Project scheduling (chapter 05)(wp)

Project Scheduling
7th Semester, Project Management
Chapter-05
Bipul Kumar Sarker
Lecturer
Department of BBA Professional
Habibullah Bahar College

A project is an endeavour involving a connected sequence of activities and a range of
resources, which is designed to achieve a specific outcome and which operates
within a time frame, cost and quality constraints and which is often used to introduce
change.
Bipul Kumar Sarker, Lecturer, Department of BBA Professional, Habibullah Bahar College
Project:
i. A unique, one-time operational activity or effort
ii. Requires the completion of a large number of interrelated activities
iii. Established to achieve specific objective
iv. Resources, such as time and/or money, are limited
v. Typically has its own management structure
vi. Need Leadership
Characteristic of a project:

Examples:
i. Constructing Houses, Factories, Shopping Malls, Athletic Stadiums
ii. Developing military weapons systems, aircrafts, new ships, launching
satellite systems
iii. Constructing oil pipelines
iv. Developing and implementing new computer systems
v. Planning concert, football games, or basketball tournaments our National
Event ‘Mythri’
vi. Introducing new products into market

Project management is the application of the ‘functions of management’ to get
a project done.
Project Management:
Project management is the discipline of initiating, planning, executing,
controlling, and closing the work of a team to achieve specific goals and meet
specific success criteria.
Initiate
• Form the team
• Write a Charter
Plan
• Communication Plan
• Project Plan
Project Close
• Closure of project activities
• Capture lessons learned
• Celebrate
Execute
• Complete Tasks
• Monitor Progress

A project is a singular effort of defined duration, whereas a program is
comprised of a collection of projects.
Project vs Program

Project vs Program

Project Scheduling and Control Techniques
1. Network Diagram:
ii. Critical Path Method (CPM)
iii. Program Evaluation and Review Technique (PERT)
2. Bar Chart
i. Gantt Chart
ii. Milestone Chart

Network Diagram:
Network diagrams are one of the project management tools a project manager
uses for project planning. It is also sometimes referred to as an “Arrow”
diagram, because it uses arrows to connect activities and represent precedence
and interdependencies between activities of a project.

Network Analysis Method:
Network Analysis Methods is a group of special analytical methods that are
used in cases where it is necessary to analyze and optimize a network of
interconnected and related elements that have some connection between one
another.
i. Its primary aim is to program and monitor the progress of a project so that
the project is completed in the minimum time.
ii. It can also be used in allocation resources such as labor and equipment and
thus helps to make the total cost of a project minimum.

Terms Related to Network Analysis:

Terminology of Network Analysis

Problem 01:
For the project data in below table, answer the following question:
a. Draw an AOA and AON network of the project.
b. Perform forward path and backward path calculations.
Activity Predecessor Duration (days)
A - 2
B A 6
C A 3
D B 1
E B 6
F C,D 3
G E,F 2

Solution:
AOA Network :
C
A - 2
B A 6
C A 3
D B 1
E B 6
F C,D 3
G E,F 2
A
B D
F
E
G
2
3
6
1
1 2
3
4
5
6
6
3
2
AON Network:

Solution:
Forward Path From AOA Network:
C
A
B D
F
E
G
2
3
6
1
1 2
3
4
5
6
6
3
2
14
0 0 2
8
14
16
9
Note: When more than one
successor, pick the smallest
one
Backward Path From AOA Network:
predecessor, pick the larger
one
A
B D
F
E
G
2
3
6
1
1 2
3
4
5
6
6
3
2
14
0 0 2
8
16
11
14
ES EF
Note:
ES = Early Start (Forward Path)
EF = Early Finish (Backward Path)

Solution:
Forward Path and Backward Path From AOA Network :
C
A
B D
F
E
G
2
3
6
1
1 2
3
4
5
6
6
3
2
14
0 0 2 2
8 8
14
16 16
9 11
14
Note:
i. When more than one predecessor, pick the larger one (Forward Path)
ii. When more than one successor, pick the smallest one (Backward Path)

