project scheduling a. a. elimam finishstart. project scheduling need to plan and control large/time...
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Project SchedulingProject Scheduling
Need to plan and Need to plan and control large/time control large/time consuming projectsconsuming projects
Projects CharacteristicsProjects Characteristics
Projects are uniqueProjects are unique Time Estimation DifficultyTime Estimation Difficulty ControlControl
• Decomposition into smaller tasksDecomposition into smaller tasks
• Responsibility of a task given to a Responsibility of a task given to a specific individualspecific individual
Project Management: StagesProject Management: Stages
1.1. Define:Define: Describe goalDescribe goal
or Final outcome of Projector Final outcome of Project
2.2. Plan:Plan: Identify tasks / resources / Identify tasks / resources / timetime
3.3. Execute / Control:Execute / Control:
Time-cost Trade-offTime-cost Trade-off
ActivityActivity
The smallest unit of work The smallest unit of work effort consuming both effort consuming both timetime and and resources resources that the that the project manager can project manager can schedule and control.schedule and control.
Precedence RelationshipPrecedence Relationship
A sequencing constraint A sequencing constraint between interrelated activities between interrelated activities by which one activity cannot by which one activity cannot start until a preceeding activity start until a preceeding activity has been completed.has been completed.
ScheduleSchedule
A plan that sets priorities, A plan that sets priorities, determines determines start and finish start and finish timestimes, and allocates , and allocates resourcesresources to accomplish to accomplish the activities.the activities.
ExamplesExamples Constructing a building or amusement parkConstructing a building or amusement park Constructing a road, dam, or oil pipelineConstructing a road, dam, or oil pipeline Renovating a blighted urban areaRenovating a blighted urban area Developing a prototype for a new airplaneDeveloping a prototype for a new airplane Installing a large computer systemInstalling a large computer system Introducing a new productIntroducing a new product Organizing a state fairOrganizing a state fair Redesigning an office layoutRedesigning an office layout
Measuring Success of a projectMeasuring Success of a project
ConformanceConformance
TimeTime
BudgetBudget
Basic Questions
1.1. Project completion time?Project completion time?
2.2. Critical activities?Critical activities?
3.3. Activities that can be delayed?Activities that can be delayed?
How Long?How Long?
4.4. Starting / ending time of each activity?Starting / ending time of each activity?
5.5. Range of $’s spent on project?Range of $’s spent on project?
6.6. Time-cost trade-offTime-cost trade-off
Project ManagementProject ManagementBasic StepsBasic Steps
i.i. Describe projectDescribe project
ii.ii. Draw a network diagramDraw a network diagram
iii.iii. Provide time estimatesProvide time estimates
iv.iv. Analyze networkAnalyze network
v.v. Develop project planDevelop project plan
vi.vi. Update project planUpdate project plan
i. Describe projecti. Describe project
Activities / precedenceActivities / precedence end pointsend points
ii. Draw a network diagramii. Draw a network diagram
AOA: AOA: Arcs: Arcs: ActivitiesActivitiesNodes: Nodes: EventEvent
AON: AON: Nodes: Nodes: Activities ActivitiesArcs: Arcs: SequenceSequence
AOA and AON relationshipsAOA and AON relationships
1
2
AA
BB
CC3 4
(a) AOA approach: Event 4 cannot(a) AOA approach: Event 4 cannottake place until activities A, B andtake place until activities A, B andC have been completed.C have been completed.
(b) AON approach: Activity C(b) AON approach: Activity Ccannot take place until cannot take place until activities A and B completed.activities A and B completed.
A
B
C
Event
Event
Event Event
Activity
Activity
Activity
Implies time and resource consumption
Software
Activity RelationshipsActivity RelationshipsActivity Relationship
S precedes T, which precedes U.
AOA AON
1 2S
3T
4U
S T U
Activity RelationshipsActivity RelationshipsActivity Relationship
S and T must be completed before U can be started.
AOA AON
S
T
U
1
2
3T
S
4U
Activity RelationshipsActivity RelationshipsActivity Relationship
T and U cannot begin until S has been completed.
