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
 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
US Census 2000 Project
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•
•
•
•
A US Census takes place every 10 years in the form of a questionnaire from the
US Census Bureau. Census information helps the government in making
policies regarding health, education, transportation, community services etc.
Census participation takes only a few minutes, but it takes years for the
employees of the Census Bureau. Census 2000 was a 13-year project that’s total
life cycle cost $65 billion
Planning for data collection is important. 520 local census offices across the US
verify and collect as many addresses as possible
Project’s goal was 70% response rate to the 2000 Census. The Bureau
implemented a plan to spread the word about the census and stress its
importance. A non-response plan was also established to reach those that failed
to complete the census
The 2000 Census was considered to be the most accurate population count in
US history. For the first time, census data was made available on the Internet
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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. However, for large projects it may not be practical to have
each person provide activity duration estimates.
– An activity’s duration estimate must be based on the quantity of resources
expected to be used on the activity.
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Study Project,
Showing Duration Estimates
Project Start and Finish Times
• It is necessary to select an estimated start time and a
required completion time for the overall project.
• The project’s required completion time is normally part of
the project objective and stated in the contract.
• If a project must be completed in 130 working days, we
define the project’s estimated start time as 0 and its
required completion time is day 130.
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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
• The ES and EF times are determined by calculating
forward through the network diagram.
• Rule: 1
– The earliest start time for a particular 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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Earliest Start Times
Study Project,
Showing Earliest Start and Finish
Times
The ES and EF times are sometimes
listed in a separate schedule table
Latest Start and Finish Times
• Latest finish time (LF) is the latest time by which a particular activity
must be finished in order for the entire project to be completed by its
required completion time, calculated on the basis of the project’s
required completion time and the duration estimates for succeeding
activities.
• Latest start time (LS) is the latest time by which a particular activity
must be started in order for the entire project to be completed by its
required completion time, calculated by subtracting the activity’s
duration estimate from the activity’s latest finish time:
• LS = LF – Duration Estimate
• The LF and LS times are determined by calculating backward
through the network diagram.
• 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.
11
Latest Finish Times
Showing Latest Start and Finish Times
12
Latest Start and Finish Times
• The very first activity, “Identify Target Consumers,” has
an LS of –8! This means that in order to complete the
entire project by its required completion time of 130
days, the project must start 8 days earlier than it is
estimated to start.
• Like the earliest start and earliest finish times, the latest
start and latest finish times are sometimes shown in a
separate schedule table
Study Project,
Showing Latest Start and Finish
Times
Total Slack, Defined
• The difference between the calculated earliest finish time of the very
last activity and the project’s required completion time is the total
slack (TS), sometimes called float.
• If total slack is positive, it represents the maximum amount of time
that the activities on a particular path can be delayed without
jeopardizing completion of the project by its required completion
time.
• On the other hand, if total slack is negative, it represents the amount
of time that the activities on a particular path must be accelerated in
order to complete the project by its required completion time.
• Total Slack = LF – EF or Total Slack = LS – ES
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Critical Path
• This longest path in the overall network diagram
is called the critical path.
• One way to determine which activities make up
the critical path is to find which ones have the
least slack.
• All the activities with this value are on the critical
path of activities.
• The values of total slack for the consumer
market study project are shown in Figure on next
slide
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Study Project,
Showing Total Slack Values
Critical Path
• The lowest value is –8 days.
• he activities that have this same value of total slack make up the
path 1–2–3–4–6–9–11–12–13.
• To eliminate the –8 days of slack, the estimated durations of one or
more activities on this critical path need to be reduced.
• Suppose we reduce the estimated duration of “Mail Questionnaire &
Get Responses” from 65 days to 55 days. The total slack changes
from –8 days to +2 days.
• Those paths with positive values of total slack are sometimes
referred to as noncritical paths, while those paths with zero or
negative values of total slack are referred to as critical paths.
• n this case the longest path is often referred to as the most critical
path.
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Free Slack
• Free slack is the amount of time a particular activity can
be delayed without delaying the earliest start time of its
immediately succeeding 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
• In the network diagram (Figure on Next slide), there are
three instances where a particular activity has more than
one activity entering into it:
– Activity 9, “Mail Questionnaire & Get Responses,” has activities
5 and 6 entering into it.
– Activity 10, “Test Software,” has activities 7 and 8 entering into it.
– Activity 11, “Input Response Data,” has activities 9 and 10
entering into it.
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Free Slack
17
Free Slack
• The values of total slack for activities 5 and 6 are 0 and –
8 days, respectively.
• The lesser of these two values is –8 days for activity 6.
• The free slack for activity 5 is the relative difference
between its total slack, 0, and –8. This relative
difference is 8 days: 0 – (–8) = 8 days.
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Scheduling-PERT
Programme Evaluation and Review
Technique
• PERT developed in 1956-58 by a research team to aid in the
planning and scheduling of the US Navy’s Polaris Missile
Programme which involved over three thousand different
contracting organization.
• The objective of the team was to efficiently plan and produce the
Polaris missile system.
• Since 1958, PERT has proved to be useful for all jobs or
projects which have an element of uncertainty in the matter of
estimation of duration, as in the case with new types of projects
the like of which have never been taken up before
20
CPM- Critical Path Method
• CPM was developed jointly by E.I DuPont Company and
Remington Rand Univac Division.
• The aim behind its development was to have a better planning
in controlling the overhaul and maintenance of chemical plants.
PERT and CPM both are based on the network
representation of activities and their scheduling
that determines the most critical activities to be
controlled so as to meet the completion date of
the project
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PERT
• Since PERT was developed in connection with an R&D work,
therefore it has to cope with the uncertainties which are
associated with R&D activities. In PERT, total project duration is
regarded as a random variable and therefore associated
probabilities are calculated so as to characterize it.
• It is an event-oriented network because in the analysis of
network emphasis is given on important stages of completion of
task rather than the activities required to be performed to reach
to a particular event or task
• A PERT is normally used for projects involving activities of nonrepetitive nature in which time estimates are uncertain.
• It helps in pin pointing critical areas in a project so that necessary
adjustment can be made to meet the scheduled completion date
of the project.
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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.
• Probability of these three time estimates are not
same, rather they assume beta distribution, which is
further estimate of normal distribution
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The Beta Probability Distribution
• When using three time estimates, it is assumed that
they follow a beta probability distribution.
211
The Beta Probability Distribution
• By property of distribution, the probability of t0, tm, tp are
1/6, 2/3,1/6
• The expected duration and variance is calculated using the
following formula:
1
t e  t o  4t m  t p 
6
1