Solution:
Forward Path From AON Network:
Backward Path From AON Network:

0 2
0 2
A(2)
8 14
8 14
E(6)
8 9
10 11
D(1)
9 12
11 14
F(3)
14 16
14 16
G(2)
2 5
8 11
C(3)
2 8
2 8
B(6)
Solution:
Forward Path and Backward Path From AON Network :
Note:

Problem 02:
a. Draw an AOA network of the project.
c. Determine the critical path and project completion time.
Events Activity Duration (days)
1-2 A 3
2-3 B 4
2-4 C 5
3-5 D 4
4-5 E 8
5-6 F 6

Solution:
(a) AOA Network :
Events Activity Duration (days)
1-2 A 3
2-3 B 4
2-4 C 5
3-5 D 4
4-5 E 8
5-6 F 6
5
1 2
3
4
6
A
3
B
C
D
E
F
4 6
4
5
8

Solution:
Forward Path From AOA Network:
one
Backward Path From AOA Network:
one
ES EF
Note:
ES = Early Start (Forward Path)
EF = Early Finish (Backward Path)
5
1 2
3
4
6
A
3
B
C
D
E
F
4 6
4
5
8
0 22
16
7
3
8
5
1 2
3
4
6
A
3
B
C
D
E
F
4 6
4
5
8
0 0 22
16
12
3
8
11 or 16
8 or 3

Solution:
(b) Forward Path and Backward Path From AOA Network :
Note:
5
1 2
3
4
6
A
3
B
C
D
E
F
4 6
4
5
8
0 0 22 22
16 16
7 12
3 3
8 8

Solution:
(c) Critical Path and Project Completion Time:
5
1 2
3
4
6
A
3
B
C
D
E
F
4 6
4
5
8
0 0 22 22
16 16
7 12
3 3
8 8

Example 01:
A - 1
B A 4
C A 1
D B 1
E C 2
F C 2
G D 1
H E 1
I G 2
J G 7
K F,H 4
L I,J,K 2

Example 02:
A - 3
B A 4
C A 2
D B 5
E C 1
F C 2
G D,E 4
H F,G 3

Rules for Network Construction:
i. The starting event and ending event of an activity are called tail event and head
event, respectively.
ii. The network should have a unique starting node (tail event).
iii. The network should have a unique completion node (head event).
iv. No activity should be represented by more than one arc in the network.
v. No two activities should have the same starting node and the same ending node.
vi. No set of activities can form a circular loop.
vii. Dummy activity is an imaginary activity indicating precedence relationship only.
Duration of a dummy activity is zero.
viii. Dummy activities must be used only if it is necessary to reduce the complexity
of a network
The following are the primary rules for constructing AOA diagram.

Some conventions of network diagram are shown in figure below:

Bar Chart
A bar chart is a graphical tool that can be used to present data in a way that is
easy to read, easy to understand, and provides the ability for easy comparison
of all provided data.
It can be used to provide the project team and all of those looking for
project related information data from the individual schedule activities and
work breakdown structure components

Gantt Chart:
i. Graph or bar chart with a bar for each project activity that shows passage of time
ii. Provides visual display of project schedule

1. Critical Path Method (CPM)
i. Morgan R. Walker of DuPont and James E. Kelley, Jr. of Remington Rand
ii. Deterministic task times
iii. Activity-on-node network construction
iv. Repetitive nature of jobs
2. Project Evaluation and Review Technique (PERT)
i. U.S Navy (1958) for the POLARIS missile program
ii. Multiple task time estimates (probabilistic nature)
iii. Activity-on-arrow network construction
iii. Non-repetitive jobs (R & D work)
History of CPM/PERT

Critical path method (CPM) is a resource-utilization algorithm for scheduling a
set of project activities. The essential technique for using CPM is to construct a
model of the project that includes the following:
Critical Path Method:
i. A list of all tasks required to complete the project
ii. The dependencies between the tasks
iii. The estimate of time (duration) that each activity will take to complete
The critical path is the sequence of activities with the longest duration. A delay in
any of these activities will result in a delay for the whole project.