AOA AON
T
U
S
3
4
1
T
U2S
Activity RelationshipsActivity RelationshipsActivity Relationship
U and V cannot begin until both S and T have been completed.
AOA AON
1
2
4
5
U
V
S
T 3
S
T
U
V
Activity RelationshipsActivity RelationshipsActivity Relationship
U cannot begin until both S and T have been completed; V cannot begin until T has been completed.
AOA AON
S
T
U
V
1 3
Dummy
5
2 4 6
S U
T V
Activity RelationshipsActivity RelationshipsActivity Relationship
T and U cannot begin until S has been completed; V cannot begin until both T and U have been completed.
AOA AON
1 2 4
3
S T5
V
UDummy
S T V
U
iii. Provide Time Estimatesiii. Provide Time Estimates
Deterministic Deterministic CPMCPM
CCritical ritical PPath ath MMethodethod
oror Probabilistic Probabilistic PERT PERT
PProgram rogram EEvaluation and valuation and RReview eview TTechnique echnique then CPMthen CPM
iv. Analyze Networkiv. Analyze Network
Identify critical path (CP) and Identify critical path (CP) and activities on it activities on it
Estimate probability of Estimate probability of completing project on timecompleting project on time
Explore time-cost trade-offExplore time-cost trade-off
v. Develop project plan
Schedule each activity Schedule each activity (particularly on CP)(particularly on CP)
Monitor actual Monitor actual planned. planned.
vi. Update project planvi. Update project plan
Adjust schedule on Adjust schedule on
the basis of actualsthe basis of actuals
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff.BSelect site and do site survey.CSelect equipment.DPrepare final construction plans and layout.EBring utilities to the site.FInterview applicants and fill positions in nursing,support staff, maintenance, and security.GPurchase and take delivery of equipment.HConstruct the hospital.IDevelop and information system.JInstall the equipment.KTrain nurses and support staff.
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A
B
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A
C
B
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A
C
DB
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A
C
D
E
B
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A F
C
D
E
B
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A F
C G
D
E
B
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A F
C G
D
E
HB
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A F
I
C G
D
E
HB
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A F
I
C G
D
E
HB J
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A F
I
C G
D
E
HB J
K
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
AON Network
A F
I
C G Finish
D
E
HB J
K
Start
St. Adolf’s HospitalSt. Adolf’s HospitalImmediate
Activity Description Predecessor(s)
ASelect administrative and medical staff. —BSelect site and do site survey. —CSelect equipment. ADPrepare final construction plans and layout. BEBring utilities to the site. BFInterview applicants and fill positions in nursing,support staff, maintenance, and security. AGPurchase and take delivery of equipment. CHConstruct the hospital. DIDevelop and information system. AJInstall the equipment. E,G,HKTrain nurses and support staff. F,I,J
Completion Time
FinishStart
A 12
C 10
G 35
H 40
D 10
E 24
J 4
K 6
F 10
I 15
B 9
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
F
10
Earliest StartandEarliest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0
I
15
F
10
Earliest StartandEarliest Finish Times
Earliest start time
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
Earliest StartandEarliest Finish Times
Earliest start time Earliest finish time
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
0 9
Earliest StartandEarliest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
