数据模型与决策运筹学课后习题和案例答案008.docx
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数据模型与决策运筹学课后习题和案例答案008
Chapter8
Pert/cpmmodelsforProjectManagement
ReviewQuestions
8.1-1Thebidisfor$5.4millionwithapenaltyof$300,000ifthedeadlineof47weeksisnotmet.Inaddition,abonusof$150,000willbepaidiftheplantiscompletedwithin40weeks.
8.1-2Hehasdecidedtofocusonmeetingthedeadlineof47weeks.
8.1-3Animmediatepredecessorisanactivitythatmustbecompletedjustpriortostartingthegivenactivity.Giventheimmediatepredecessorsofanactivity,thisactivitythenbecomestheimmediatesuccessorofeachoftheseimmediatepredecessors.
8.1-4
（1）theactivitiesoftheproject;
（2）theimmediatepredecessorsoftheactivities;and（3）theestimateddurationoftheactivities
8.2-1
（1）activityinformation;
（2）precedencerelationships;and（3）timeinformation（duration）
8.2-2InanAOAnetwork,eachactivityisrepresentedbyanarc,whileinanAONnetwork,eachactivityisrepresentedbyanode.AONnetworksarebeingusedhere.
8.2-3ThebarsinaGanttchartshowthescheduledstartandfinishtimesforactivitiesinaproject.
8.3-1（a）Apaththroughaprojectnetworkisoneoftheroutesfollowingthearrows（arcs）fromthestartnodetothefinishnode;（b）thelengthofapathisthesumoftheestimateddurationsoftheactivitiesonthepath;（c）thelongestpathiscalledthecriticalpath.
8.3-2
（1）Theactualdurationofeachactivitymustbethesameasitsestimatedduration;and
（2）eachactivitymustbeginassoonasallitsimmediatepredecessorsarefinished.
8.3-3Theearlieststarttimeofanactivityisequaltothelargestoftheearliestfinishtimesofitsimmediatepredecessors.
8.3-4Aforwardpassistheprocessofstartingwiththeinitialactivitiesandworkingforwardintimetowardthefinalactivities.
8.3-5Itisalastchanceschedulebecauseanythinglaterwilldelaythecompletionoftheproject.
8.3-6Thelatestfinishtimeofanactivityisequaltothesmallestofthelateststarttimesofitsimmediatesuccessors.
8.3-7Abackwardpassstartswiththefinalactivitiesandworksbackwardintimetowardtheinitialactivitiesinsteadofstartingwiththeinitialactivities.
8.3-8Anydelayalongthecriticalpathwilldelayprojectcompletion.
8.3-9
（1）Identifythelongestpaththroughtheprojectnetwork;and
（2）identifytheactivitieswithzeroslack—theyareonthecriticalpath.
8.4-1Thethreeestimatesarethemostlikelyestimate,optimisticestimate,andpessimisticestimate.
8.4-2Theoptimisticandpessimisticestimatesaremeanttolieattheextremesofwhatispossible,whereasthemostlikelyestimateprovidesthehighestpointoftheprobabilitydistribution.
8.4-3Itisassumedthatthemeancriticalpathwillturnouttobethelongestpaththroughtheprojectnetwork.
8.4-4Itisassumedthatthedurationsoftheactivitiesonthemeancriticalpatharestatisticallyindependent.
8.4-5μp=sumofthemeansofthedurationsfortheactivitiesonthemeancriticalpath.
8.4-6σp2=sumofthevariancesofthedurationsfortheactivitiesonthemeancriticalpath.
8.4-7Itisassumedthattheformoftheprobabilitydistributionofprojectdurationisthenormaldistribution.
8.4-8Itisusuallyhigherthanthetrueprobability.
8.5-1Usingovertime,hiringadditionallabor,andusingspecialmaterialsorequipmentareallwaysofcrashinganactivity.
8.5-2Thetwokeypointsarelabelednormalandcrash.Thenormalpointshowsthetimeandcostoftheactivitywhenitisperformedinthenormalway.Thecrashpointshowsthetimeandcostwhentheactivityisfullycrashed.
8.5-3No,onlycrashingactivitiesonthecriticalpathwillreducethedurationoftheproject.
8.5-4Crashcostsperweeksavedarebeingexamined.
8.5-5Thedecisionstobemadearethestarttimeofeachactivity,thereductioninthedurationofeachactivityduetocrashing,andthefinishtimeoftheproject.
8.5-6Anactivitycannotstartuntilitsimmediatepredecessorstartsandthencompletesitsduration.
8.5-7Becauseofuncertainty,theplanforcrashingtheprojectonlyprovidesa50%chanceofactuallyfinishingwithin40weeks,sotheextracostoftheplanisnotjustified.
8.6-1PERT/Costisasystematicproceduretohelpthemanagerplan,schedule,andcontrolprojectcosts.
8.6-2Itbeginsbydevelopinganestimateofthecostofeachactivitywhenitisperformedintheplannedway.
8.6-3Acommonassumptionisthatthecostsofperforminganactivityareincurredataconstantratethroughoutitsduration.
8.6-4Aworkpackageisagroupofrelatedactivities.
8.6-5PERT/Costusesearlieststarttimeandlateststarttimeschedulesasabasisfordevelopingcostschedules.
8.6-6APERT/Costscheduleofcostsshowstheweeklyprojectcostandcumulativeprojectcostforeachtimeperiod.
8.6-7APERT/Costreportshowsthebudgetedvalueoftheworkcompletedofeachactivityandthecostoverrunstodate.
8.6-8Sincedeviationsfromtheplannedworkschedulemayoccur,aPERT/Costreportisneededtoevaluatethecostperformanceofindividualactivities.
