Project management

1. CHAPTER-5
SCHEDULING

2. What is Scheduling?
Scheduling is a plan expressed in time frame. It is conversion of
project action plan into an operating time table. Scheduling express
future activities to be performed in a sequence. Scheduling express
start and end of particular activity. The amount of materials and
human force are required in different stages of project are stated in
scheduling.
When, what activities will be started, when it will be completed can
be known from scheduling. Project manager acquire money and
material resources as per time table of scheduling.
• According to Punmias and Khandelwal “Schedule is the
determination of time required for execution of each operation and
the time order in which each operation is to be carried out to meet
the project objectives”.

3. Feature of scheduling
1. Activities involved in a project: Scheduling express
different activities are to be performed in a project.
2. Relation among the activities: Scheduling makes
relationship among the activities involves in a project.
3. Expected start and finished time of each activity:
Scheduling defines each activity in terms of start and finish
time.
4. Duration of a project: Scheduling is used to calculate
duration of a project. Critical path indicate duration of
project.
5. Resource requirement: Scheduling indicates resources are
required in different activities at different time.

4. Stages in scheduling
.

5. Contd…
1. Determination of schedule objectives: At first stage
the schedule maker has to determine specific activities
are to be performed to meet schedule objectives.
2. Division of project activities: The entire project has to
make divide into some easily supervised and
controllable proportion.
3. Setting order of activities: Once the project activities
are divided, then make a rational order of each activity
involved.
4. Time planning: In this stage, allocate time for each
activity involved.

6. Contd…
5. Determination of terminal time of project: In this
stage the schedule maker will determine possible
duration of project on the basis of time allocate for
different activities involved.
6. Coordinating resources: Available resources should
have to coordinate with activities involved other than
revise scheduling.
7. Allocating responsibility: This is final stage of
scheduling. Here scheduling maker has to allocate
responsibility of the respective individuals involved in
project scheduling.

7. Project scheduling Methods
There are two common methods of project
scheduling-
1. Bar Chart
2. Network Technique

8. Bar Chart
• This technique was originated by H.L Gant, a
management specialist contemporary to F.W Taylor
when the world war-I was in situation. Bar Chart is
mostly known as Gant Chart.
• It is a symbolic technique of preparing project
schedule. The project activities are presented here
with the help of corresponding stick on time axis. The
left terminal of the stick represents the starting time
and the right terminal represents the ending time. The
length of the stick indicates the total time required to
finish the project.

9. Symbols used in Bar chart
Activities start
Project condition at specific point of time
Real growth of activities
Activities end

10. Advantages of Bar chart
Bar Chart has the following advantages:
• It represents the full mode symbol of the project. One can
avail the entire concept about the project at a glance through
it.
• It requires easy effort to make it. No special training is
required to compose it.
• It enables the presenter to show the actual growth of the
project.
• The manpower planning required to complete the project
activities is also shown in this chart.

11. Disadvantages of Bar chart
Bar Chart is not free from disadvantages, some disadvantages are:
• Bar Chart is useless in showing the interrelationship of the
project activities.
• It has also the size limitation that makes it useless in case of large
scale project.
• It requires high time and cost to make it fit to changing situation.

12. Network Technique
• Once a project is selected, the focus shifts to its implementation.
This involves completion of numerous activities (project
components). The activities of a project have interrelationship
arising from physical, technical and other considerations.
• For proper planning, scheduling and control of activities of a
project, given their interrelationships and constraints on the
availability of resources, Network Technique have been found quite
useful; includes two in special:
– CPM (Critical Path Method) and
– PERT (Performance Evaluation Review Technique).
• It is noted that it was developed in America (1950 - 1960) to
support the composition of proper planning and scheduling for
large scale critical and complex projects.

13. Network Technique
Advantages of network Technique
• The network Technique contains the following objectives:
• It helps to show the mutual interrelationship among the projects
activities.
• The schedule for the large scale project is possible to compose with
the help of this.
• The critical events required to complete the project can be known
by using the network diagram.
• The growth of the project can be traced in a specified time.
• Necessary changes can be made in any changed situation.
• The use of modern computer is possible.