   t p  t o 
6

2
2
211
Time
As we are expecting a variability in the activity duration, the total project
may not be completed exactly in time. Thus, it is necessary to calculate the
probability of actually meeting the scheduled time of the project as well as
activities
The standard normal variate is given by
Z
Ts  Te
 2 cp
Where Te = expected completion time of the Project
 
Variance  2 of the critical path can be known by adding variances of the critical
activities
211
Example - PERT
A project is represented by the network shown below and has the following data
Task
A
B
C
D
E
F
G
H I
Optimistic
5
18 26 16 15 6
7
7
3
Pessimistic 10 22 40 20 25 12 12 9
5
Most likely 8
20 33 18 20 9
10 8
4
Determine the following
a) Expected task times and their variance
b) The earliest and latest expected times to reach each event
c) The critical path
d) The probability of an event occurring at the proposed completion date if the
original contract time of completing the project is 41.5 weeks
F
B
1
I
6
3
7
E
A
2
H
D
G
5
C
4
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Solution
Activity
1 -2
1-3
1-4
2–5
2–6
3–6
4–7
5–7
6-7
to
5
18
26
16
15
6
7
7
3
tp
10
22
40
20
25
12
12
9
5
tm
8
20
33
18
20
9
10
8
4
te 
7.8
20.0
33.0
18.0
20.0
9.0
9.8
8.0
4.0
t
o  4t m  t p 
6
 t p t 0 
 

 6 
0.696
0.444
5.429
0.443
2.780
1.000
0.694
0.111
0.111
2
2
Solution
E1=0
E2 = E1+ T1-2 = 0 + 7.8
E3 = E1+ T1-3 = 0 + 20.0 = 20.0
E4 = E1+ T1-4 = 0 + 33.0 = 33.0
E5 = E2+ T2-5 = 7.8 + 18.0 = 25.8
E6 = max {Ei + ti,6 } = max {E2 + t2,6 ; E3 + t3,6}
=max {7.8 + 20.0 ; 20 +9.0}= 29.0
E7 = max {Ei + ti,7 } = max {E5 + t5,7 ; E6 + t6,7 ; E4 + t4,7}
=max {25.8 + 8 ; 29 +4; 33+9.8}= 42.8
Earliest Start and Earliest Finish ( Forward Pass)
Expected Length of Critical Path = t e  42.8
Variance of Critical Path = 5.429  0.694  6.123
It is given that Ts =41.5, Te  42.8 and  e 6.123  2.474
Therefore, probability of meeting the schedule time is given by

