数据模型与决策第二版课后答案([美]希利尔Hillier)第15章参考答案

15-1CHAPTER15COMPUTERSIMULATION:BASICCONCEPTSReviewQuestions15.1-1Computersimulationimitatestheoperationofastochasticsystembyusingthecorrespondingprobabilitydistributionstorandomlygeneratethevariouseventsthatoccurinthesystem.15.1-2Computersimulationtypicallytakesalotoftimeandeffort,whichtendstoberelativelyexpensive.15.1-3Computersimulationtypicallyisusedwhenthestochasticsysteminvolvedistoocomplextobeanalyzedsatisfactorilybymathematicalmodels.15.1-4Arandomnumberisanumberbetween0and1whichisgeneratedinsuchawaythateverypossiblenumberwithinthisintervalhasanequalchanceofoccurring.Thesenumbersarethenusedtogeneraterandomoccurrencesfromprobabilitydistributions.15.1-5Theinversetransformationmethodisamethodforgeneratingrandomobservationsfromaprobabilitydistribution.Thefirststepistogenerateauniformrandomnumberr.ThesecondstepistofindthevalueofxsuchthatF(x)=r.Thevalueofxisthedesiredrandomobservationfromtheprobabilitydistribution.15.2-1HerrCuttermustdecidewhetherornottohireanassociate.15.2-2Thefirstruleofthumbisthatinawellrunbarbershopwithalong-establishedclientele,theseloyalcustomersarewillingtotolerateanaveragewaitingtimeofabout20minutesuntilthehaircutbegins.Thesecondruleofthumbisthatinawellrunbarbershop,newcustomersarewillingtotolerateanaveragewaitingtimeofabout10minutesbeforethehaircutbegins.15.2-3Theprobabilitydistributionsforservicetimesandinterarrivaltimesneedtobeestimated.15.2-4Uniformrandomnumbersandtheinversetransformationmethodareusedtogeneraterandomobservationsfromthesedistributions.15.2-5Asimulationclockisavariableinthecomputerprogramthatrecordshowmuchsimulatedtimehaselapsed.15.2-6Themainprocedureforadvancingthetimeonthesimulationclockiscallednext-eventtimeadvance.15.2-7ThestateofthesystemisN(t)=numberofcustomersinthesystemattimet.15.2-8Theonlydifferencecomeswhenthenext-eventtime-advanceprocedureisdeterminingwhicheventoccursnext.Insteadofjusttwopossibilitiesforthisnextevent,therearethree.15-215.3-1Fritzbeganbysimulatingthecurrentoperationoftheshop.Thiswaslargelytotestthevalidityofhissimulationmodel.15.3-2TheQueueingSimulatorobtainsapointestimateanda95%confidenceinterval.15.3-3Fritzcomparedtheresultsfromthesimulationrunwiththeanalyticalresultsavailable.HealsoaskedHerrCutterwhetherthenumbersseemconsistentwithwhathehasbeenexperiencinginthebarbershop.15.3-4Fritz’ssimulationmodelassumesthatthesystemhasaninfinitequeueandthatoncestarted,thesystemoperatescontinuallywithouteverclosingandreopening.Asimulationmodeldoesnotneedtobeacompletelyrealisticrepresentationoftherealsystem.15.3-5ItisestimatedthatHerrCutter’sincomewouldeventuallyincreaseifheaddsanassociate.15.4-1Thecasestudyisanexampleofqueueingsystemsimulation.15.4-2Themanagementscienceteamsimulatedvariousredesignsofthecompany’sentiresupplychain.15.4-3TheprobabilityofmeetingadeadlineisbeingestimatedwhencomputersimulationisusedtosupplementthePERTthree-estimateapproach.15.4-4Howmanymachinesofeachtypeshouldbeprovided?15.4-5Anewdistributionsystemwithcentraldispatchingwasbeingdesigned.15.4-6Computersimulationprovidesaprobabilitydistributionofthereturnfromtheinvestment.15.4-7Simulatingtheuseofhospitalresourceswhentreatingpatientswithcoronaryheartdiseasehasbeendone.15.4-8Anautomatedsystemtohandlemailwasbeingplanned.Itwasprojectedtoachievelaborsavingsofover$4billionperyear.15.5-1Themanagementscienceteamneedstobeginbymeetingwithmanagement.15.5-2Asimulationmodeloftenisformulatedintermsofaflowdiagram.15.5-3Beforeconstructingacomputerprogram,themanagementscienceteamshouldengagethepeoplemostintimatelyfamiliarwithhowthesystemwilloperateincheckingtheaccuracyofthesimulationmodel.15.5-4Ageneral-purposesimulationlanguageiscapableofprogrammingalmostanykindofsimulationmodel.Applications-orientedsimulatorsaredesignedforsimulatingfairlyspecifictypesofsystems.15.5-5Inananimation,keyelementsofasystemarerepresentedinacomputerdisplaybyiconsthatchangeshape,colororpositionwhenthereisachangeinthestateofthesimulationsystem.15.5-6Willthemeasuresofperformancefortherealsystembecloselyapproximatedbythevaluesofthesemeasuresgeneratedbythesimulationmodel?15-315.5-7Eachsimulationruncanbeviewedasastatisticalexperimentthatisgeneratingstatisticalobservationsoftheperformanceofthesimulatedsystem.15.5-8Theoutputfromthesimulationrunnowprovidestatisticalestimatesofthedesiredmeasuresofperformanceforeachsystemconfigurationofinterest.15.5-9Presentationisusuallydonethroughbothawrittenreportandaformaloralpresentationtothemanagersresponsibleformakingthedecisionsregardingthesystemunderstudy.Problems15.1a)Letthenumbers0.0000to0.4999correspondtoheadsandthenumbers0.5000to0.9999correspondtotails.Therandomobservationsforthrowinganunbiasedcoinare0.3039=heads,0.7914=tails,0.8543=tails,0.6902=tails,0.3004=heads,and0.0383=heads.b)Letthenumbers0.0000to0.5999correspondtostrikesandthenumbers0.6000to0.9999correspondtoballs.Therandomobservationsforpitchesare0.3039=strike,0.7914=ball,0.8543=ball,0.6902=ball,0.3004=strike,and0.0383=strike.c)Letthenumbers0.0000to0.3999correspondtogreenlights,thenumbers0.4000to0.4999correspondtoyellow