Critical Path Method:

Key Steps in the CPM

Terms Related to CPM

Program Evaluation Review Technique (PERT) is a project management planning
tool used to calculate the amount of time it will take to realistically finish a
project. PERT charts are used to plan tasks within a project -making it easier to
schedule and coordinate team members.
Program Evaluation Review Technique:
However with PERT, you create three different time estimates for the project:
i. The shortest possible amount of time each task will take
ii. The most probable amount of time
iii. The longest amount of time tasks might take if things don't go as planned
PERT is calculated backward from a fixed end date since contractor deadlines
typically cannot be moved.

There are four definitions of time used to estimate project time requirements:
Optimistic time:
The least amount of time it can take to complete a task
Pessimistic time:
The maximum amount of time it should take to complete a task
Most likely time:
Assuming there are no problems, the best or most reasonable estimate of how long it should take to
complete a task.
Expected time
Assuming there are problems, the best estimate of how much time will be required to complete a
task.

Important Formula:

Important Terms Used in a PERT Chart:
Here are several terms used in a PERT chart:
•Float/Slack: Refers to the amount of time a task can be delayed without resulting in an overall
delay in completion of other tasks or the project
•Critical Path: Indicates the longest possible continuous path from the start to the end of a task
or event
•Critical Path Activity: Refers to an activity without any slack
•Lead Time: Refers to the amount of time needed to finish a task without affecting subsequent
tasks
•Lag Time: The earliest time by which a successor event/task can follow a prior event/task
•Fast Tracking: Refers to handling tasks or activities in parallel
•Crashing Critical Path: Shortening the amount of time to do a critical task

To Implement a PERT Chart
To implement a PERT chart:
i. Identify the different tasks needed to complete a project. Make sure to add these
in the right order and indicate the duration of each task.
ii. Create a network diagram. Use arrows to represent the activities and use nodes as
milestones.
iii. Determine the critical path and possible slack.

Comparing CPM and PERT

Example 01:
For the given activities determine:
a. Critical Path (CP) using PERT
b. Calculate variance and standard deviation (SD)
c. Calculate Probability of Completing the project in 26 days
Activity
1-2 6 9 12
1-3 3 4 11
2-4 2 5 14
3-4 4 6 8
3-5 1 1.5 5
2-6 5 6 7
4-6 7 8 15
5-6 1 2 3

Following table gives the necessary information’s
Solution:
Activity
1-2 6 9 12 9 1.00
1-3 3 4 11 5 1.78
2-4 2 5 14 6 4.00
3-4 4 6 8 6 0.44
3-5 1 1.5 5 2 0.44
2-6 5 6 7 6 0.11
4-6 7 8 15 9 1.78
5-6 1 2 3 2 0.11

Solution:
Activity
1-2 9
1-3 5
2-4 6
3-4 6
3-5 2
2-6 6
4-6 9
5-6 2
Network Diagram:
5
1
2
3
9
5
9 9
0 0
5 9
4 6
15 15
7 22
24 24
6
6
6
2
2
9

Solution:

Example 02:
The time estimates (in weeks) for the activities of a PERT network are given below:
Activity
1-2 1 1 7
1-3 1 4 7
1-4 2 2 8
2-5 1 1 1
3-5 2 5 14
4-6 2 5 8
5-6 3 6 15
a. Draw the project network
b. Determine the expected project length
c. Calculate the Standard Deviation and Variance of the project
length
d. If the project due date is 19 weeks, what’s the probability of not
meeting the due date?
e. The probability that the project will be completed on schedule if
the scheduled completion time is 20 weeks?
f. What should be the scheduled completion time for the
probability of completion to be 90%?

