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

2. Learning Goals 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.
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.
Understand the steps that can be employed to reduce the critical path.

3. 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.”

4. Project Scheduling
Represents the conversion of project goals into an achievable methodology.
Creates a timetable and reveals the network logic that relates project activities to each other.
A graphical set of sequential relationships between project task which, when performed, result in the completion of the project goals.
Vitally important to obtaining project goals, being on time and on budget.

5. Project Network Diagrams (PND)
Allows project teams to use a method for planning and scheduling
There are several advantages when project networks and scheduling are done well
Show interdependence
Help schedule resources
Facilitate communication
Show start & finish dates for task
Identify critical activities
Determine project completion
See slide 26 for an example

6. Project Scheduling Terms
Successors
Predecessors
Network diagram
Serial activities
Concurrent activities
Merge activities
Burst activities
Node
Path
Critical Path E D C B A F

7. Most Common Methods for Constructing Activity Networks
AOA vs. AON
The same mini-project is shown with activities on arrow… E C D B F
…and activities on node. E D B F C

8. Rules for Developing Activity Networks
Some determination of activity precedence ordering must be done prior to creating the network.
Network diagrams usually flow from left to right.
An activity cannot begin until all preceding connected activities have been completed.
Arrows on networks indicate precedence and logical flow. Arrows can cross over each other, although it is helpful for clarity’s sake to limit this effect when possible.
Each activity should have a unique identifier associated with it (number, letter, code, etc.).
Looping, or recycling through activities, is not permitted.
Although not required, it is common to start a project on a single node. A single node point also is typically used as a project end indicator.

9. Example of Creating a Project Activity Network
Information for Network Construction Name: Project Delta
Activity Description Predecessors
A Contract signing None
B Questionnaire design A
C Target market ID A
D Survey sample B, C
E Develop presentation B
F Analyze results D
G Demographic analysis C
H Presentation to client E, F, G
Construct a Network Diagram

10. Activity Network Example
Dev. Present. B
Design
A Contract D
Survey
F Analysis
H Present C
Market ID G
Demog.

11. Project Activities Linked In Series/Parallel (Concurrent)
College research paper example

12. Merge/Burst Activities
Activity A
Activity B
Activity B
Activity D
Activity A
Activity C
Activity D
Activity C

13. Node Labels Early Start Activity Float Activity Descriptor Late Start
ID Number
Activity Duration
Late Finish
Early Finish
ES ID EF
Slack Task Name
LS Duration LF D
Survey

14. Duration Estimation Assumptions Methods
Based on normal working methods during normal hours
Durations are always somewhat uncertain
Timeframes can be from minutes to weeks
Methods
Past experience
Expert opinion
Mathematical derivation based on Beta Distribution
Most optimistic (a) time – better then planned
Most likely (m) time – realistic expectation
Most pessimistic (b) time – Murphy’s Law kicks in
There are only two types of estimates…lucky and wrong.

15. Variability in Activity Times
Critical Path Method (CPM) assumes we know a fixed time estimate for each activity and there is no variability in activity times
Program Evaluation and Review Technique (PERT) uses a probability distribution for activity times to allow for variability

16. Activity Duration Estimation – Beta Distribution
Where:
 a = Most optimistic time
 m = Most likely time
 b = Most pessimistic time

17. Probability of Project Completion
Project variance is computed by summing the variances of activities on the critical path
Project variance = (variances of activities on critical path)
Project standard deviation = Project Variance

18. Network Example Task Predecessor a m b mean variance Z -- 7 8 15 9.00
1.78 Y 13 16 19
16.00
1.00 X 14 18 22
18.00 W
Y, X 12
14.00
0.44 V 1 4
5.00
4.00 T 6 10
10.00 S
T, V 11
14.33
Task a m b 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
Determine the expected duration and variance of each activity.
Sketch the network described in the table.
Determine the expected project time and standard deviation.

