Chapter 6
Scheduling
Learning Objectives
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Estimate the duration for each activity
Establish the estimated start time and
required completion time for the overall
project
Calculate the earliest times at which
each activity can start and finish, based
on the project’s estimated start time
2
Learning Objectives (Cont.)
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Calculate the latest times by which each
activity must start and finish in order to
complete the project by its required
completion time
Determine the amount of positive or
negative slack
Identify the critical (longest) path of
activities
3
Real World Example
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Vignette: The World Cup Tournament
South Africa is the host country for the Federation Internationale
de Football Association (FIFA) World Cup tournament in 2010.
The South African government is projected to invest more than
R400 billion on infrastructure projects.
Additionally, between R2 billion and R5 billion will be spent on
information and communication technology projects.
Large investments will be made to ensure all transit systems
form an effective public transport network.
Additionally $1.1 billion has been earmarked for new and
renovated stadiums to hold the games of the World Cup.
Unfortunately there are reports of schedule delays and budget
overruns.
“Many people do not fully understand the details of
project management as a specific entity – such as detailed
work breakdown structures and critical paths.”
Link 1
Link 2
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Real World Example
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Vignette: Fast-Track Innovation in Indiana
The major improvements necessary on a stretch of the
combined I-65 and I-70 arteries posed numerous challenges to
the Indiana Department of Transportation (INDOT).
Project would involve 33 bridges and 35 lane miles of highway,
and one side of the highway would need to be shut down.
The project, was completed in just 55 days, earning its name,
‘‘Hyperfix.’’
To decrease the duration of construction time, the whole
stretch of affected highway would be closed and numerous
contractors would be working each day, 24 hours a day, 7
days a week.
Excellent project management at all phases of this project
resulted in successfully and quickly improving the highways,
while minimizing any inconvenience to the drivers.
 Massive communications effort
 Met with community stakeholders for buy-in
5
Activity Duration Estimates
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The first step in scheduling is to estimate
how long each activity will take.
The duration estimate is the total elapsed
time for the work to be done PLUS any
associated waiting time.
The person responsible for performing the
activity should help make the duration
estimate.
6
Activity Duration Estimates
(contd)
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An activity’s duration estimate must be based on
quantity of resources expected to be used.
 Estimate should be aggressive, yet realistic.
Playing the game of inflating or padding duration
estimates is not a good practice.
Over the life of a project that involves many
activities, delays and accelerations will tend to
cancel one another out.
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8
Project Start and Finish
Times
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It is necessary to select an estimated
start time and a required completion time
for the overall project.
These two times define the overall
window (envelope) of time in which the
project must be completed.
The project’s required completion time is
normally part of the project objective and
stated in the contract.
9
Schedule Calculations

A project schedule includes:
 the earliest times (or dates) at which
each activity can start and finish,
based on the project's estimated start
time (or date)
 the latest times (or dates) by which
each activity must start and finish in
order to complete the project by its
required completion time (or date)
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Earliest Start and Finish
Times
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Earliest start time (ES) is the earliest time
at which a particular activity can begin.
Earliest finish time (EF) is the earliest
time by which a particular activity can be
completed.
EF = ES + Duration Estimate
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Earliest Start and Finish Times
Rule #1
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The earliest start time for an activity
must be the same as or later than the
latest of all the earliest finish times of all
the activities leading directly into that
particular activity.
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The earliest start time for an activity
must be the same as or later than
the latest of all the earliest finish
times of all the activities leading
directly into that particular activity
13
Latest Start and Finish
Times
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Latest finish time (LF) is the latest time
an activity must be finished in order for
the entire project to be completed by its
completion time.
Latest start time (LS) is the latest time an
activity must be started in order for the
entire project to be completed by its
completion time.
LS = LF – Duration Estimate
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Latest Start and Finish Times
Rule #2
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The latest finish time for a particular
activity must be the same as or earlier
than the earliest of all the latest start
times of all the activities emerging
directly from that particular activity.
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The latest finish time for a particular
activity must be the same as or
earlier than the earliest of all the
latest start times of all the activities
emerging directly from that
particular activity
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Total Slack, Defined
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Total slack (TS) or float is the difference
between the calculated earliest finish time
of the very last activity and the project’s
required completion time.
Total Slack = LF - EF or
Total Slack = LS - ES
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Total Slack (Cont.)
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If total slack is positive, it is the
maximum time the activities on the path
can be delayed.
If total slack is negative, it is the amount
of time the activities on the path must be
accelerated.
The total slack for a particular path of
activities is common to and shared
among all the activities on that path.
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Critical Path
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The critical path is the longest path in
the diagram.
The activities that make up the critical
path have the least slack.
All activities with this value are on the
critical path.
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Types of Critical Paths
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Noncritical paths have positive values of
total slack.
Critical paths have zero or negative
values of total slack.
The most critical path is the longest
critical path.
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Free Slack
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The amount of time an activity can be
delayed without delaying the start of
other activities.
It is the relative difference between the
amounts of total slack for activities
entering into the same activity.
It is always a positive value.
22
2
5
5
B
0
2
7
E
2
3
2
5
5
1
5
9
A
1
2
-7
-5
6
6
2
6
6
C
3
-5
9
D
4
4
-1
-1
3
2
19
H
2
8
5
7
7
12
14
13
9
5
7
19
7
4
8
12
22
I
9
12
G
F
2
14
3
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Scheduling for Information
System Development
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Some common problems that push IS
projects past their required completion
time:
 Failure to identify all user requirements
 Logical design flaws
 Continuing growth of project scope
 Underestimating learning curves for
new software packages
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Project Management
Software
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Allows one to perform scheduling
functions.
Activity durations can be estimated in a
variety of ways.
Project start and finish times can be
entered in a variety of ways.
Can calculate dates, times, total and
free slack.
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Appendix 1
Probability Considerations
(will not cover for undergraduate class)
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Probability Considerations
Activity Duration Estimates
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Optimistic time: time to complete an
activity if everything goes perfectly
well.
Most likely time: time to complete an
activity under normal conditions.
Pessimistic time: time to complete an
activity under adverse circumstances.
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Probability Considerations
The Beta Probability Distribution
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When using three time estimates, it is
assumed that they follow a beta
probability distribution.
The expected duration is calculated using
the following formula:
te = (to + 4(tm) + tp) / 6
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Peak represents most likely time;
divides curve into two equal parts
Probability Considerations
Probability Fundamentals
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Network planning that uses three time
estimates for each activity can be
considered a stochastic or probabilistic
technique, since it allows for
uncertainty.
Any technique that uses only one time
estimate is considered to be a
deterministic technique.
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Probability Fundamentals (Cont.)
The total probability distribution is a
normal probability distribution.
 The variance for the beta probability
distribution of an activity is:
 Variance = s2 = ((tp – to) / 6)2
 The standard deviation, s, is another
measure of the dispersion of a
distribution and is equal to the
square root of the variance.
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Normal
Distribution
Standard deviation measures dispersion
Probability Fundamentals (Cont.)
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The total probability distribution of the
critical path activities is a normal
distribution.
The mean equals the sum of the
individual activity expected durations.
The variance equals the sum of the
individual activity variances.
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Calculating Probability
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The probability of completing a project
before its required completion time:
Z = (LF – EF / st)
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LF = the required completion time (latest
finish).
EF = the earliest expected finish time (mean of
the normal distribution).
st = the standard deviation of the total
distribution of activities on the longest path.
Z = number of standard deviations between EF
and LF on the normal probability curve
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50%
68%
95%
99%
50%
42.922%