Solution:
Activity
1-2 1 1 7 2 1
1-3 1 4 7 4 1
1-4 2 2 8 3 1
2-5 1 1 1 1 0
3-5 2 5 14 6 4
4-6 2 5 8 5 1
5-6 3 6 15 7 4

Solution:
Activity
1-2 2
1-3 4
1-4 3
2-5 1
3-5 6
4-6 5
5-6 7
4
1
2
2
3
2 9
0 0
3 12
3
4
5
6
17 17
10 10
4 4
1
6
5
7
Network Diagram:

Solution:
4
1
2
2
3
2 9
0 0
3 12
3
4
5
6
17 17
10 10
4 4
1
6
5
7
Network Diagram:

Example 03 :
Draw network. Find project duration. Draw critical path. Also find EST, LST, EFT, LFT, TF, FF.
Activity Duration (days)
1-2 3
2-3 4
2-4 5
3-5 4
4-5 8
5-6 6

Solution:
Network Diagram:
Activity Duration
(days)
1-2 3
2-3 4
2-4 5
3-5 4
4-5 8
5-6 6
5
1 2
3
4
6
A
3
B
C
D
E
F
4 6
4
5
8
0 0 22 22
16 16
7 12
3 3
8 8

Solution:
Following table gives the necessary information:
Activity
1-2 3 0 3 0 3 0 3 0
2-3 4 3 7 8 12 5 7 0
2-4 5 3 8 3 8 0 8 0
3-5 4 7 11 12 16 5 16 5
4-5 8 8 16 8 16 0 16 0
5-6 6 16 22 16 22 0 22 0

Example 04 :
A project schedule has the following characteristics
Activity 1-2 1-3 2-4 3-4 3-5 4-9 5-6 5-7 6-8 7-8 8-10 9-10
Time
(days)
4 1 1 1 6 5 4 8 1 2 5 7
a. Construct Network Diagram
b. Compute the earliest event time and latest event time
c. Determine the critical path and total project duration
d. Compute total float and free float for each activity.

Solution:
a. Network Diagram:
Activity 1-2 1-3 2-4 3-4 3-5 4-9 5-6 5-7 6-8 7-8 8-10 9-10
Time
(days)
4 1 1 1 6 5 4 8 1 2 5 7
0 0
1
1
3
2
4
7
9
5
6
8
10
4 9
1 1 7 7
11 16
17 17
15 15
5 10
10 15
22 22
1
4
1
6
1
4
8
2
5
7
5

Solution:
b. Earliest event time and Latest event time:
Following table gives the necessary information:
Activity Earliest Latest
1-2 4 0 4 5 9
1-3 1 0 1 0 1
2-4 1 4 5 9 10
3-4 1 1 2 9 10
3-5 6 1 7 1 7
4-9 5 5 10 10 15
5-6 4 7 11 12 16
5-7 8 7 15 7 15
6-8 1 11 12 16 17
7-8 2 15 17 15 17
8-10 5 17 22 17 22
9-10 7 10 17 15 22

Solution:
0 0
1
1
3
2
4
7
9
5
6
8
10
4 9
1 1 7 7
11 16
17 17
15 15
5 10
10 15
22 22
1
4
1
6
1
4
8
2
5
7
5

Solution:
d. Total float and Free float:
Activity
1-2 4 0 4 5 9 5 4 0
1-3 1 0 1 0 1 0 1 0
2-4 1 4 5 9 10 5 5 0
3-4 1 1 2 9 10 8 5 3
3-5 6 1 7 1 7 0 7 0
4-9 5 5 10 10 15 5 10 0
5-6 4 7 11 12 16 5 11 0
5-7 8 7 15 7 15 0 15 0
6-8 1 11 12 16 17 5 17 5
7-8 2 15 17 15 17 0 17 0
8-10 5 17 22 17 22 0 22 0
9-10 7 10 17 15 22 5 22 5
Following table gives the necessary calculation of TF and FF

Thank You Every One

Project scheduling (chapter 05)(wp)

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