Lecture 9

Project Scheduling: Networks,

Duration Estimation, and

Critical Path

By : Prof. Lili Saghafi

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Learning Objectives

After completing this chapter, students will be able to:

� Understand and apply key scheduling terminology.

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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.

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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.

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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.

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Project Scheduling

� Project scheduling requires us to follow some carefully laid-out steps, in order, for the schedule to take shape.

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� 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.

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Project Scheduling Terms

�Successors

�Predecessors

�Network diagram

�Serial activities

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�Serial activities

�Concurrent activities

ED

C

B

A F

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Project Scheduling Terms

• Merge activities

• Burst activities

• Node

• Path

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ED

C

B

A F

• Path

• Critical Path

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Network Diagrams

FIGURE 9.2 Alternative Activity Networks for Term Paper Assignment Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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AOA Versus AON

The same mini-project is shown with activities on arc…

E

C

DB F

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C

ED

B F

C

…and activities on node.

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Node Labels

Early Start ID Number Early Finish

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Activity FloatActivity Descriptor

Late Start Activity Duration Late Finish

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Activity Node Labels Using MS Project 2010

FIGURE 9.4

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Serial Activities

Serial activities are those that flow from one to the next, in sequence.

FIGURE 9.5

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Activities Linked in Parallel (Concurrent)

When the nature of the work allows for more than one activityto be accomplished at the same time, these activities are calledconcurrent and parallel project paths are constructed through thenetwork.

FIGURE 9.6

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Merge Activity

FIGURE 9.7

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Burst Activity

FIGURE 9.8

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Complete Activity Network

FIGURE 9.10

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Developing the Activity Network Using MS

Project 2010

FIGURE 9.11

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Duration Estimation Methods

� Past experience

� Expert opinion

� Mathematical derivation – Beta distribution

� Most likely (m)

� Most pessimistic (b)

� Most optimistic (a)

2

2 = 6

b aActivity Variance s

− =

4 = TE

6

a m bActivity Duration

+ +=

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FIGURE 9.14 Symmetrical (Normal) Distribution for

Activity Duration Estimation

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FIGURE 9.15 Asymmetrical (Beta) Distribution for Activity Duration Estimation

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Activity Duration and VarianceName: Project Delta

Durations are listed in weeks

Activity Description Optimistic Likely Pessimistic

A Contract signing 3 4 11

Table 9.2

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B Questionnaire design 2 5 8

C Target market ID 3 6 9

D Survey sample 8 12 20

E Develop presentation 3 5 12

F Analyze results 2 4 7

G Demographic analysis 6 9 14

H Presentation to client 1 2 4

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Constructing the Critical Path

� Forward pass – an additive move through the network from start to finish

� Backward pass – a subtractive move through the

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� 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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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

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� 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

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Project Delta Information

Project Delta

Activity Description Predecessors Estimated Duration

A Contract signing None 5

Table 9.4

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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

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FIGURE 9.16 Partial Project Activity Network with Task Durations

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FIGURE 9.18 Activity Network with Forward Pass

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FIGURE 9.19 Activity Network with Backward Pass

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FIGURE 9.20 Project Network with Activity Slack and Critical Path

Note: Critical path is indicated with bold arrows.

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AON Network with Laddering Effect

FIGURE 9.24

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Laddering ActivitiesProject ABC can be completed more efficiently if subtasks are used

A(3) B(6) C(9) ABC=18 days

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Laddered ABC=12 days

A1(1) A2(1) A3(1)

B1(2) B2(2) B3(2)

C1(3) C2(3) C3(3)

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Example of a Hammock Activity

FIGURE 9.25

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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

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� 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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Summary

1. Understand and apply key scheduling terminology.

2. Apply the logic used to create activity networks, including predecessor and successor tasks.

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

including predecessor and successor tasks.

3. Develop an activity network using Activity-on-Node (AON) techniques.

4. Perform activity duration estimation based on the use of probabilistic estimating techniques.

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Summary

5. Construct the critical path for a project schedule network using forward and backward passes.

6. Identify activity float and the manner in which it is determined.

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

is determined.

7. Calculate the probability of a project finishing on time under PERT estimates.

8. Understand the steps that can be employed to reduce the critical path.

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