesystem.Copyright©2016PearsonEducation,Inc.Exhibit14.6ComputerSimulationwithExcelBurlinghamMillsExampleThisformulaisenteredinD15andcopiedtoD16:D23Clocktimeisgeneratedbyentering=MAX(E15,J14)inF15andcopyingtoF16:F23Arrivaltimesaregeneratedbyentering=E14+D15inE15andcopyingtoE16:E23Copy=VLOOKUP(H14,Lookup2,2)toI14:I23=AVERAGE(G14:G23)Copyright©2016PearsonEducation,Inc.ContinuousProbabilityDistributionsCopyright©2016PearsonEducation,Inc.MachineBreakdownandMaintenanceSystemSimulation(1of6) BigelowManufacturingCompanymustdecideifitshouldimplementamachinemaintenanceprogramatacostof$20,000peryearthatwouldreducethefrequencyofbreakdownsandthustimeforrepairwhichis$2,000perdayinlostproduction. Acontinuousprobabilitydistributionofthetimebetweenmachinebreakdowns: f(x)=x/8,0

x

4weeks,wherex=weeksbetween machinebreakdowns x=4*sqrt(ri),valueofxforagivenvalueofri.Copyright©2016PearsonEducation,Inc.Table14.8ProbabilitydistributionofmachinerepairtimeMachineBreakdownandMaintenanceSystemSimulation(2of6)Copyright©2016PearsonEducation,Inc.Table14.9RevisedprobabilitydistributionofmachinerepairtimewiththemaintenanceprogramMachineBreakdownandMaintenanceSystemSimulation(3of6)Revisedprobabilityoftimebetweenmachinebreakdowns: f(x)=x/18,0

x

6weekswherex=weeksbetween machinebreakdownsCopyright©2016PearsonEducation,Inc.Table14.10SimulationofmachinebreakdownsandrepairtimesMachineBreakdownandMaintenanceSystemSimulation(4of6) Simulationofsystemwithoutmaintenanceprogram(totalannualrepaircostof$84,000):Copyright©2016PearsonEducation,Inc.Table14.11SimulationofmachinebreakdownsandrepairwiththemaintenanceprogramMachineBreakdownandMaintenanceSystemSimulation(5of6) Simulationofsystemwithmaintenanceprogram(totalannualrepaircostof$42,000):Copyright©2016PearsonEducation,Inc.MachineBreakdownandMaintenanceSystemSimulation(6of6)Resultsandcaveats:Implementthemaintenanceprogramsincethecostsavingsappeartobe$42,000peryearandthemaintenanceprogramwillcost$20,000peryear.However,therearepotentialproblemscausedbysimulatingbothsystemsonly

once.Simulationresultscouldexhibitsignificantvariationsincetimebetweenbreakdownsandrepairtimesareprobabilistic.Tobesureofaccuracyofresults,simulationsofeachsystemmustberunmanytimesandtheaverageresultscomputed.Efficientcomputersimulationisrequiredtodothis.Copyright©2016PearsonEducation,Inc.Exhibit14.7MachineBreakdownandMaintenanceSystemSimulationwithExcel(1of2)Originalmachinebreakdownexample:FromTable14.8Spreadsheetfrozenatrow24toshowfirst10breakdownsandlast6Copy=E14+D15toE15:E113Copy=VLOOKUP(F14,Lookup,2)toG14:G113Copyright©2016PearsonEducation,Inc.Exhibit14.8MachineBreakdownandMaintenanceSystemSimulationwithExcel(2of2)Simulationwithmaintenanceprogram.ProbabilitydistributionorrepairtimefromTable14.9RevisedformulafortimebetweenbreakdownsCopyright©2016PearsonEducation,Inc.Outcomesofsimulationmodelingarestatisticalmeasures

suchasaverages.Statisticalresultsaretypicallysubjectedtoadditionalstatisticalanalysistodeterminetheirdegreeofaccuracy.Confidencelimits

aredevelopedfortheanalysisofthestatisticalvalidityofsimulationresults.StatisticalAnalysisofSimulationResults(1of2)Copyright©2016PearsonEducation,Inc.Formulasfor95%confidencelimits: upperconfidencelimit lowerconfidencelimit whereisthemeanandsthestandarddeviationfromasampleofsizenfromanypopulation. Wecanbe95%confidentthatthetruepopulationmeanwillbebetweentheupperconfidencelimitandlowerconfidencelimit.StatisticalAnalysisofSimulationResults(2of2)Copyright©2016PearsonEducation,Inc.SimulationResultsStatisticalAnalysiswithExcel(1of2)Simulationwithmaintenanceprogram.Exhibit14.9ConfidencelimitsCopyright©2016PearsonEducation,Inc.SimulationResultsStatisticalAnalysiswithExcel(2of2)Exhibit14.10Clickon“DataAnalysis”Statisticalsummaryreport“InputRange”arethecost($)valuesincolumnH“OutputRange”specifiesthelocationofthestatisticalsummaryreportonthespreadsheetCopyright©2016PearsonEducation,Inc.CrystalBallOverviewManyrealisticsimulationproblemscontainmorecomplexprobabilitydistributions

