Network Analysis and Duration
Estimating
Kathy S. Schwaig
A Roadmap of the Project
Planning Process
Develop a business case
Select a project
Develop project charter
Establish work breakdown structure
Analyze sequencing relationships
Estimate “normal” activity durations
Perform network calculations
Validate/revise initial schedule
Perform time-cost tradeoff analysis
Load resources to activities
Resolve any resource/workload imbalances
Develop budget and cash flow plan based on analysis of direct and
indirect costs
Network-based tools to model
sequencing relationships
Critical path method (CPM) Our Focus Here
Developed by Dupont and Remington Rand in the late 1950s
for managing plant maintenance projects
Uses one duration estimate for each activity
Provides basic framework for project planning and control
Program evaluation and review technique (PERT)
Developed in conjunction with Lockheed’s development of
the Polaris Missile in the late 1950s
Requires three duration estimates for each activity
(optimistic, most likely, pessimistic)
Allows for crude risk assessment on overall project duration
Analyzing Sequencing
Relationships
The work breakdown structure gives
you the tasks or activities that have to
be accomplished
The next step is to determine the
sequencing of those activities
The sequence of activities can be
represented in the form of a network
Activities-on-nodes (AON)
project network
In an AON project network:
the activities are the nodes in the network
the precedence relationships are shown by arrows
An AON project network should have one
starting node and one ending node
The project network represents a model of the
project and shows the relationships among
activities
Example:
B
A
D
C
E
Developing a project network:
adding activities
In developing a project network, you may
identify additional activities
To determine which activities should be
added to the network, it is helpful to ask the
following question:
Given where we are in the project, what
activity(s) can we perform next?
Developing a project network:
determining relationships
In developing a project network, you will
need to determine the relationships among
activities
To determine how to connect an activity
into the network, it is helpful to ask the
following question:
Which activity(s) would have to be finished
before this activity could start?
Precedence Relationships
S
Finish-to-Start (FS)
Start-to-Start (SS)
F
S
A
S
F
B
F
A
S
F
B
S
Finish-to-Finish (FF)
F
A
S
F
B
Building a Project Network:
An Example
Suppose our project charter is to bake a birthday
cake from scratch with homemade chocolate
frosting
Assumptions and constraints:
All required ingredients and utensils are on-hand
Recipe exists and must be read first before any other
activity can begin
Cleanup at end of project (hint: this is your last
activity)
Draw AON project network using finish-to-start (FS)
precedence relationships
Exercise: Draw an AON
network for this project
Activities A and B have no predecessors
Activity C can start when A is completed
When both A and B are finished, activity D
can start
Activity E is dependent only on the
completion of B
Activity F can start when C and E are
completed
When D is finished, activity G can start
Activity H cannot start until both E and G are
finished
Guidelines for Developing
Project Network Diagrams
Make sure that your precedence
relationships reflect technical reasons for
task A preceding task B
Label your nodes with short activity
descriptions (not codes)
AON networks should have one starting
node and one ending node
Guidelines for Developing
Project Network Diagrams
Use FS precedence relationships wherever
possible
Each precedence arrow should connect two
activities
Do not put any “feedback loops” in your
network diagram
Limit your AON project network to no
more than about 50 nodes
Estimating Activity Durations
Activity duration is the amount of time
between the start and completion of the
activity (not equal to staff hours)
days is the typical unit of time
“normal point” is the duration associated with
the most efficient use of resources (i.e. lowest
cost)
“crash point” is the shortest amount of time in
which the activity can be done successfully
Guidelines for Estimating
Activity Durations
Define activity scope and content
Determine most cost efficient technological
approach
Determine which staff members will be assigned
Estimate staff hours to complete activity
Estimate average availability of assigned staff
members
Duration days = staff hours required/available
staff hours per day
Selectively adjust durations of activities that are
subject to common problems
Guidelines for Estimating
Activity Durations
Don’t confuse duration (days) with resource
usage (staff hours or days)
Allow for less than full time resource availability
Base your estimates on clearly defined activity
scope
Allow for delays caused by common problems
Don’t “pad” or “low ball” estimates
No duration estimates should be longer than 2
weeks (80 hour rule)
Seek commitment to duration estimates from the
people who are doing the work
Labeling of Network Nodes
Each node is labeled with certain
information
EPS
EPC
ACT
ACT=name of activity
D
D=duration of activity
LAS
EPS=earliest possible starting time
EPC=earliest possible completion time
LAS=latest allowable starting time
LAC=latest allowable completion time
TS=total slack
TS
LAC
Total Slack vs. Free Slack
Total (Path) Slack (sometimes called float)
Amount of time by which the activity can be delayed
beyond its earliest possible completion time (EPC)
without delaying the project beyond its latest
allowable completion time (LAC)
Total Slack, TS = LAC - EPC
Free (Activity) Slack
Amount of time by which the activity can be delayed
beyond its earliest possible completion time (EPC)
without delaying the start of any other activity beyond
its earliest possible starting time (EPS)
Network Calculations
Forward pass calculations (EPS & EPC)
The EPS for the first activity in the project
network is usually set at zero
The EPS for any other activity is the largest (or
latest) of the EPC values for all immediately
preceding connected activities
The EPC for any activity is calculated as
follows: EPC=EPS+D
Network Calculations
Backward pass calculations (LAS & LAC)
The LAC for the last activity in the project network is
usually set equal to the EPC for that activity (or to
some specified completion deadline)
The LAC for any other activity is the smallest (or
earliest) of the LAS values for all immediately
following connected activities
The LAS for any activity is computed as follows:
LAS=LAC-D
When calculations are complete, LAS-EPS for
the first activity in the network should equal
LAC-EPC for the last activity in the network
Network Calculation Example
B
8
E
4
H
2
A
2
C
6
F
6
0
D
4
END
G
10
Finding the Critical Path(s)
A critical path is a connected series of activities
whose combined duration is the longest of any
path through the project network
Critical path can be found by:
Tracing EPS
Go to last activity
Circle earliest possible start (EPS)
Find which predecessor activity node is supplying that
EPS
Repeat until you get back to the start of the AON
network
Why the Critical Path Matters
The critical path determines project duration
(because it’s the longest path through the
network)
A project can have more than one critical path
To shorten project, it is necessary to shorten the
durations of all critical paths
Any delay along any critical path will delay
project completion
Activities on the critical path have the lowest
total slack value in the network
Crashing the Network to Shorten
the Project Duration
Focus on activities that are on the critical
path
Look for activities with relatively long
durations
Look for activities that are on multiple
critical paths