8.7-1Planning,scheduling,dealingwithuncertainty,time-costtrade-offs,andcontrollingcostsareaddressedbyPERT/CPM.
8.7-2Computerimplementationhasallowedforapplicationtolargerprojects,fasterrevisionsinprojectplansandeffortlessupdatesandchangesinschedules.
8.7-3Theaccuracyandreliabilityofend-pointestimatesarenotasgoodforpointsthatarenotattheextremesoftheprobabilitydistribution.
8.7-4ThetechniqueofcomputersimulationtoapproximatetheprobabilitythattheprojectwillmeetitsdeadlineisanalternativeforimprovingonPERT/CPM.
8.7-5ThePrecedenceDiagrammingMethodhasbeendevelopedasanextensionofPERT/CPMtodealwithoverlappingactivities.
8.7-6PERT/CPMassumesthateachactivityhasavailablealltheresourcesneededtoperformtheactivityinanormalway.
8.7-7Itencourageseffectiveinteractionbetweentheprojectmanagerandsubordinatesthatleadstosettingmutualgoalsfortheproject.
8.7-8Newimprovementsandextensionsarestillbeingdevelopedbuthavenotbeenincorporatedmuchintopracticeyet.
Problems
8.1a）
b）StartACFinishLength=4weeks
StartADEFinishLength=7weeks
StartBCFinishLength=5weeks
StartBDEFinishLength=8weeks*criticalpath
c）
Activity
ES
EF
LS
LF
Slack
CriticalPath
Start
0
0
0
0
0
Yes
A
0
2
1
3
1
No
B
0
3
0
3
0
Yes
C
3
5
6
8
3
No
D
3
5
3
5
0
Yes
E
5
8
5
8
0
Yes
Finish
8
8
8
8
0
Yes
CriticalPath:
StartBDEFinish
d）No,thiswillnotshortenthelengthoftheprojectbecausetheactivityisnotonthecriticalpath.
8.2a）
b）StartADFinishLength=4weeks
StartAEFinishLength=5weeks
StartAFKFinisLength=8weeks*criticalpath
StartAGHIJFinishLength=8weeks*criticalpath
StartBDFinishLength=3weeks
StartBCEFinishLength=6weeks
StartBCHIJFinishLength=8weeks*criticalpath
StartBCKFinishLength=7weeks
c）
Activity
ES
EF
LS
LF
Slack
CriticalPath
Start
0
0
0
0
0
Yes
A
0
2
0
2
0
Yes
B
0
1
0
1
0
Yes
C
1
3
1
3
0
Yes
D
2
4
6
8
4
No
E
3
6
5
8
2
No
F
2
4
2
4
0
Yes
G
2
3
2
3
0
Yes
H
3
4
3
4
0
Yes
I
4
5
4
5
0
Yes
J
5
8
5
8
0
Yes
K
4
8
4
8
0
Yes
Finish
8
8
8
8
0
Yes
CriticalPaths:
StartAFKFinish
StartAGHIJFinish
StartBCHIJFinish
d）No,thiswillnotshortenthelengthoftheprojectbecauseAisnotonallofthecriticalpaths.
8.3a）
b,c,&d）
Activity
ES
EF
LS
LF
Slack
CriticalPath
Start
0
0
0
0
0
Yes
A
0
1
0
1
0
Yes
B
1
3
1
3
0
Yes
C
3
7
3
7
0
Yes
D
3
6
3
6
0
Yes
E
3
5
4
6
1
No
F
7
10
7
10
0
Yes
G
6
11
6
11
0
Yes
H
10
11
10
11
0
Yes
I
11
15
11
15
0
Yes
J
15
17
15
17
0
Yes
K
15
18
16
19
1
No
L
17
20
17
20
0
Yes
M
18
23
19
24
1
No
N
20
24
20
24
0
Yes
Finish
24
24
24
24
0
Yes
CriticalPaths:
StartABCFHIJLNFinish
StartABDGIJLNFinish
8.4a）
b）StartABJLFinishLength=75minutes*criticalpath
StartCDJLFinishLength=45minutes
StartEFJLFinishLength=72minutes
StartGHIJLFinishLength=67minutes
StartKLFinishLength=45minutes
c,d&e）
Activity
ES
EF
LS
LF
Slack
CriticalPath
Start
0
0
0
0
0
Yes
A
0
30
0
30
0
Yes
B
30
35
30
35
0
Yes
C
0
2
30
32
30
No
D
2
5
32
35
30
No
E
0
7
3
10
3
No
F
7
32
10
35
3
No
G
0
15
8
23
8
No
H
15
25
23
33
8
No
I
25
27
33
35
8
No
J
35
45
35
45
0
Yes
K
0
15
30
45
30
No
L
45
75
45
75
0
Yes
Finish
75
75
75
75
0
Yes
CriticalPath:
StartABJLFinish
f）Dinnerwillbedelayed3minutesbecauseofthephonecall.Ifthefoodprocessorisusedthendinnerwillnotbedelayedbecausetherewas3minutesofslackand5minutesofcuttingtimesavedandthecallonlyused6minutesofthe8total.
8.5a）StartADHMFinishLength=19weeks
StartBEJMFinishLength=20weeks*criticalpath
StartCFKNFinishLength=16weeks
StartAIMFinishLength=17weeks
StartCGLNFinishLength=20weeks*criticalpath
b）
Activity
ES
EF
LS
LF
Slack
CriticalPath
Start
0
0
0
0
0
Yes
A
0
6
1
7
1
No
B
0
3
0
3
0
Yes
C
0
4
0
4
0
Yes
D
6
10
7
11
1
No
E
3
10
3
10
0
Yes
F
4
8
8
12
4
No
G
4
10
4
10
0
Yes
H
10
13
11
14
1
No
I
6
11
9
14
3
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