1. Project Scheduling: Networks, Duration Estimation, and Critical Path
Chapter 9
Project Scheduling: Networks, Duration Estimation, and
Critical Path

2. Chapter 9 Learning Objectives
After completing this chapter, students will be able to:
Understand and apply key scheduling terminology.
Apply the logic used to create activity networks, including predecessor and successor tasks.
Develop an activity network using Activity-on-Node (AON) techniques.
Perform activity duration estimation based on the use of probabilistic estimating techniques.

3. Chapter 9 Learning Objectives
After completing this chapter, students will be able to:
Construct the critical path for a project schedule network using forward and backward passes.
Identify activity float and the manner in which it is determined.
Calculate the probability of a project finishing on time under PERT estimates.
Understand the steps that can be employed to reduce the critical path.

4. Project Scheduling
Project scheduling requires us to follow some carefully laid-out steps, in order, for the schedule to take shape.
Project planning, as it relates to the scheduling process, has been defined by the PMBoK as:
The identification of the project objectives and the ordered activity necessary to complete the project including the identification of resource types and quantities required to carry out each activity or task.

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

6. Project Scheduling Terms
Merge activities
Burst activities
Node
Path
Critical Path E D C B A F

7. Network Diagrams
FIGURE 9.2  Alternative Activity Networks for Term Paper Assignment
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8. AOA Versus AON …and activities on node.
The same mini-project is shown with activities on arc… E C D B F
…and activities on node. C E D B F

9. Node Labels Early Start Activity Float Activity Descriptor Late Start
ID Number
Activity Duration
Late Finish
Early Finish

10. Activity Node Labels Using MS Project 2010
FIGURE 9.4  
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11. Serial Activities Serial activities are those that flow from one to
the next, in sequence.
FIGURE 9.5  
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12. Activities Linked in Parallel (Concurrent)
When the nature of the work allows for more than one activity
to be accomplished at the same time, these activities are called
concurrent and parallel project paths are constructed through the
network.
FIGURE 9.6  
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13. Merge Activity
FIGURE 9.7 
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14. Burst Activity
FIGURE 9.8 
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15. Complete Activity Network
FIGURE 9.10 
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16. Developing the Activity Network Using MS Project 2010
FIGURE 9.11 
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17. Duration Estimation Methods
Past experience
Expert opinion
Mathematical derivation – Beta distribution
Most likely (m)
Most pessimistic (b)
Most optimistic (a)
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18. FIGURE 9.14 Symmetrical (Normal) Distribution for
Activity Duration Estimation
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19. FIGURE 9.15  Asymmetrical (Beta) Distribution for Activity Duration Estimation
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20. Activity Duration and Variance
Table 9.2
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21. 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

22. 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

23. Project Delta Information
Table 9.4
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24. FIGURE 9.16 Partial Project Activity Network with Task Durations
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25. FIGURE 9.18 Activity Network with Forward Pass
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26. FIGURE 9.19 Activity Network with Backward Pass
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27. FIGURE 9.20 Project Network with Activity Slack and Critical Path
Note: Critical path is indicated with bold arrows.
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28. AON Network with Laddering Effect
FIGURE 9.24 
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29. Laddering Activities ABC=18 days Laddered ABC=12 days
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

30. Example of a Hammock Activity
FIGURE 9.25  
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31. 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

32. Summary Understand and apply key scheduling terminology.
Apply the logic used to create activity networks, including predecessor and successor tasks.
Develop an activity network using Activity-on-Node (AON) techniques.
Perform activity duration estimation based on the use of probabilistic estimating techniques.

33. Summary
Construct the critical path for a project schedule network using forward and backward passes.
Identify activity float and the manner in which it is determined.
Calculate the probability of a project finishing on time under PERT estimates.
Understand the steps that can be employed to reduce the critical path.

34. Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall