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.docx
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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.docx
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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
Chapter15
computersimulation:
BasicConcepts
ReviewQuestions
15.1-1Computersimulationimitatestheoperationofastochasticsystembyusingthecorrespondingprobabilitydistributionstorandomlygeneratethevariouseventsthatoccurinthesystem.
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.
15.3-1Fritzbeganbysimulatingthecurrentoperationoftheshop.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$4billionperyear.
15.5-1Themanagementscienceteamneedstobeginbymeetingwithmanagement.
15.5-2Asimulationmodeloftenisformulatedintermsofaflowdiagram.
15.5-3Beforeconstructingacomputerprogram,themanagementscienceteamshouldengagethepeoplemostintimatelyfamiliarwithhowthesystemwilloperateincheckingtheaccuracyofthesimulationmodel.
15.5-4Ageneral-purposesimulationlanguageiscapableofprogrammingalmostanykindofsimulationmodel.Applications-orientedsimulatorsaredesignedforsimulatingfairlyspecifictypesofsystems.
15.5-5Inananimation,keyelementsofasystemarerepresentedinacomputerdisplaybyiconsthatchangeshape,colororpositionwhenthereisachangeinthestateofthesimulationsystem.
15.5-6Willthemeasuresofperformancefortherealsystembecloselyapproximatedbythevaluesofthesemeasuresgeneratedbythesimulationmodel?
15.5-7Eachsimulationruncanbeviewedasastatisticalexperimentthatisgeneratingstatisticalobservationsoftheperformanceofthesimulatedsystem.
15.5-8Theoutputfromthesimulationrunnowprovidestatisticalestimatesofthedesiredmeasuresofperformanceforeachsystemconfigurationofinterest.
15.5-9Presentationisusuallydonethroughbothawrittenreportandaformaloralpresentationtothemanagersresponsibleformakingthedecisionsregardingthesystemunderstudy.
Problems
15.1a)Letthenumbers0.0000to0.4999correspondtoheadsandthenumbers0.5000to0.9999correspondtotails.Therandomobservationsforthrowinganunbiasedcoinare0.3039=heads,0.7914=tails,0.8543=tails,0.6902=tails,0.3004=heads,and0.0383=heads.
b)Letthenumbers0.0000to0.5999correspondtostrikesandthenumbers0.6000to0.9999correspondtoballs.Therandomobservationsforpitchesare0.3039=strike,0.7914=ball,0.8543=ball,0.6902=ball,0.3004=strike,and0.0383=strike.
c)Letthenumbers0.0000to0.3999correspondtogreenlights,thenumbers0.4000to0.4999correspondtoyellowlights,andthenumbers0.5000to0.9999correspondtoredlights.Therandomobservationsforlightsare0.3039=green,0.7914 = red,0.8543 = red,0.6902 = red,0.3004=green,and0.0383=green.
15.2a)Answerswillvary.
b)TheformulaincellD13is=VLOOKUP(C13,$G$5:
$H$6,2).
c)Asimulationwith14replications:
d)Asimulationwith1000replications:
15.3a)Answerswillvary.
b)Letthenumbers0.0000to0.4999correspondtoheadsandthenumbers0.5000to0.9999correspondtotails.
Group1:
0.7142=T,0.4546=H,0.3142=H
Group2:
0.1722=H,0.0932=H,0.3645=H
Group3:
0.1636=H,0.7572=T,0.3067=H
Group4:
0.9520=T,0.8548=T,0.7464=T
Group5:
0.9781=T,0.6584=T,0.8829=T
Group6:
0.7861=T,0.0679=H,0.9296=T
Group7:
0.4430=H,0.1223=H,0.4530=H
Group8:
0.3972=H,0.9289=T,0.2195=H
Groupswith0heads=2,with1heads=1,with2heads=3,with3heads=2
c)
d)Answerswillvary.Thefollowing8replicationshave0replicationswith0heads(0/8),5replicationswith1head(5/8),2replicationwith2heads(2/8),and1replicationwith3heads(1/8).Thisisnotveryclosetotheexpectedprobabilitydistribution.
e)Answerswillvary.Withthefollowing800replications,97have0heads(97/800),324have1head(324/800),289have2heads(289/800),and90have3heads(90/800).Thisisquiteclosetotheexpectedprobabilitydistribution.
15.4a)Ifitisrainingthenletthenumbers0.0000to0.5999correspondtorainforthenextdayand0.6000to0.9999correspondtoclearforthenextday.Ifitisclearthenletthenumbers0.0000to0.7999correspondtoclearforthenextdayandthenumbers0.8000to0.9999correspondtorainforthenextday.
Day
RandomNumber
Weather
1
0.3039
clear
2
0.7914
clear
3
0.8543
rain
4
0.6902
clear
5
0.3004
clear
6
0.0383
clear
7
0.3883
clear
8
0.6052
clear
9
0.2231
clear
10
0.4250
clear
b)
15.5a)
b)Answerswillvary.Hereisonesimulationof25replications.
c)Answerswillvary.Forthese25tosses,alossoccursontoss2,awinontoss3,alossontoss5,alossontoss11,alossontoss17,awinontoss21,alossontoss23,andwinontoss25.
15.6a)Prob
(2)=4/25;Prob(3)=7/25;Prob(4)=8/25;Prob(5)=5/25;Prob(6)=1/25
b)Mean=
(2)(4/25)+(3)(7/25)+(4)(8/25)+(5)(5/25)+(6)(1/25)=3.68stoves
c)Randomnumberscanbeassignedtothevarioussaleslevelstosimulatedailysales.Letthenumbers0.000to0.1599correspondto2stovesbeingsoldinaday,thenumbers0.1600to0.4399correspondto3stoves,thenumbers0.4400to0.7599correspondto4stoves,thenumbers0.7600to0.9599correspondto5stoves,andthenumbers0.9600to0.9999correspondto6stoves.
d)Salesare0.4476=4stoves,0.9713=6stoves,and0.0629=2stovesonthethreedays.Theaverageis4,whichis0.32higherthanthemeanobtainedinpartb.
e)Answerswillvary.Thefollowing300-daysimulationyieldedanaveragedemandof3.617.
15.7a)
b)F(x)=(x+10)/50=0.0965whenx=–5.18
F(x)=(x+10)/50=0.5692whenx=18.46
F(x)=(x+10)/50=0.6658whenx=23.29
c)=–10+50*RAND()
15.8a)
b)F(x)=(x–3)/5=0.6506whenx=6.25
F(x)=(x–3)/5=0.0740whenx=3.37
F(x)=(x–3)/5=0.8443whenx=7.22
F(x)=(x–3)/5=0.4975whenx=5.49
F(x)=(x–3)/5=0.8178whenx=7.09
c)Average=5.88whichishigherthatthemeanof5.5
d)Resultswillvary.Thefollowing500-daysimulationyieldedanaverageof5.426.
15.9a)Letthenumbers0.0000to0.3999correspondtoaminorrepairand0.4000to0.9999correspondtoamajorrepair.Therandomnumbersthenindicate0.7256=major,0.0817=minor,0.4392=major.
Usingtherandomnumbers,theaveragelengthofthethreerepairsisthen
1.2243hours(firstmajorrepair)
0.9503hours(minorrepair)
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