9 33
0 9 9 19
Earliest StartandEarliest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22
9 33
0 9 9 19
12 22
Earliest StartandEarliest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22
19 59
9 33
0 9 9 19
12 22
Earliest StartandEarliest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22
22 57
19 59
9 33
0 9 9 19
12 22
Earliest StartandEarliest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22
22 57
59 6319 59
9 33
0 9 9 19
12 22
Earliest StartandEarliest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
Earliest StartandEarliest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
Latest StartandLatest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
Latest StartandLatest Finish Times
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
63 69 Latestfinishtime
St. Adolf’s HospitalSt. Adolf’s Hospital
Latest StartandLatest Finish Times
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
63 69
Lateststarttime
Latestfinishtime
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
53 63 63 69
59 63Latest StartandLatest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
53 63 63 69
24 59
19 59
35 59
59 63Latest StartandLatest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
53 63 63 69
14 24 24 59
9 19 19 59
35 59
59 63Latest StartandLatest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 69
14 24 24 59
0 9 9 19 19 59
35 59
59 63Latest StartandLatest Finish Times
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 69
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Activity Slack Analysis
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 69
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Activity Slack Analysis
LS - ES = S
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 69
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Activity Slack Analysis
LS - ES = S63 - 63 = 0
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 69
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Activity Slack Analysis
LF - EF = S69 - 69 = 0
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 69
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Activity Slack Analysis
0
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 69
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Activity Slack Analysis
0000 00 00
0
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
0 12
I
15
F
10
12 27
12 22 63 69
22 57
59 6319 59
9 33
0 9 9 19
12 22
48 63
2 14 53 63 63 69
14 24 24 59
0 9 9 19 19 59
35 59
59 63
Activity Slack Analysis
0000 00 00
22
22
2626
4141
3636
0
22
St. Adolf’s HospitalSt. Adolf’s Hospital
FinishStart
A
12
C
10
G
35
E
24
0 12
I
15
F
10
12 27
12 22
22 57
9 33
12 22
48 63
2 14 53 63
14 24 24 59
35 59
0000 00 00
22
22
2626
4141
3636
0
22
B
9
0 9
0 9
D
10
9 19
9 19
H
40
19 5919 59
J
4
59 6359 63
K
6
63 6963 69
Critical Path
St. Adolf’s HospitalSt. Adolf’s Hospital
A F
I
C G Finish
D
E
HB J
K
Start
Probabilistic Time Estimates
St. Adolf’s HospitalSt. Adolf’s Hospital
Activity B
MostOptimistic Likely Pessimistic
(a) (m) (b)7 8 15
Probabilistic Time Estimates
A F
I
C G Finish
D
E
HB J
K
Start
St. Adolf’s HospitalSt. Adolf’s Hospital
Activity B
MostOptimistic Likely Pessimistic
(a) (m) (b)7 8 15
Probabilistic Time Estimates
te = = 9 weeks7 + 4(8) + 15
6
A F
I
C G Finish
D
E
HB J
K
Start
St. Adolf’s HospitalSt. Adolf’s Hospital
Activity B
MostOptimistic Likely Pessimistic
(a) (m) (b)7 8 15
Probabilistic Time Estimates
te = = 9 weeks7 + 4(8) + 15
6
2 = = 1.78( )15 - 7
6
2
A F
I
C G Finish
D
E
HB J
K
Start
St. Adolf’s HospitalSt. Adolf’s Hospital
Optimistic Likely Pessimistic Expected VarianceActivity (a) (m) (b) Time (te ) (2 )
Time Estimates (wk) Activity Statistics
A F
I
C G Finish
D
E
