Network Diagrams and
Critical Path
ENGR 301
Project Management Principles and Engineering Economics
WORK BREAKDOWN STRUCTURES
Why Plan?
• Why should we develop plans for projects?
– Project management helps us plan activities
– Estimate and control costs
– Estimate times to completion
– Assign resources and responsibilities
• In the course of project management
– Formally define scope
– Break down the activities into tasks
– Determine the path to successfully finishing the project
How Do You Define a Project
• Start with a set of definitions
– Project scope
– Project priorities
• Then use these definitions to
– Create the Work Breakdown Structure (WBS)
Project Scope
• What is one of the biggest risks to a project?
– Scope Creep!
• You fight scope creep with a well-defined project scope
statement
• The deliverable needs to be clear to all parties
• So the client/user is happy
• And so the project team has clearly defined steps and
metrics
• The scope allows us to measure success
Work Breakdown Structures
• Once we have defined the scope, we start to determine
the individual tasks necessary to complete the project
• This is the Work Breakdown Structure (WBS)
• This can start as a list of jobs
• Eventually we break this list into categories that show the
order in which tasks will take place
• This will form the basis of the formal management tool
that we choose
Getting Started
• Suppose your goal is to build a house. You can divide this
activity into three major project components:
• House
– Foundation
– Exterior
– Interior
• This can define the first two levels of the WBS
– These are the major deliverables
Need More Details!
• Obviously, that isn’t much of a project management tool
• We need to define more subtasks beyond these major
three deliverables
• In a three-level WBS, we define the work packages in the
third level.
Work Package
• The lowest level of the WBS are defined as work
packages
• “80 hour rule”
– Each work package should be no more than 80 hours
– A good rule of thumb to see if the task could be further
divided or separated
Source: https://www.workamajig.com/blog/guide-to-work-breakdown-structures-wbs
Source: https://www.workamajig.com/blog/guide-to-work-breakdown-structures-wbs
Source: https://www.workamajig.com/blog/guide-to-work-breakdown-structures-wbs
Scope, WBS and work packages
• We use scope as an opportunity to ensure that all parties
understand and agree on what the completed work
should look like
– This ensures that we can measure the outcomes
• We keep the project on track by using the scope to list all
project activities
• We arrange this list hierarchically
• Noting which items are dependent on one another
• The lowest level of the WBS are the work packages
Again, the critical question
WHY DO WE PLAN
Planning for Success
• Project planning is fundamental to successfully completing
projects
• Well detailed project plans and work breakdown
structures (WBS) allow us to articulate the details of the
work
• This gives us the structure to develop budgets and
schedules
– That are as accurate as possible
Project Vocabulary
• Scope
• Work Breakdown Structure (WBS)
• Work package
Project Network Diagram
Vocabulary tested
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•
•
•
•
•
•
•
•
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Path
Event
Node
Predecessors
Successors
Early/Late Start/Finish (ES, EF, LS, LF)
Forward Pass/Backward Pass
Merge Activities
Burst Activities
Float
Critical Path
• Network Diagrams Help Identify
– Critical Path
• Critical Path Method (CPM)
• Program Evaluation & Review Technique (PERT)
• Also allows us to look at what constrains our schedule
– Ex. Resource-limited schedule
• For more on schedule limitations, see:
– https://www.pmi.org/learning/library/four-ways-projectschedules-limited-7265
How we develop a network
MORE PLANNING AND
SCHEDULING
Networks are Sequential
• Networks are sequential, logical representations of the
steps needed to complete a project
• This is why WBS and task identification is so important
• Two main methods for network representation
• Project Evaluation and Review Technique (PERT)
• Critical Path Method (CPM)
For both PERT and CPM
BASIC NETWORK RULES ARE THE
SAME
Rules for a Network
• Use boxes, nodes (or sometimes arrows) to represent
activities
Activity
A
Activity
B
A simple activity
network
• Arrows (rarely boxes) represent logical flow/order
– Network diagram moves from left to right
– Each activity has a unique identifier
• Thou shalt not Loop!