14. Network Technique
Disadvantages of Network Technique The network
technique, however not free from certain limitations:
• The main limitation of Network Technique is
complexity. The use and composition of it is
comparatively complex than of the Bar Chart.
• It doesn’t specify who accomplish and when the task
does, though it indicates the interrelationship among
the activities.
• It is not fit to compose the schedule for all kinds of
project.

15. Network Technique
The characteristics must a project have for application of
network technique
There must have some characteristics of the project(s) that make
it fit when using Network Technique which are as follows:
• The project activities should have contained nature that make
them easily identifiable and when the identified activities will
be completed, it would declare the termination of the project.
• The activities should be specific in nature that makes it
possible to start, postpone and directing separately.
• The activities should be decorated in such manners that help
them follow in a gradual order.

16. Types of Network Diagram
• There are two types of network diagram, which are-
1. Arrow Diagram and
2. Node Diagram.
• Arrow Diagram: Activity of a project and their
relationship are shown with the help of arrow ( ). In
this diagram dummy (- - ) is used for showing the
relevant mutual relationship among the activities.
• Node Diagram: The function of a project is presented
with the help of cycle ( ) and the relationship is
shown by the arrow. This type of diagram does not
have dummy function.

17. Contd…
Project
activities
Preceding
activities
A
B
C A
D B
E B
F C
G D , E
Arrow diagram
Node Diagram

18. Rules for constructing network
1. All works must have event after finishing work or in before. Each
work should symbolize different letter.
2. In staring each work must be finished before work (if home).
3. Every event must be trace different number. The numbering
should be in this way as the back number of arrow is smaller than
the number of front of arrow.
4. The length of arrow is not important; small work can be directed
by big arrow and large work can be directed by small arrow.
5. To show the relation among the activities of project, dummy can
be used if necessary.
6. From the discussion above we get the assumption of network
construction

19. CPM (Critical Path Method)
Critical path method was invented be J.E Kelly
and M. R. Worker in 1957. this method is
invented for the planning of chemical
processing plant and for controlling this
method is for the presentation of various work
related to a project, relation for each other,
performing time, critical path etc. through
design or diagram.

20. Advantages of Critical Path Method
It has the following advantages:
• It figures out the activities which can run parallel to each other.
• It helps the project manager in identifying the most critical elements of
the project.
• It gives a practical and disciplined base which helps in determining how to
reach the objectives.
• CPM is effective in new project management.
• CPM can strengthen a team perception if it is applied properly.
• CPM provides demonstration of dependencies which helps in the
scheduling of individual activities.
• It shows the activities and their outcomes as a network diagram.
• It gives a fair and concise procedure of documenting of project.
• It helps in determining the slack time.
• An explicit and clear approach of communicating project plans, schedules,
time and cost performance is developed.

21. Disadvantages of Critical Path Method
It has the following disadvantages:
• The scheduling of personnel is not handled by the CPM.
• In CPM, it is difficult to estimate the completion time of an
activity.
• The critical path is not always clear in CPM.
• For bigger projects, CPM networks can be complicated too.
• It also does not handle the scheduling of the resource
allocation.
• In CPM, critical path needs to be calculated precisely.

22. PROBLEM-1
Activity Immediate
predecessor
activity
Time
( In days)
A - 6
B A 9
C A 8
D A 12
E B 11
F C,D 7
G E,F 12
H D 14
I G,H 9
Requirements:-
1. Draw a network diagram.
2. Indicate critical path.
3. If activity f requires 9 days instead
of 7 days. Do you think that it
would change the critical path?

23. Solution:
Requirement-1
.
Figure: Network Diagram
8
I
9

24. Requirement-2
Alternative path of network diagram
• Path-1. A-B-E-G-I = 6+9+11+12+9 = 47 days
• Path-2. A-C-F-G-I = 6+8+7+12+9 = 42 days
• Path-3. A-D-Dummy-F-G-I = 6+12+0+7+12+9 = 46 days
• Path-4. A-D-H-I = 6+12+14+9 =41 days
We know, critical path is the largest path among alternative
paths of network diagram.
Here path-1 (A-B-E-G-I) is critical path and length of this
path is 47 days.