HB J
K
Start
St. Adolf’s HospitalSt. Adolf’s Hospital
Optimistic Likely Pessimistic Expected VarianceActivity (a) (m) (b) Time (te ) (2 )
Time Estimates (wk) Activity Statistics
A 11 12 13 12 0.11B 7 8 15 9 1.78C 5 10 15 10 2.78D 8 9 16 10 1.78E 14 25 30 24 7.11F 6 9 18 10 4.00G 25 36 41 35 7.11H 35 40 45 40 2.78I 10 13 28 15 9.00J 1 2 15 4 5.44K 5 6 7 6 0.11
A F
I
C G Finish
D
E
HB J
K
Start
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Probabilities
Critical Path = B - D - H - J - K
T = 72 days TE = 69 days
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
2 = (variances of activities) z = T - TE
2
Probabilities
Critical Path = B - D - H - J - K
T = 72 days TE = 69 days
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
2 = (variances of activities) z = T - TE
2
2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
Probabilities
Critical Path = B - D - H - J - K
T = 72 days TE = 69 days
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
2 = (variances of activities) z = T - TE
2
2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
z =72 - 69
11.89
Probabilities
Critical Path = B - D - H - J - K
T = 72 days TE = 69 days
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
2 = (variances of activities) z = T - TE
2
2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
z = = 0.8772 - 69
11.89
Probabilities
Critical Path = B - D - H - J - K
T = 72 days TE = 69 days
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
2 = (variances of activities) z = T - TE
2
2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
z = = 0.8772 - 69
11.89
Probabilities
Critical Path = B - D - H - J - K
T = 72 days TE = 69 days
From Appendix 2Pz = .8078 .81
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Project duration (weeks)
69 72
Probability of meeting the schedule is 0.8078
Length of critical path
Normal distribution: Mean = 69 weeks; = 3.45 weeks
Probability of exceeding 72 weeks is 0.1922
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
2 = (variances of activities) z = T - TE
2
2 = 0.11 + 2.78 + 7.11 + 5.44 + 0.11 = 15.55
z = = 1.2772 - 67
15.55
Probabilities
Path = A - C - G - J - K
T = 72 days TE = 67 days
From Appendix 2Pz = .8980 .90
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Project duration (weeks)
67 69
Probability path B-D-H-J-K is less than 67 weeks
Normal distribution for path B-D-H-J-K: Mean = 69 weeks; = 3.45 weeks
Probability path A-C-G-J-K is more than 69 weeks
Normal distribution for path A-C-G-J-K: Mean = 67 weeks; = 3.94 weeks
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
8000 —
7000 —
6000 —
5000 —
4000 —
3000 —
0 —
Dir
ect
cost
(d
oll
ars)
| | | | | |5 6 7 8 9 10 11
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
8000 —
7000 —
6000 —
5000 —
4000 —
3000 —
0 —
Dir
ect
cost
(d
oll
ars)
Crash cost (CC)
Normal cost (NC)
| | | | | |5 6 7 8 9 10 11
Time (weeks)(Crash time) (Normal time)
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
8000 —
7000 —
6000 —
5000 —
4000 —
3000 —
0 —
Dir
ect
cost
(d
oll
ars)
Crash cost (CC)
Linear cost assumption
Normal cost (NC)
| | | | | |5 6 7 8 9 10 11
Time (weeks)(Crash time) (Normal time)
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
8000 —
7000 —
6000 —
5000 —
4000 —
3000 —
0 —
Dir
ect
cost
(d
oll
ars)
5200
Crash cost (CC)
Linear cost assumption
Normal cost (NC)
Estimated costs for a 2-week reduction, from 10 weeks to 8 weeks
| | | | | |5 6 7 8 9 10 11
Time (weeks)(Crash time) (Normal time)
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Minimum Cost ScheduleA-I-K: 33 weeks B-D-H-J-K: 69 weeksA-F-K: 28 weeks B-E-J-K: 43 weeksA-C-G-J-K: 67 weeks
Total cost = $2,624,000Indirect costs = $8,000/weekPenalty cost = $20,000/week after week 65
