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Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-1
Project Management
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-2
Definitions• Activity-on-Node (A-O-N) - Network
diagram convention in which nodes designate activities
• Activity-on-Arrow (A-O-A) - Network diagram convention in which arrows designate activities
Activity
(arrow)
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-3
Definitions• Path - a sequence of activities that
leads from the starting node to the finishing node.
Event1
Event2
Event3
Activity A Activity B
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-4
How many paths are in this network?
Event5
Event1
Event3
Event2
Event4
Event6
A(5)
B(2)
D(2)
E(3)
F(1)
G(4)
H(2)
C(3)
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-5
Event5
Event1
Event3
Event2
Event4
Event6
1-2-5-6
A(5)
C(3)
B(2)
D(2)
E(3)
F(1)
G(4)
H(2)
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-6
Event5
Event1
Event3
Event2
Event4
Event6
A(5)
C(3)
B(2)
D(2)
E(3)
F(1)
G(4)
H(2)
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-7
Event5
Event1
Event3
Event2
Event4
Event6
A(5)
C(3)
B(2)
D(2)
E(3)
F(1)
G(4)
H(2)
1-2-4-6
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-8
Event5
Event1
Event3
Event2
Event4
Event6
A(5)
C(3)
B(2)
D(2)
E(3)
F(1)
G(4)
H(2)
1-3-4-5-6
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-9
Event5
Event1
Event3
Event2
Event4
Event6
A(5)
C(3)
B(2)
D(2)
E(3)
F(1)
G(4)
H(2)
1-3-4-6
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-10
Event5
Event1
Event3
Event2
Event4
Event6
Critical Path - The longest path - determines the project duration.
A(5)
C(3)
B(2)
D(2)
E(3)
F(1)
G(4)
H(2)
1-2-5-6 (10)1-2-4-5-6 (10)1-2-4-6 (11)1-3-4-6 (9)1-3-4-5-6 (8)
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-11
Critical Activities - activities on the critical path
Event5
Event1
Event3
Event2
Event4
Event6
A(5)
C(3)
B(2)
D(2)
E(3)
F(1)
G(4)
H(2)
A-D-G
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-12
Definitions• Slack - Allowable slippage for a path;
the difference between the length of a path and the length of the critical path.
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-13
Algorithm Definitions• Earliest Start (ES) - the earliest time an activity
can start, assuming all preceding activities start as early as possible
• Earliest Finish (EF) - the earliest time an activity can finish
• Latest Start (LS) - the latest time the activity can start and not delay the project
• Latest Finish (LF) - the latest time the activity can finish and not delay the project
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-14
Algorithm Formulas
EF = ES + t
ES EFt
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-15
2
1
4
5 6
3
1
8
9
6
311
4
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-16
Example 2
2
1
4
5 6
3
1
80
9
6
11
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-17
2
1
4
5 6
3
1
88
0
9
6
11
4
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-18
Example 2
2
1
4
5 6
3
1
88
0
9
4
6 8
118
4
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-19
2
1
4
5 6
3
1
88
0
9
13
4
6 14 8
11
19
8
4
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-20
Example 2
2
1
4
5 6
3
1
88
0
9
13
4
6 14 8
314
11
19
8
4
10
6
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-21
2
1
4
5 6
3
1
88
0
9
13
4
6 14 8
317
1411
19
8
4
10
6
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-22
2
1
4
5 6
3
1
88
0
9
13
4
6 14 8
317
1411
19
8
4
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-23
2
1
4
5 6
3
1
88
0
9
13
4
6 14 8
317
1411
19
8
4
4
019
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-24
2
1
4
5 6
3
1
88
0
9
13
4
6 14 8
317
1411
19
8
4
4
019 20
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-25
Algorithm Formulas
EF = ES + tLS = LF - t
ES EFt
LS LF
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-26
2
1
4
5 6
3
1
20
2019
88
0
9
13
4
6 14 8
317
1411
19
8
4
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-27
2
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5 6
3
1
20
20
19
19
88
0
9
13
4
6 14 8
317
1411
19
8
4
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-28
2
1
4
5 6
3
1
20
20
19
19
88
0
9 19
13
4
6 14 8
3
1917
1411
1919
8
4
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-29
2
1
4
5 6
3
1
20
20
19
19
88
0
9 19
1013
4
6 14 8
3
19171614
11
1919
88
4
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-30
2
1
4
5 6
3
1
20
20
19
19
88
0
9 19
1013
4
6
16
14 8
3
19171614
11
1919
88
4
104
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-31
2
1
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5 6
3
1
20
20
19
19
88
0
9 19
1013
4
6
16
14
10
8
3
19171614
11
1919
88
4
10
6
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-32
2
1
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5 6
3
1
20
20
19
19
88
0
9 19
1013
4
6
16
14
10
8
3
19171614
11
1919
88
4
10
6
4
0
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-33
2
1
4
5 6
3
1
20
20
19
19
88
0
9 19
1013
4
6
16
14
10
8
3
19171614
11
1919
88
4
10
6
4
0
8
Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 1999
PROJECT MANAGEMENT
18-34
2
1
4
5 6
3
1
20
20
19
19
88
0
9 19
1013
4
6
16
14
10
8
3
19171614
11
1919
88
4
10
6
4
0
8
0