25. Requirement-3
If the activity f requires 9 days instead of 7 days than length
of each alternative path will be-
• Path-1. A-B-E-G-I = 6+9+11+12+9 = 47 days
• Path-2. A-C-F-G-I = 6+8+9+12+9 = 44 days
• Path-3. A-D-Dummy-F-G-I = 6+12+0+9+12+9 = 48 days
• Path-4. A-D-H-I = 6+12+14+9 =41 days
From above calculation we see that, if F activity requires 9
days instead of 7 days than critical path is changed. New
critical path is path-3(A-D-Dummy-F-G-I) and its length is 48
days.

26. PERT (Performance Evaluation Review
Technique)
Program Evaluation and review technique (PERT) is a technique for estimating. It
applies a weighted average of optimistic, pessimistic, and most likely estimates
when there is uncertainty with the individual task/activity estimates. So, PERT is a
method to evaluate and estimate the time required to complete a task. This is like
a Three-Point estimate but here we give more weightage to the most likely
estimate. PERT uses three estimates to define an approximate range for a task’s
duration:
• Most likely estimate (m): This estimate is based on the duration of the task,
given the resources likely to be assigned, their productivity, realistic
expectations of availability for the activity, dependencies on other participants,
and interruptions.
• Optimistic (O): The task duration based on analysis of the best-case scenario
for the task. This will tell the minimum time the task may take.
• Pessimistic (P): The task duration based on analysis of the worst-case scenario
for the task. This will tell the maximum time a task can potentially take.

27. Advantages of PERT
• Planning for Large Project: It is used in scheduling large project by the
project manager
• PERT chart explicitly defines and makes visible dependencies (precedence
relationships) between the work breakdown structure (WBS) elements.
• PERT facilitates the identification of early start, late start, and slack for each
task.
• Optimistic and Pessimistic times considered in the calculation. More
weightage is given to most-likely time. Helps in better estimation
• PERT provides for potentially reduced project duration due to a better
understanding of dependencies leading to improved overlapping of activities
and tasks where feasible.
• A large amount of project data can be organized and presented in a diagram
for use in decision making.
• PERT can provide a probability of completing before a given time.

28. Disadvantages of PERT
• There can be potentially hundreds or thousands of tasks and individual
dependent relationships.
• PERT is not easily scalable for smaller projects.
• The network charts tend to be large and unwieldy, requiring several pages to
print and requiring specially sized paper.
• Time Focused Method: PERT is a time-bound method, so finishing projects or
activities on time is of high importance. If it does not happen than a problem
can arise
• Subjective Analysis: Here, the project activities are recognized according to the
available data. However, it is difficult in PERT projects as it is applicable for the
only new projects which are not repetitive in nature, therefore, the collection
of information is subjective in nature.
• Prediction Inaccuracy: PERT does not have any past records for a framework of
a project, so prediction comes into play. The project will have a negative
impact if the prediction is not accurate.

29. Steps in developing and solving PERT
Network
1. Identify the activities need to be performed for project implementation.
2. The time required for completing each activity of the project is estimated
and noted on network.
3. Time is estimated for each activity of the project. In ease of pert, three
types of time estimation is needed for each activity. Three types of time
estimation are-
– Optimistic time: Logical time estimation of project completion. In case of
optimistic time it presumes that everything will be done normally. Optimistic
time is denoted by “a”
– Pessimistic time: The delay estimated time for completing a project. Pessimistic
time is estimated with due consideration of adverse situation and is denoted by
“b”
– Most likely time: Most possible time of completing a project. Most likely time is
denoted by “m” . Time dimension of most likely time is middle ground of
optimistic and pessimistic time.

30. Contd…
5. Expected time account (TE): Expected time is to count with the help of the
following formula
a+4m+b
Expected time =
6
The weight of most likely time is given four times more than optimistic or
pessimistic time. Expected time (TE), in really, in the overage of three time
estimation. The formula of determining expected time is based on the
“Beta Distribution”.
6. Calculation of variance of activities of alternative path:
Formula = = Where, = variance
b = pessimistic time
a=optimistic time
2

2
6





  a
b 2


31. Contd…
7. Determination of critical path: Critical path is the
largest path of alternative paths of network diagram.
8. Probability of completing project:
Where, D= due date
• Formula Z= TE= expected time
cp = Variance of
critical path
Table value of Z is the probability of completing a project.
cp
TE
D


