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# Project Scheduling: Networks, Duration Estimation, and Critical Path

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

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.

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.

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.

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

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

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

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

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

Activity Node Labels Using MS Project 2010
FIGURE 9.4   Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

Serial Activities Serial activities are those that flow from one to
the next, in sequence. FIGURE 9.5   Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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

Merge Activity FIGURE 9.7  Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

Burst Activity FIGURE 9.8  Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

Complete Activity Network
FIGURE 9.10  Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

Developing the Activity Network Using MS Project 2010
FIGURE 9.11  Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

Duration Estimation Methods
Past experience Expert opinion Mathematical derivation – Beta distribution Most likely (m) Most pessimistic (b) Most optimistic (a) Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

FIGURE 9.14 Symmetrical (Normal) Distribution for
Activity Duration Estimation Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

FIGURE 9.15  Asymmetrical (Beta) Distribution for Activity Duration Estimation
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

Activity Duration and Variance
Table 9.2 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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

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

Project Delta Information
Table 9.4 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

FIGURE 9.16 Partial Project Activity Network with Task Durations
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

FIGURE 9.18 Activity Network with Forward Pass
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

FIGURE 9.19 Activity Network with Backward Pass
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

FIGURE 9.20 Project Network with Activity Slack and Critical Path
Note: Critical path is indicated with bold arrows. Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

AON Network with Laddering Effect
FIGURE 9.24  Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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

Example of a Hammock Activity
FIGURE 9.25   Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall

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

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.

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.

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

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