1. Project Scheduling: Networks, Duration estimation, and Critical Path

2. Project Scheduling Terms
Successors
Predecessors
Network diagram
Serial activities
Concurrent activities E D C B A F

3. Project Scheduling Terms
Merge activities
Burst activities
Node
Path
Critical Path E D C B A F
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4. Network Diagrams Help schedule resources Show interdependence
Show start & finish dates
Facilitate communication
Determine project completion
Identify critical activities
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5. AOA vs. AON The same mini-project is shown with activities on arrow…D B F
…and activities on node. C E D B F

6. Node and activity labels in AoA diagrams (NOT following the textbook)
Deadline
Activity identifier
Duration 1 2
EET
LET
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7. Node Labels in AoN diagrams (NOT completely following the textbook)
Free float
Early Start
Total Float
Early Finish
Activity Descriptor
Late Start
Activity Duration
Late Finish

8. Duration Estimation Methods
Past experience
Expert opinion
Mathematical derivation – Beta distribution
Most likely (m)
Most pessimistic (b)
Most optimistic (a)

9. Beta distribution
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10. Sketch the network described in the table.
Determine the expected duration and variance of each activity.
Task
Predecessor a m b A -- 7 8 15 B 13 16 19 C 14 18 22 D
B, C 12 E 1 4 F 6 10 G
F, E 11 TE s2 9
1.8 16
1.0 18 14
0.4 5
4.0 10
14.3
1.4
Task a b c Mean Variance Z Y X W V T S
Task Early Start Early Finish Late Start Late Finish Slack Z Y X W V T S
Project Length 64
Project Variance
Project Std.dev

11. Solution with AoN diagram2 2 b 9 25 2 11 27 16 e 41 46 5 51 a 9 d 27 41 14 g 51 65 14 c 9 27 18 f 41 51 10
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12. Constructing the Critical Path
Forward pass – an additive move through the network from start to finish
Backward pass – a subtractive move through the network from finish to start
Critical path – the longest path from end to end which determines the shortest project length
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13. Rules for Forward/Backward Pass
Forward Pass Rules (ES & EF)
ES + Duration = EF
EF of predecessor = ES of successor
Largest preceding EF at a merge point becomes EF for successor
Backward Pass Rules (LS & LF)
LF – Duration = LS
LS of successor = LF of predecessor
Smallest succeeding LS at a burst point becomes LF for predecessor

14. Sketch the network described in the table.
Task
Predecessor
Time A -- 4 B 9 C 11 D 5 E 3 F 7 G
D, F H
E, G 2 K 1
Sketch the network described in the table.
Determine the ES, LS, EF, LF, and total float of each activity
Task ES EF LS LF Slack A B C D E F G H K

15. Laddering Activities
Project ABC can be completed more efficiently if subtasks are used
ABC=18 days
A(3)
B(6)
C(9)
A1(1)
A2(1)
A3(1)
B1(2)
B2(2)
B3(2)
C1(3)
C2(3)
C3(3)
Laddered ABC=12 days

16. Useful with a complex project or one that has a shared budget
Hammock Activities
Used as summaries for subsets of activities
0 A 5
B 15
15 C 18
0 Hammock 18
Useful with a complex project or one that has a shared budget

17. Reducing the Critical Path
Eliminate tasks on the CP
Convert serial paths to parallel when possible
Overlap sequential tasks
Shorten the duration on critical path tasks
Shorten
early tasks
longest tasks
easiest tasks
tasks that cost the least to speed up
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18. Optional HW
Create the AoA & AoN networks of your project using the symbols of this class.
Prize: 15%
Task list with cost estimation: +5%
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

19. Thanks for your attention