Chapter 6
Scheduling
Learning Objectives
 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
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Learning Objectives (Cont.)
 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
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Real World Example
• Vignette: R. R. Donnelley & Sons
• Project: Convert 18,000 users dispersed across
200 facilities throughout the world from a dozen
major e-mail systems into one standardized
system.
• The project was completed six months ahead of
schedule without any disruption to business
processing.
• Lessons Learned: detailed planning and
scheduling are essential; resource management is
crucial; and you must have great teamwork.
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Real World Example
• Vignette: London Ambulance Service
• Project: After two failed attempts, develp an ambulance
dispatching system capable of handling a million calls per
year based on 800 vehicles, 7.5 million residents, 2.5
million tourists, dispersed over 640 square miles.
• Results: the number of ambulances on the way within three
minutes doubled; the number of ambulances on the scene
within 8 minutes tripled. Lives are being saved.
• Lessons Learned: encourage open communications; involve
the team in planning; break the project into manageable
pieces.
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Activity Duration Estimates
• 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.
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Project Start and Finish Times
• It is necessary to select an estimated start time and
a required completion time for the overall project.
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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
• 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
• 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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Latest Start and Finish Times
• 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
• 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
• 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.)
• 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.
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Critical Path
• 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
• 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
• 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.
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Scheduling for Information
System Development
• 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
• 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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Probability Considerations
Activity Duration Estimates
• 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
• 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 = F(to + 4(tm) + tp)/6
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Probability Considerations
Probability Fundamentals
• 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 = BBC((F(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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Probability Fundamentals
(Cont.)
• 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
• The probability of completing a project before its
required compleiton time:
• Z = F(LF – EF,st)
 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.
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Calculating Probability (Cont.)
• Z measures the number of standard deviations
between EF and LF on the normal probability
curve.
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