Critical Path Method

Chapter – 6Critical Path Method (CPM)

Course Code - CIE 403

Mr. Ramesh Nayaka, (M.Tech. – IIT Madras)

Assistant Professor

Department of Civil Engineering

Manipal Institute of Technology, Manipal - 576104

Karnataka, India

Content…

• Introduction to CPM

• Difference between CPM and PERT

• Terms and Definitions

• Calculation of Float

• Critical Path

Introduction to CPM

CPM network are usually used for repetitive type of projects,

where fairly accurate estimates of time can be made for the

activities of the project.

The activities of these projects are characteristically subject

to relatively small amount of variation. Hence CPM is not

suitable for research and development type of projects.

Examples from fairly diverse field where application of CPM

can be made:

Building a new bridge across river ganga, Constructing a

multi-storeyed building, extension of a factory building, shifting a

manufacturing unit to other site and manufacturing of a new car

etc.

Difference between CPM and PERT

CPM PERT

Activity Oriented network Event oriented network

The time estimates are of a fair

degree of accuracy

Time estimates are not that

accurate and there is an

uncertainty attached to it

Follows deterministic approach Follows probabilistic approach

Cost is governing factor Time is governing factor

Project duration is so fixed such

that the cost is minimum

Assumed that cost is directly

proportional to time so time is

reduced maximum possible to

enjoy least cost

Critical path is that path which

joins the critical activities

Critical path is the path which

joins the critical events

Terms and Definitions

Activity Times

Forward Passing :

Earliest Start Time (EST) : earliest time by which an

activity start

EST = earliest event time of tail event = TEi

Earliest Finish Time (EFT) : Earliest time by which an

activity can be completed

EFT = EST + tEij = TE

i + tEij

Terms and Definitions

Activity Times

Backward Passing :

Latest Finish Time (LFT) : latest time by which an activity

can completed without delaying the completion of the

project

LFT = Latest Finish Time of head event = TLj

Latest Start Time (LST) : latest time by which an activity

can start without delaying the completion of the project

LST = LFT - tEij = TL

j - tEij

Terms and Definitions

FLOATS

Similar to slack in PERT

Associated with activity times

Denotes flexibility range within which the activity start

and finish time may fluctuate without affecting the total

duration of the project

Terms and Definitions

TYPES OF FLOATS

Total Float (FT) : timespan by which starting or finishing

of an activity can be delayed without affecting the overall

completion time of the project.

It refers to the amount of time by which the completion of

activity could be delayed beyond earliest expected

completion time without affecting overall project duration

time

FT= LST – EST or LFT - EFT

Terms and Definitions

TYPES OF FLOATS

Free Float (FF) : duration by which an activity can be

delayed without delaying any other succeeding activity.

It refers to the amount of time by which the completion of

an activity can be delayed beyond the earliest finish time

without affecting the earliest start time of a subsequent

succeeding activity.

This float is concerned with the commencement of

subsequent activity

FF = FT – Sj , Sj= Slack of head event = TLj – TE

j

Terms and Definitions

TYPES OF FLOATS

Independent Float (FID): It is excess time available if the

preceding activity ends as late as possible and the

succeeding activity starts as early as possible

It is refers to that the amount of time by which the start of

an activity can be delayed, without affecting earliest start

time of any immediately following activities

This float concerned with prior and subsequent activities

FID= FF – Si

Si = slack of tail event =TLi– TE

i

Terms and Definitions

TYPES OF FLOATS

Interfering Float (FIT) : Another name for head event slack

(Sj), it is the difference between total float and free float

FIT = FT – FF = TLj – TE

j = Sj

Note : if the total float (FT) for any activity is zero then such

activity is called critical activity

Critical Activity : an activity is said to be critical, if a delay in

its start cause a further delay in the completion of the entire

project

Terms and Definitions

Critical Path : The sequence of critical activities in a network

which determines the duration of a project is called critical

path.

• It is the longest path in the network from the starting event to

the ending event

• For activities lies on critical path

EST =LST , EFT = LFT and EST –EFT = LST – LFT

Sub critical activity : When total float (FT ) is positive

Critical Activity :When total float (FT ) is zero

Super critical activity : When total float (FT ) is negative

Calculating Critical Path & Float for a

Network Diagram

Find out the length of all the paths in the

network diagram

The longest path is the critical path

Float = EF – LF = ES - LS

Terms and Definitions

Critical Path : The sequence of critical activities in a network

which determines the duration of a project is called critical

path.

• It is the longest path in the network from the starting event to

the ending event

• For activities lies on critical path

EST =LST , EFT = LFT and EST –EFT = LST – LFT

Sub critical activity : When total float (FT ) is positive

Critical Activity :When total float (FT ) is zero

Super critical activity : When total float (FT ) is negative

Terms and Definitions

Critical Path : The sequence of critical activities in a network

which determines the duration of a project is called critical

path.

• It is the longest path in the network from the starting event to

the ending event

• For activities lies on critical path

EST =LST , EFT = LFT and EST –EFT = LST – LFT

Sub critical activity : When total float (FT ) is positive

Critical Activity :When total float (FT ) is zero

Super critical activity : When total float (FT ) is negative

CPM Analysis

F

1

2

4

3

5

6

7 8

A

B

C

D

EH

K

J

I

10 8 12

8 10

6

5

126

12

8

A project consists of 11 activities, represented by the

network shown below in figure and also the normal

durations required to perform various activities of the

project are given in network. Compute (a) Event times

(b) activity times and total float. Also determine

the critical path.

a. Computation of Event times

Event

No.

PredecessorSucces

sor

Event Event

1

2

3

4

5

6

7

8

Earliest Expected Time (↓ ) Latest occurrence Time ( ↑ )

tE TE TE (Max) tE TL TL (Min)

b. Computation of activity times and floats

Activity Duration Earliest (Units) Latest (Units)Total

Float

Free

Float

Independe

nt Float

(i - j) tEij EST EFT LST LFT FT

FF FID

1 - 2

1 - 3

2 – 5

2 – 7

3 – 4

3 – 6

4 – 5

5 - 6

5 - 7

6 - 7

7 - 8

c. Location of Critical path

• 1- 3 – 4 – 5 – 6 – 7 = 52 units

F

1

2

4

3

5

6

7 8

A

B

C

D

EH

K

J

I

10 8 12

8 10

6

5

126

12

8

Problem – 2

F

1

2

4

3

5

6

7

8

A

B

G

E

D I L

J

54

4

6 2

6

7

8

0

6

7C

K

3

Network shown below in figure and also the normal

durations required to perform various activities of the

project are given in network. Compute (a) Event times (b)

activity times (c) total float for each activity and establish

the critical path. Also determine the free float and

independent float .

Problem – 2

1

2

3

6

4

5

A

B

E

D

G

H

3

5

3

114

4

C

F

4

Network shown below in figure and also the normal

durations required to perform various activities of the

project are given in network. Compute (a) Event times (b)

activity times (c) total float for each activity and establish

the critical path. Also determine the free float and

independent float .

6 1I