Transcript Lecture_13_ProjectMgmt_Rosen.ppt

Project Management – Part 1
Overview
 What is a project?
 Project management techniques
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Activity lists
Network diagrams
Critical path analysis
Gant charts
Definition
 Project
 a series of jobs usually directed toward
some major output and requiring a
significant period of time to perform
Over the next few days we’ll cover some
project management techniques…
Activity Lists
 Breakdown of all activities/tasks in a project
 Precedence constraints
 One task can’t be started until another is finished
 Duration of activities
Activity List for Example Problem
Network Diagrams
 Show the sequence of activities in a project
 Consists of nodes and arrows
 Nodes show activities (AON: activity on node)
 Arrows show precedence
 We won’t cover AOA (activity-on-arrow)
 So don’t worry about p. 270-271
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Critical Path Analysis
 Find all paths and compute expected length
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ADEJ
BCDEJ
BCFGJ
BCFHJ
BI
= 18
= 23
= 17
= 15
= 10
Critical Path
 Longest path is duration of the project
 Delays in activities on the critical path will delay the
project
Early Start/Early Finish (ES/EF)
 The earliest an activity can be started and
finished (without delaying the project).
 ES = 0 if no predecessors
 ES = maximum EF of the predecessors
 EF = ES + activity duration
Work forward
through time
ES
0
EF
3
4
A
8
D
E
4
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5
B
3
C
J
3
2
F
2
H
ES = 0 because no predecessors
EF = 3 since 0 + 3 = 3
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5
ES
0
EF
3
A
3
4
8
D
E
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0
5
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3
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3
C
2
F
2
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ES
0
EF
3
A
3
4
8
D
E
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0
5
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3
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ES
0
EF
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0
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5
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F
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ES
0
EF
3
A
3
4
8
D
E
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0
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5
5
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3
8
3
C
2
F
2
H
5
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ES
0
EF
3
A
3
4
8
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E
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0
5
B
5
5
J
3
8
3
C
2
F
2
H
5
Remember: ES is always the largest
of the predecessors’ Early Finishes
10
I
5
ES
0
EF
3
A
8
3
4
8
D
E
4
G
0
5
B
5
5
J
3
8
3
C
2
F
2
H
5
10
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5
ES
0
EF
3
A
8
3
4
12
8
D
E
4
G
0
5
B
5
5
J
3
8
3
C
2
F
2
H
5
10
I
5
ES
0
EF
3
A
8
3
4
D
12
12 8
E
4
G
0
5
B
5
5
8
3
C
8
J
3
2
F
2
H
5
10
I
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ES
0
EF
3
A
8
3
4
D
12
12 8 20
E
4
G
0
5
B
5
5
8
3
C
8
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3
10
2
F
2
H
5
10
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5
ES
0
EF
3
A
8
3
4
D
12
12 8 20
E
10
4
G
0
5
B
5
5
8
3
C
8
J
3
10
2
F
10 2
H
5
10
I
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ES
0
EF
3
A
8
3
4
D
12
12 8 20
E
10 4 14
G
0
5
B
5
5
8
3
C
8
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3