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Minimum Cost ScheduleA-I-K: 33 weeks B-D-H-J-K: 69 weeksA-F-K: 28 weeks B-E-J-K: 43 weeksA-C-G-J-K: 67 weeks
Total cost = $2,624,000Indirect costs = $8,000/weekPenalty cost = $20,000/week after week 65
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Minimum Cost ScheduleA-I-K: 33 weeks B-D-H-J-K: 69 weeksA-F-K: 28 weeks B-E-J-K: 43 weeksA-C-G-J-K: 67 weeks
Total cost = $2,624,000Indirect costs = $8,000/weekPenalty cost = $20,000/week after week 65
Critical Path B-D-H-J-K: 69 weeks
Crash Activity J by 3 weeks @ $1,000/week
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Minimum Cost ScheduleA-I-K: 33 weeks B-D-H-J-K: 69 weeksA-F-K: 28 weeks B-E-J-K: 43 weeksA-C-G-J-K: 67 weeks
Total cost = $2,624,000Indirect costs = $8,000/weekPenalty cost = $20,000/week after week 65
Critical Path B-D-H-J-K: 69 weeks
Crash Activity J by 3 weeks @ $1,000/week
3($28,000) - 3($1,000) = $81,000
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Minimum Cost ScheduleA-I-K: 33 weeks B-D-H-J-K: 69 weeksA-F-K: 28 weeks B-E-J-K: 43 weeksA-C-G-J-K: 67 weeks
Total cost = $2,624,000Indirect costs = $8,000/weekPenalty cost = $20,000/week after week 65
Critical Path B-D-H-J-K: 66 weeks
Crash Activity J by 3 weeks @ $1,000/week
3($28,000) - 3($1,000) = $81,000$2,624,000 - $81,000 = $2,543,000
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
Minimum Cost ScheduleA-I-K: 33 weeks B-D-H-J-K: 69 weeksA-F-K: 28 weeks B-E-J-K: 43 weeksA-C-G-J-K: 67 weeks
Total cost = $2,624,000 $2,543,000Indirect costs = $8,000/weekPenalty cost = $20,000/week after week 65
Critical Path B-D-H-J-K: 66 weeks
Crash Activity J by 3 weeks @ $1,000/week
3($28,000) - 3($1,000) = $81,000$2,624,000 - $81,000 = $2,543,000
St. Adolf’s HospitalSt. Adolf’s HospitalA F
I
C G Finish
D
E
HB J
K
Start
FinishStart
A
12
C
10
G
35
E
24
0 12
I
15
F
10
12 27
12 22
22 57
9 33
12 22
48 63
2 14 53 63
14 24 24 59
35 59
0000 00 00
22
22
2626
4141
3636
0
22
B
9
0 9
0 9
D
10
9 19
9 19
H
40
19 5919 59
J
4
59 6359 63
K
6
63 6963 69
Precedence for Playground activitiesPrecedence for Playground activities
CodeCode Activity Activity DescriptionDescription TimeTime Immediate Immediate Name Name (days) (days) PredecessorsPredecessors
AA PlanningPlanning Find location,Find location,determine resourcedetermine resourcerequirementsrequirements 2020 NoneNone
BB PurchasingPurchasing Requisition lumberRequisition lumberand sandand sand 6060 Planning (A)Planning (A)
CC ExcavationExcavation Dig and gradeDig and grade 100100 Planning (A)Planning (A)DD SawingSawing Saw lumber intoSaw lumber into
appropriate sizesappropriate sizes 3030 Purchasing (B)Purchasing (B)EE PlacementPlacement Position lumber inPosition lumber in
correct locationscorrect locations 2020 Sawing, excavation (D,C)Sawing, excavation (D,C)FF AssemblyAssembly Nail lumber together`Nail lumber together` 1010 Placement (E)Placement (E)GG InfillInfill Put sand in and underPut sand in and under
equipmentequipment 2020 Assembly (F)Assembly (F)HH OutfillOutfill Put dirt aroundPut dirt around
equipmentequipment 1010 Assembly( F)Assembly( F)II DecorationDecoration Landscape, paintLandscape, paint 3030 Infill, outfill (G,H)Infill, outfill (G,H)
Playground ProjectPlayground Project
AAPlanningPlanning
BBPurchasingPurchasing
DDSawingSawing
EEPlacementPlacement
CCExcavationExcavation
FFAssemblyAssembly
HHOutfillOutfill
IIDecorationDecoration
GGInfillInfill
Playground ProjectPlayground Project
APlanning
BPurchasing
DSawing
EPlacement
CExcavation
FAssembly
HOutfill
IDecoration
GInfill
ES=20ES=20EF=80EF=80
ES=80ES=80EF=110EF=110
ES=120ES=120EF=140EF=140
ES=20ES=20EF=120EF=120
ES=140ES=140EF=150EF=150