thanthoseusedintheexamples.Howeverthereareseveralsimulationadd-ins

forExcelthatprovideacapabilitytoperformsimulationanalysiswithavarietyofprobabilitydistributionsinaspreadsheetformat.CrystalBall,publishedbyOracle,isoneofthese.CrystalBallisariskanalysisandforecastingprogramthatusesMonteCarlosimulationtoprovideastatisticalrangeofresults.Copyright©2016PearsonEducation,Inc. RecapoftheWesternClothingCompanybreak-evenandprofitanalysis:Price(p)forjeansis$23variablecost(cv)is$8Fixedcost(cf)is$10,000ProfitZ=vp-cf–vcbreak-evenvolumev =cf/(p-cv) =10,000/(23-8) =666.7pairs.CrystalBallSimulationofProfitAnalysisModel(1of13)Copyright©2016PearsonEducation,Inc.ModificationstodemonstrateCrystalBallAssumevolumeisnowvolumedemanded

andisdefinedbyanormalprobabilitydistributionwithmeanof1,050andstandarddeviationof410pairsofjeans.Thepriceisuncertainanddefinedbyauniformprobability distributionfrom$20to$26.Thevariablecostisnotconstantbutdefinedbyatriangular probabilitydistribution.Wecandeterminethe

averageprofitandprofitabilitywiththegivenprobabilisticvariables.CrystalBallSimulationofProfitAnalysisModel(2of13)Copyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(4of13)Exhibit14.112.Clickon“DefineAssumption”1.ClickoncellC4todefinenormaldistributionparameters=C4*C5-C6-(C4*C7)Copyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(6of13)Exhibit14.12Namepulledfromoriginalspreadsheet1.Entermeanandstandarddeviation3.Clickon“OK”toreturntothespreadsheet2.Click“Enter”toconfiguredistributioninwindowCopyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(7of13)Exhibit14.13EnterminimumandmaximumvaluesforthedistributionCopyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(8of13)Exhibit14.14EnterthreeestimatesCopyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(9of13)Exhibit14.151.Clickon“DefineForecast”2.TypeinunitsCopyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(10of13)Exhibit14.162.Clickon“Start”tobeginthesimulation1.Clickon“RunPreferences”toindicatethenumberoftrialsandseednumberCopyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(11of13)Exhibit14.171.Enterthenumberoftrials2.Gotothe“Sampling”screentoentertheseednumberCopyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(12of13)Exhibit14.18ClickheretorepeatthesamesimulationCopyright©2016PearsonEducation,Inc.Exhibit14.19CrystalBallSimulationofProfitAnalysisModel(13of13)Clickon“View”,then“Statistics”togotothestatisticalsummaryscreen(Exhibit14.20)2.Clickheretostartthesimulation1.ClickheretoestablishthenumberoftrialsandtheseednumberSetnewrunpreferencesClickheretoresetthesimulationandrunitagainCopyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(13of13)Exhibit14.20Clickon“View”toreturntotheFrequencywindowMeanprofitvalueCopyright©2016PearsonEducation,Inc.CrystalBallSimulationofProfitAnalysisModel(14of14)Exhibit14.21Movearrowto“0.00”orsetlowerlimitequalto0.00Probability(.8136)thatthecompanywillbreakevenCopyright©2016PearsonEducation,Inc.Theanalystwantstobecertainthatthemodelisinternallycorrectandthatalloperationsarelogicalandmathematicallycorrect.Testingproceduresforvalidity: Runasmallnumberoftrialsofthemodelandcompare withmanuallyderivedsolutions.

Dividethemodelintopartsandrunpartsseparatelyto reducethecomplexityofchecking.

Simplifymathematicalrelationships(ifpossible)for easiertesting.

Compareresultswithactualreal-worlddata.VerificationoftheSimulationModel(1of2)Copyright©2016PearsonEducation,Inc.Theanalystmustdetermineifthemodel’sstartingconditionsarecorrect(systemempty,etc.).Mustdeterminehowlongmodelshouldruntoinsuresteady-stateconditions.Astandard,fool-proofprocedureforvalidationisnotavailable.Validityofthemodelrestsultimatelyontheexpertiseandexperienceofthemodeldeveloper.VerificationoftheSimulationModel(2of2)Copyright©2016PearsonEducation,Inc.QueuingInventoryControlProductionandManufactu