10
2
F
10 2 12
H
5
10
I
5
ES
0
EF
3
A
8
3
4
D
12
12 8 20
E
10 4 14 20
G
0
5
B
5
5
8
3
C
8
J
3
10
2
F
10 2 12
H
5
10
I
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ES
0
EF
3
A
8
3
4
D
12
12 8 20
E
10 4 14 20 23
3
G
0
5
B
5
5
8
3
C
8
J
10
2
F
10 2 12
H
5
10
I
5
Late Start/Late Finish (LS/LF)
 The latest an activity can start and finish
(without delaying the project)
 If last activity, LF = EF of last activity on critical path
 LF = minimum LS of successors
 LS = LF – activity duration
Work backwards
through time
3
4
A
8
D
E
ES
4
G
5
B
3
C
EF
20 323
J
23
2
F
LF
2
H
I
Remember: at the last activity,
LF = EF of last activity on Critical Path
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3
4
A
8
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E
4
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3
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3
20 23
2
F
LS
LF
2
H
I
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3
4
A
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D
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B
3
C
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3
20 23
2
F
LS
LF
2
H
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5
23
3
4
A
8
D
E
4
G
5
B
3
C
J
3
20 23
2
F
LS
LF
2
H
I
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18 23
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A
8
D
E
20
4
G
5
B
3
C
J
3
20 20 23
2
F
LS
LF
2
H
20
I
5
18 23
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4
A
8
D
E
12 20
4
G
5
B
3
C
2
J
3
16 20 20 23
F
LS
LF
2
H
18 20
Recall, LF is equal to the
smallest LS of the activity’s
successors
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5
18 23
3
4
A
8
D
E
12 20
4
G
5
B
3
C
J
3
16 20 20 23
2
F
LS
16
LF
2
H
18 20
I
5
18 23
3
4
A
8
D
E
12 20
4
G
5
B
3
C
2
3
16 20 20 23
F
14 16
J
LS
LF
2
H
18 20
I
5
18 23
3
4
A
8
D
E
12
12 20
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G
5
B
3
C
2
3
16 20 20 23
F
14 16
J
LS
LF
2
H
18 20
I
5
18 23
3
4
A
8
D
8
E
12
12 20
4
G
5
B
3
C
2
3
16 20 20 23
F
14 16
J
LS
LF
2
H
18 20
I
5
18 23
3
4
A
8
D
8
E
12
12 20
4
G
5
B
3
2
C
14 16
3
16 20 20 23
F
8
J
LS
LF
2
H
18 20
I
5
18 23
3
4
A
8
D
8
E
12
12 20
4
G
5
3
B
2
C
5
14 16
3
16 20 20 23
F
8
J
LS
LF
2
H
18 20
I
5
18 23
3
4
A
8
D
8
8
E
12
12 20
4
G
5
3
B
2
C
5
14 16
3
16 20 20 23
F
8
J
LS
LF
2
H
18 20
I
5
18 23
3
4
A
5
8
D
8
8
E
12
12 20
4
G
5
3
B
2
C
5
14 16
3
16 20 20 23
F
8
J
LS
LF
2
H
18 20
I
5
18 23
3
4
A
5
8
D
8
8
E
12
12 20
4
G
5
3
B
2
C
5
5
14 16
3
16 20 20 23
F
8
J
LS
LF
2
H
18 20
I
5
18 23
3
4
A
5
8
D
8
8
E
12
12 20
4
G
5
3
B
0
2
C
5
5
14 16
3
16 20 20 23
F
8
J
LS
LF
2
H
18 20
I
5
18 23
0
3
A
5
3
8
8
8
4
12
D
12 8 20
E
12
12 20
ES
10 4 14 20 23
3
G
0
5
5
5
B
0
3
8
C
5
5
8
2
10
14 16
J
16 20 20 23
F
8
EF
10 2 12
LS
LF
5
10
H
18 20
I
5
18 23
Slack
 The most you can delay an activity without
delaying the project
 Slack = LS - ES = LF - EF
 Critical activities have zero slack
 Helps to set priorities, scrutiny of management
0
3
A
5
3
8
8
8
4
12
D
12 8 20
E
12
12 20
ES
10 4 14 20 23
3
G
0
5
5
5
B
0
3
8
C
5
5
8
2
10
14 16
J
16 20 20 23
F
8
EF
10 2 12
LS
LF
5
10
H
18 20
Critical activities have zero slack
I
5
18 23
0
3
A
5
3
8
8
8
4
12
D
12 8 20
E
12
12 20
ES
10 4 14 20 23
3
G
0
5
5
5
B
0
3
8
C
5
5
8
2
10
14 16
J
16 20 20 23
F
8
EF
10 2 12
LS
LF
5
10
H
18 20
Critical activities have zero slack
I
5
18 23
Gantt Chart: Early Start/Finish
0
Early
Start of
Activity F
Scheduled
Time of
Activity F
Late Finish
of Activity F
Gantt Chart: Late Start/Finish
For next time
 Finish reading the project management chapter