Ts  Te 

 = Prob Z  0.52 = 0.30 from normal distribution table
Pr ob Z 
e 

Thus, the probability that the project can be completed in less than
or equal to 41.5 weeks is 0.30. In other words, probability that
the project will get delayed beyond 41.5 weeks is 0.70
Schedule Control
Learning Objectives
 Perform the steps in the project control process
 Determine the effects of actual schedule performance
on the project schedule
 Incorporate project changes into the schedule
 Calculate an updated project schedule
 Control the project schedule
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Project Control Process
The project control process involves :
– Regularly gathering data on project
performance,
– Comparing actual performance to planned
performance
– Taking corrective actions if actual
performance is behind planned performance
Project Control Process
Project Control Process
• The key to effective project control is to measure actual progress
and compare it to planned progress on a timely and regular basis
and to take necessary corrective action immediately.
• Establish a regular reporting period.
• During each reporting period, collect:
– data on actual performance
– information on any changes to project scope, schedule and budget.
• If changes are incorporated, a new plan must be established.
Project management is a proactive approach to
controlling a project, to ensure that the project objective
is achieved even when things don't go according to plan
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Performance
•
•
•
Throughout a project, some activities will be completed on time, some will be
finished ahead of schedule, and others will be finished later than the
schedule
Actual Progress – whether faster or slower than planned – will have an effect
on the schedule of the remaining uncompleted activities of the project
Actual finish times (AFT) of completed activities will determine the earliest
start and earliest finish times for the remaining activities.
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the Schedule
• Changes might be initiated by the customer or the
project team, or they might be the result of an
unanticipated occurrence.
• The degree of impact may depend on when the
changes are requested.
• If they’re requested early in the project, they may have
less impact on cost and schedule
• When the customer requests a change, additional
costs might need to be charged.
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Network Diagram for Consumer
Market Study Project,
Showing the Critical Path
Revised Schedule for Consumer
Market Study Project
Updating the Project Schedule
• Once data have been collected on the actual finish times
of completed activities and the effects of any project
changes, an updated project schedule can be calculated
based on the actual finish times of completed activities.
• Changes in the Network diagram studied in last class
– Completed Activities
Activity 1: “Identify Target Consumers” actually finished on day 2
Activity 2: “Develop Draft Questionnaire” actually finished on day 11
Activity 3 : “Pilot-Test Questionnaire” actually finished on day 30
– Project Changes
• It was discovered that the database to be used to prepare the mailing labels
was not up to date. A new database needs to be purchased before the
mailing labels can be prepared. This new database was ordered on day 23.
It will take 21 days to get it from the supplier
• A preliminary review of comments from the pilot test of the questionnaire
indicates that substantial revisions to the questionnaire are required.
Therefore, the duration estimate for activity 4 needs to be increased from 5
days to 15 days
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Market Study Project, Incorporating
Actual Progress and Changes
Market Study Project Consumer
Market Study Project
Four Steps
Schedule control involves four steps:
– Analyzing the schedule to determine which areas may need
corrective action
– Deciding what specific corrective actions should be taken
– Revising the plan to incorporate the chosen corrective actions
– Recalculating the schedule to evaluate the effects of the planned
corrective actions
• If the planned corrective actions do not result in an
acceptable schedule, these steps need to be repeated
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Approaches to Schedule
Control (Cont.)
• A change in the estimated duration of any
activity on that path will cause a corresponding
change in the slack for that path.
• When analyzing a path of activities that has
negative slack, you should focus on two kinds of
activities:
– Activities that are near term (that is, in progress or to
be started in the immediate future).
– Activities that have long estimated durations
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Durations
There are various approaches to reducing the estimated
durations of activities.
– One obvious way is to apply more resources to speed up an
activity. Sometimes, however, adding people to an activity may in
fact result in the activity’s taking longer.
– Another approach is to assign a person with greater expertise or
more experience to perform or help with the activity.
– Reducing the scope or requirements for an activity is another
way to reduce its estimated duration.
– In an extreme case, it may be decided to totally eliminate some
activities.
– Increasing productivity through improved methods or technology
is yet another approach.
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Approaches to Schedule
Control (Cont.)
• In most cases, eliminating negative slack by reducing
durations of activities will involve a trade-off in the form
of an increase in costs or a reduction in scope.
• Some contracts include a bonus provision, whereby the
customer will pay the contractor a bonus if the project is
completed ahead of schedule.
• Conversely, some contracts include a penalty provision,
whereby the customer can reduce final payment to the
contractor if the project is not completed on time.
• The key to effective schedule control is to aggressively