ES=170ES=170EF=200EF=200
ES=150ES=150EF=160EF=160
ES=150ES=150EF=170EF=170
ES=0ES=0EF=20EF=20
Two passTwo passapproachapproach
Forward PassForward Pass
Playground ProjectPlayground Project
APlanning
BPurchasing
DSawing
EPlacement
CExcavation
FAssembly
HOutfill
IDecoration
GInfill
ES=20ES=20EF=80EF=80LF=90LF=90LS=30LS=30
ES=80ES=80EF=110EF=110LF=120LF=120LS=90LS=90
ES=120ES=120EF=140EF=140LF=140LF=140LS=120LS=120
ES=20ES=20EF=120EF=120LF=120LF=120LS=20LS=20
ES=140ES=140EF=150EF=150LF=150LF=150LS=140LS=140
ES=170ES=170EF=200EF=200LF=200LF=200LS=170LS=170
ES=150ES=150EF=160EF=160LF=170LF=170LS=160LS=160
ES=150ES=150EF=170EF=170LF=170LF=170LS=150LS=150
ES=0ES=0EF=20EF=20LF=20LF=20LS=0LS=0
Two passTwo passapproachapproach
Backward PassBackward Pass
Playground ProjectPlayground Project
APlanning
BPurchasing
DSawing
EPlacement
CExcavation
FAssembly
HOutfill
IDecoration
GInfill
ES=20ES=20EF=80EF=80LF=90LF=90LS=30LS=30SSBB=10=10
ES=80ES=80EF=110EF=110LF=120LF=120LS=90LS=90SSDD=10=10
ES=120ES=120EF=140EF=140LF=140LF=140LS=120LS=120SSEE=0=0ES=20ES=20
EF=120EF=120LF=120LF=120LS=20LS=20SSCC=0=0
ES=140ES=140EF=150EF=150LF=150LF=150LS=140LS=140SSFF=0=0
ES=170ES=170EF=200EF=200LF=200LF=200LS=170LS=170SSII=0=0
ES=150ES=150EF=160EF=160LF=170LF=170LS=160LS=160SSHH=10=10
ES=150ES=150EF=170EF=170LF=170LF=170LS=150LS=150SSGG=0=0
ES=0ES=0EF=20EF=20LF=20LF=20LS=0LS=0SSAA=0=0
Two passTwo passapproachapproach
Playground ProjectPlayground Project
APlanning
BPurchasing
DSawing
EPlacement
CExcavation
FAssembly
HOutfill
IDecoration
GInfill
ES=20ES=20EF=80EF=80LF=90LF=90LS=30LS=30SSBB=10=10
ES=80ES=80EF=110EF=110LF=120LF=120LS=90LS=90SSDD=10=10
ES=120ES=120EF=140EF=140LF=140LF=140LS=120LS=120SSEE=0=0ES=20ES=20
EF=120EF=120LF=120LF=120LS=20LS=20SSCC=0=0
ES=140ES=140EF=150EF=150LF=150LF=150LS=140LS=140SSFF=0=0
ES=170ES=170EF=200EF=200LF=200LF=200LS=170LS=170SSII=0=0
ES=150ES=150EF=160EF=160LF=170LF=170LS=160LS=160SSHH=10=10
ES=150ES=150EF=170EF=170LF=170LF=170LS=150LS=150SSGG=0=0
ES=0ES=0EF=20EF=20LF=20LF=20LS=0LS=0SSAA=0=0
Critical PathCritical Path
Cost-time relationships analysisCost-time relationships analysis
55 66 77 88 99 1010 1111
Activity time duration (weeks)Activity time duration (weeks)
To
tal d
irec
t ac
tivi
ty c
ost
($)
To
tal d
irec
t ac
tivi
ty c
ost
($) 8,0008,000
7,0007,000
6,0006,000
5,0005,000
4,0004,000
3,0003,000
Crash time, costCrash time, cost
Linear cost assumptionLinear cost assumption
Estimated costs forEstimated costs fora 2-week reductiona 2-week reduction
Normal time, costNormal time, costHypotheticalHypotheticalactual cost curveactual cost curve NTNT NCNC
CTCT CCCC Cost to crash perCost to crash perweek = week = CC - NCCC - NC
NT - CTNT - CT
Limitations of PERT / CPMLimitations of PERT / CPM
project activities must be clearly defined, project activities must be clearly defined, independent, and stable in their relationshipsindependent, and stable in their relationships
precedence relationships must be specified precedence relationships must be specified and networked togetherand networked together
time activities in PERT are assumed to follow time activities in PERT are assumed to follow the beta probability distribution this may be the beta probability distribution this may be difficult to verifydifficult to verify
time estimates tend to be subjective, and are time estimates tend to be subjective, and are subject to fudging by managerssubject to fudging by managers
there is inherent danger in too much there is inherent danger in too much emphasis being placed on the critical pathemphasis being placed on the critical path
Resource LimitationsResource Limitations
2
B
5
4
C
2
5
A
1
6
D
3
Activity time in days
Workers required per day
FinishStart
3
E
3