2
 
2


32. PERT vs CPM
S.N
O.
PERT CPM
1. PERT is that technique of project management
which is used to manage uncertain (i.e., time is
not known) activities of any project.
CPM is that technique of project management
which is used to manage only certain (i.e., time
is known) activities of any project.
2. It is event oriented technique which means that
network is constructed on the basis of event.
It is activity oriented technique which means
that network is constructed on the basis of
activities.
3. It is a probability model. It is a deterministic model.
4. It majorly focuses on time as meeting time target
or estimation of percent completion is more
important.
It majorly focuses on Time-cost trade off as
minimizing cost is more important.
5. It is appropriate for high precision time
estimation.
It is appropriate for reasonable time
estimation.
6. It has Non-repetitive nature of job. It has repetitive nature of job.
7. There is no chance of crashing as there is no
certainty of time.
There may be crashing because of certain time
boundation.
8. It doesn’t use any dummy activities. It uses dummy activities for representing
sequence of activities.
9. It is suitable for projects which required research
and development.
It is suitable for construction projects.

33. Problem-2
.
Activity Optimistic time (A) (in
days)
Most Likely Time(m)
(in days)
Pessimistic Time(b)
(in days)
Immediate
predecessor
activity
A 10 22 22 -
B 20 20 20 -
C 4 10 16 -
D 2 14 32 A
E 8 8 20 B,C
F 8 14 20 B,C
G 4 4 4 B,C
H 2 12 16 C
I 6 16 38 G,H
J 2 8 14 D,E
Requirements:
1. Draw a network diagram.
2. Calculate expected time.
3. Indicate critical path.
4. What is the variance of critical path?
5. What is the probability of completing the project within 50 days?

34. Solution:
Requirement-1
.
Figure: Network Diagram

35. Requirement-2
Calculation of expected time (TE)
We know, expected time (TE) =
Where,
a= Optimistic time
b= Pessimistic time and
m= Most likely time
6
4 b
m
a 


36. Contd…
TE A = = 20 TE F = =14
TE B = =20 TE G = =04
TE C = =10 TE H = =11
TE D = =15 TE I = =18
TE E = =10 TE J = =08
6
22
4
22
10 
 X
6
20
4
14
8 
 X
6
20
4
20
20 
 X
6
4
4
4
4 
 X
6
16
4
10
4 
 X
6
16
4
12
2 
 X
6
32
4
15
2 
 X
6
38
4
16
6 
 X
6
20
4
8
8 
 X
6
4
4
8
2 
 X

37. Contd…
Alternative path and length of alternative path are as
follows:
• Path-1. A-D-J=20+15+8 = 43 days
• Path-5. C-H-I=10+11+18 = 39 days
• Path-2. E-B-J=20+10+8 = 38 days
• Path-6. C-Dummy-E-J=10+0+10+8 = 28 days
• Path-3. B-F=20+14 = 34 days
• Path-7. C-Dummy-F=10+0+14 = 24 days
• Path-4. B-G-I=20+4+18 = 42 days
• Path-8. C-Dummy-G-I=10+0+4+18 = 32 days

38. Requirement-3
We know, critical path is the largest path
among alternative paths of network diagram.
Network diagram has eight alternative paths.
Among these paths path-1 (A-D-J) is the
highest length of alternative path. So path A-
D-J is critical path and its duration is 43 days
and duration of project is 43 days.

39. Requirement-4
Variance of critical path
We know, variance ( ) =
where, b = pessimistic time and a=optimistic time
Alternative path comprises activities A, D and J.
So we have to calculate variance of activities A,D
and J.
2

2
6





  a
b

40. Contd….
A = = 4
D= = 25
J= = 4
So variance of critical path is = cp = A + D + J= 4+ 25 + 4 = 33
2
 




 
6
10
22
2
 




 
6
2
32
2
 




 
6
2
14
2


2
 2
 2


41. Requirement-5
Probability of completing project within 50 days.
At first we have to calculate value of Z before
arriving probability of completing project. Formula
for calculating Z is-
Z = = = = 1.22
From the chart (page 85), when value of Z is 1.2 than probability is
88.49%. So probability of completing project within 50 days is 88.49
%( time estimation is reliable).
CP
TE
D


2
 33
43
50 
745
.
5
7