address any paths with negative or deteriorating slack
values as soon as they are identified.
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Development
• Controlling the schedule for the development of an
information system is a challenge.
• Among the changes that commonly become necessary
during IS development projects are the following:
–
–
–
–
–
–
–
–
–
Changes to input screens
Changes to reports
Changes to on-line queries
Changes to database structures
Changes to software processing routines
Changes to processing speeds
Changes to storage capacities
Changes to business processes
Changes to software resulting from hardware upgrades or,
conversely, hardware upgrades resulting from the availability of
more powerful software
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Project Management Software
• The software allows you to perform various
control functions.
• The percent complete for each task can be
entered.
• Changes to the duration estimates can be
entered.
• The software will automatically revise the project
schedule and the corresponding network
diagrams.
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Resource Considerations
Learning Objectives
• Learn how to take resource constraints into
account
• Determine the planned resource utilization for
a project
• Level the use of resources within the required
time frame
• Determine the shortest project schedule with
limited resources
2
Technically Constrained
Activity Sequence
Resource-Constrained Planning
• Nearly all projects have limits on available
resources.
• Project delays often occur due to certain
resources being unavailable.
• A network diagram can be drawn to reflect the
availability of a limited number of resources.
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Resource-Constrained
Planning
Planned Resource Utilization
• If resources are to be considered in planning, it’s
necessary to indicate the amounts and types of
resources needed to perform each activity.
Painting Project Showing Needed Resources
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Planned Resource Utilization
Planned Resource Utilization
Resource Profile for Painters :
Uneven Utilization of Painters
Planned Resource Utilization
• Sometimes it’s preferable to have a more uniform, or
level, application of resources.
• Resource utilization based on each activity’s earliest
start time are said to be based on an as-soon-aspossible (ASAP) schedule.
• Resource utilization charts based on each activity’s
latest start time are said to be based on an as-late-aspossible (ALAP) schedule.
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Resource Leveling
• Resource leveling, or smoothing, is a method for developing a
schedule that attempts to minimize the fluctuations in
requirements for resources.
• This method levels the resources so that they are applied as
uniformly as possible without extending the project schedule
beyond the required completion time.
• Non critical activities are delayed beyond their earliest start times
in order to maintain a uniform level of required resources
• Example : Utilization of Painters
Looking at Figure we can see that “Bathroom” could be delayed up to 2 days,
“Basement Rooms” could be delayed up to 8 days, and “Bedrooms” could be delayed
up to 6 days—all without extending the project completion time
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Resource Leveling
Two alternative actions could be taken:
– Alternative 1. Delay the activity with the most
positive slack—“Basement Rooms” (+8 days
slack)—by 6 days so that it will start after
“Bedrooms” is finished.
– Alternative 2. Delay “Bedrooms” so that it will
start on day 4, after “Basement Rooms” is
completed.
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Resource-Leveled Utillization
Resource-Leveled Profile for
Painters
Resource-Limited Scheduling
• Resource-limited scheduling is a method for developing the shortest
schedule when the number or amount of available resources is fixed and
cannot be exceeded.
• This method will extend the project completion time if necessary in order to
keep within the resource limits.
• When several activities need the same limited resource at the same time,
the activities with the least slack have first priority
• If the resources are left over, the activities with the second least
slack have the next priority, and so forth.
• If other activities need the resource but the resource has been totally
allocated to higher-priority activities, the lower-priority activities get
delayed; as their slack becomes worse, they eventually move up the
priority ladder.
• This delaying of activities can extend the project completion time
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Effect of Limited Resource
Availability
what would happen if only a limited number of painters—
two—were available to do the painting project.
Original Resource Utilization
Figure below shows that, as the project starts, three
activities require a total of four painters
Since “First Floor Rooms” has a slack of 0 the two painters will be allocated to
the first floor rooms and will continue to be assigned to that activity until it is
finished
First Resource Allocation
This first resource allocation is shown in Figure below with
the project completion going from day 12 to day 14.
Second Resource Allocation
• The second resource allocation is shown in Figure below with the
project completion date going from day 14 to day 16.
Third Resource Allocation
• The third resource allocation is shown in Figure below with the
project completion date remaining at day 16
Project Management Software
• Provides excellent features for handling resource
considerations within a project.
• Allows you to create and maintain a list of resources.
• Resources can be assigned to various tasks within a
project.
• The user is informed if any resources have time
conflicts or if they are over-allocated.
• Numerous resource allocation reports can be
generated.
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