19. Constructing the Network Paths
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

20. Constructing the Critical Path Example
Activity Description Predecessors Estimated Duration A Contract signing None 5 B Questionnaire design A 5 C Target market ID A 6 D Survey sample B, C 13 E Develop presentation B 6 F Analyze results D 4 G Demographic analysis C 9 H Presentation to client E, F, G 2
Construct the critical path.

21. Activity Network with Task Durations and Critical PathB
Design 5 E
Dev. Present 6 A
Contract 5 D
Survey 13 F
Analysis 4 H
Present 2 C
Market ID 6 G
Demog. 9
Critical Path is indicated in bold

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 ES 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
ES ID EF
Slack Task Name
LS Duration LF
Calculate the forward/backwards pass.

23. Activity Network with Forward Pass AddedB
Design 5 E
Dev. Present 6 A
Contract 5 D
Survey 13 F
Analysis 4 H
Presentation 2 C
Market ID 6 G
Demograph. 9
ES ID EF
Slack Task Name
LS Duration LF

24. Activity Network With Backward Pass Added
Design E
Dev. Present A
Contract D
Survey F
Analysis H
Presentation C
Market ID G
Demograph.
ES ID EF
Slack Task Name
LS Duration LF

25. Activity Float - Slack Time
Informs us of the amount an activity can be delayed without delaying the overall project.
It is determined as a result of performing the forward and backward pass through the network.
Calculated either by
LF-EF = Slack
LS-ES = Slack
The critical path is the network path with “0” slack.*
*This assumes a deadline has not been set for LF that is within our calculated project time.
*Negative float is a result of the project time being longer than a set project end time.
Calculate the slack time and determine critical path.

26. Critical Path is indicated in bold
Completed Activity Network With Critical Path And Activity Slack Times Identified B
Design E
Dev. Present A
Contract D
Survey F
Analysis H
0 Presentation
Critical Path is indicated in bold C
0 Market ID G
8 Demograph.
ES ID EF
Slack Task Name
LS Duration LF

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

28. Laddering Activities ABC=18 days Laddered ABC=12 days A(3) B(6) C(9)
Project ABC can be completed more efficiently if subtasks are used.
Example: A does not need to be completely finished before work on B starts.
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

29. Hammock Activities Used as a summary 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

30. Reducing the Critical Path
Eliminate tasks on the critical path
remove task with no value
Convert serial paths to parallel when possible
Overlap sequential tasks
use laddering when possible
Shorten the duration on critical path tasks
Shorten
early tasks (have you read “The Goal”)
longest tasks
easiest tasks
tasks that cost the least to speed up – “crashing”

31. Discussion Questions
Define the following terms: Path, Activity, Early start, Early finish, Late start, Late finish, Forward pass, Backward pass, Node, AON, Float, Critical Path, PERT
Distinguish between serial activities and concurrent activities. Why do we seek to use concurrent activities as a way to shorten a project’s length?
List three methods for deriving duration estimates for project activities. What are the strengths and weaknesses associated with each method?

32. Discussion Questions
In your opinion, what are the chief benefits and drawbacks of using beta distribution calculations (based on PERT techniques) to derive activity duration estimates?
“The shortest total length of a project is determined by the longest path through the network.” Explain the concept behind this statement. Why does the longest path determine the shortest project length?
The float associated with each project task can only be derived following the completion of the forward and backward passes. Explain why this is true.

33. Case Study 5
Now that Joe has agreed to your WBS, he wants to review a schedule and present it to the president. She is a “big picture” thinker and does not usually get involved with the details, so Joe wants to limit the content of the diagram you show her to the basics that concern her.
You have also worked with your team on estimating the durations of each of the work packages in the WBS. Note that in this case, the work packages are the scheduled activities. Here is your current plan for the briefing to the president:

34. Case Study 5

35. Case Study 5 Build a network diagram
Calculate forward pass, backward pass, float, and critical path
Be ready to address—
How long will the project take?
When should you begin installing new furniture, communications equipment, and computers if you want to be in the new office by July 31?
What items are on the critical path?