– If you have a repeated or recycled action, you have created
your diagram incorrectly
Types of Activity Connections
A
A
B
B
Finish-toStart
Finish-toFinish
A
A
B
B
Start-toStart
Start-to-Finish
Beyond the basics
DETAILED ACTIVITY
REPRESENTATIONS
Activity Nodes Fleshed Out
• We can add additional information per node
Early Start
Duration
Early Finish
Iphase
Task Name
Late Start
Slack
2 help calculate
Late Finish
• Here we have early start, late start, early finish, late finish
• We’ll go over calculating these later
• But they eventually allow us to determine the slack in a
project
Many Possible Representations
Early Start
Duration
Early Finish
Task Name
Late Start
Slack
Late Finish
Another format of
Activity notation
Microsoft Visio –
PERT Chart Shapes
Microsoft
Project 2010
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Finish-to-Start
lithallflight
case
• B can’t start before A is finished a see
• Have to purchase land before you can build a road on that land
• This describes most activity connections
A
B
Finish-toStart
https://www.projectinsight.net/projectmanagement-basics/task-dependencies
Start-to-Start
• Need to excavate before you can pour asphalt
• A must start before B can start
A
B
Start-toStart
https://www.projectinsight.net/projectmanagement-basics/task-dependencies
Finish-to-Finish
• Predecessor must finish before successor can finish
• Laying Asphalt must be complete before line painting can be completed
• Can occur in parallel
A
B
Finish-toFinish
https://www.projectinsight.net/projectmanagement-basics/task-dependencies
Start-to-Finish
•
•
•
•
A can’t finish before B starts
Implies lag
Handover task
Rare
A
B
Start-to-Finish
https://www.projectinsight.net/projectmanagement-basics/task-dependencies
Activity Types
Burst
activity
b
Serial
Activities
c
d
g
a
e
f
Concurrent
Activity
Merge
activity
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Why Do We Need Scheduling?
• Scheduling lets us know when we need labor, and material
• How much we need, for how long, and when
• It helps us know when we need to receive payments or
deliveries
CPM allows project managers to optimize an activity diagram
CRITICAL PATH METHOD
Critical Path
• Once you have established your activity diagram, you can
identify the critical path in four steps
1. Forward Pass
2. Backward Pass
3. Calculate the Float/Slack
4. Identify Critical Activities
• The critical path is the path with the critical activities
(activities with zero float/slack)
1. Forward Pass – Earliest Times
Early Start
Duration
Early Finish
Task Name
Late Start
Slack
Late Finish
1. Moving from left to right, add activity times along each path
in the network: ES + Duration = EF
2. Carry the early finish (EF) to the next activity where it
becomes its early start (ES): !"!"#$%$#& $ ⇒ "#!"#$%$#& (
unless
3. The next succeeding activity is a merge activity. If so, select
the largest early finish number (EF) of all its immediate
predecessor activities.
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2. Backward Pass – Latest Times
Early Start
Duration
Early Finish
Task Name
Late Start
Slack
Late Finish
1. Moving backward from right to left, subtract activity times along
each path starting with the project end activity:
LF – Duration = LS
2. Carry the late start (LS) to the next preceding activity to
establish its late finish (LF): $#!"#$%$#& ( ⇒ $%!"#$%$#& $
Unless
3. The next preceding activity is a burst activity. If so, select the
smallest LS of all its immediate successor activities to establish its
LF
3. Determining Slack/float
Early Start
Duration
Early Finish
Task Name
Late Start
Slack
Late Finish
LF – EF = Slack/float
Or
LS – ES = Slack/float
What does slack (float) tell us about the project schedule?
Slack (or float) is the amount of time an activity can be delayed and not
delay the project.
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4. Identifying Critical Activities
Critical Activity:
• Slack = 0
• LF = EF
or
• LS = ES
Critical Path: the network path(s) that contain critical activities.
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