Critical Path Analysis
There are no pre-requisites for this
Achievement Standard so it can be
placed in any course.
No knowledge is pre-supposed.
Methods include a selection from
those related to:
precedence tables
network diagrams
critical events
scheduling
float times
Critical Path Analysis (CPA)
A complex project must be well planned,
especially if a number of people are involved.
CPA is used to ensure that the complete scheme
is completed in the minimum time.
It is used to schedule the projects.
So what is
a project?
Any activity can be
represented as a project:
planning a party
building a house/factory
planning a conference
What do the
projects have
in common?
Each project can be broken down
into tasks.
Each task takes time and uses
resources.
Tasks are structured
Step 1 – Precedence table
• To identify actual tasks that make up a project
• To identify the order these tasks need to be in
• To decide how long each task will take
Example: Constructing a garage
Task
Duration (days)
A
B
C
prepare foundations
Make and position door frame
Lay drains, floor base and screed
7
2
15
D
E
F
Install services and fittings
Erect walls
Plaster ceiling
8
10
2
G
H
I
J
Erect roof
Install door and windows
Fit gutters and pipes
Paint outside
5
8
2
3
Some of these activities must be
completed before others can start.
Task
Duration (days)
A
B
C
prepare foundations
Make and position door frame
Lay drains, floor base and screed
7
2
15
D
E
F
Install services and fittings
Erect walls
Plaster ceiling
8
10
2
G
H
I
J
Erect roof
Install door and windows
Fit gutters and pipes
Paint outside
5
8
2
3
You can’t erect the roof (G) before you
have erected the walls (E)
Task
Duration (days)
A
B
C
prepare foundations
Make and position door frame
Lay drains, floor base and screed
7
2
15
D
E
F
Install services and fittings
Erect walls
Plaster ceiling
8
10
2
G
H
I
J
Erect roof
Install door and windows
Fit gutters and pipes
Paint outside
5
8
2
3
Precedence
D must follow E
Task
A
B
prepare foundations
Make and position door frame
Duration
(days)
7
2
C
D
E
Lay drains, floor base and screed
Install services and fittings
Erect walls
15
8
10
F
G
H
Plaster ceiling
Erect roof
Install door and windows
2
5
8
I
J
Fit gutters and pipes
Paint outside
2
3
E
E must follow A and B
Task
A
B
prepare foundations
Make and position door frame
Duration
(days)
7
2
C
D
E
Lay drains, floor base and screed
Install services and fittings
Erect walls
15
8
10
F
G
H
Plaster ceiling
Erect roof
Install door and windows
2
5
8
I
J
Fit gutters and pipes
Paint outside
2
3
E
A, B
F must follow D and G
Task
A
B
prepare foundations
Make and position door frame
Duration
(days)
7
2
C
D
E
Lay drains, floor base and screed
Install services and fittings
Erect walls
15
8
10
F
G
H
Plaster ceiling
Erect roof
Install door and windows
2
5
8
I
J
Fit gutters and pipes
Paint outside
2
3
E
A, B
D, G
G must follow E
Task
A
B
prepare foundations
Make and position door frame
Duration
(days)
7
2
C
D
E
Lay drains, floor base and screed
Install services and fittings
Erect walls
15
8
10
F
G
H
Plaster ceiling
Erect roof
Install door and windows
2
5
8
I
J
Fit gutters and pipes
Paint outside
2
3
E
A, B
D, G
E
H must follow G
Task
A
B
prepare foundations
Make and position door frame
Duration
(days)
7
2
C
D
E
Lay drains, floor base and screed
Install services and fittings
Erect walls
15
8
10
E
A, B
F
G
H
Plaster ceiling
Erect roof
Install door and windows
2
5
8
D, G
E
G
I
J
Fit gutters and pipes
Paint outside
2
3
I must follow C, F
Task
A
B
prepare foundations
Make and position door frame
Duration
(days)
7
2
C
D
E
Lay drains, floor base and screed
Install services and fittings
Erect walls
15
8
10
E
A, B
F
G
H
Plaster ceiling
Erect roof
Install door and windows
2
5
8
D, G
E
G
I
J
Fit gutters and pipes
Paint outside
2
3
C, F
J must follow H and I
Task
A
B
prepare foundations
Make and position door frame
Duration
(days)
7
2
C
D
E
Lay drains, floor base and screed
Install services and fittings
Erect walls
15
8
10
E
A, B
F
G
H
Plaster ceiling
Erect roof
Install door and windows
2
5
8
D, G
E
G
I
J
Fit gutters and pipes
Paint outside
2
3
C, F
I
We call this a precedence table
Task
Duration Precedence
(days)
7
2
A
B
prepare foundations
Make and position door frame
C
D
E
Lay drains, floor base and screed
Install services and fittings
Erect walls
15
8
10
E
A, B
F
G
H
Plaster ceiling
Erect roof
Install door and windows
2
5
8
D, G
E
G
I
J
Fit gutters and pipes
Paint outside
2
3
C, F
I
• Precedence diagrams are not that useful.
• A useful visual representation of a project is a
network diagram.
Sequence
the most common sequences / dependencies
Task A
Task A
Task B
Task B
Task C
Task A
Task C
Task B
Task B depends upon Task A; B
cannot start until A is finished
Tasks B and C depend on Task A;
neither can start until A is
finished, but B and C are
independent of each other
Task C depends upon Task A and
B; C cannot start until both A
and B are finished
more unusual links and relationships
so far all links have been finish-start links...
Task A
3 days
Task B
Task A
Task C
Task A
Task C
Task B depends upon Task A, but
with a 3 day delay; B cannot start
until 3 days after A is finished
The start of Task C depends on
the start of Task A; this is a
start-to-start link; it may also
incorporate a delay
The finish of Task C depends
upon the finish of Task A
Drawing a NETWORK – how do we get here?
Algorithm
Draw in the links
Task
Precedence
A
B
C
D
E
F
G
H
I
J
E
A, B
D, G
E
G
C, F
I
Draw in A, B, C on a rough diagram
STEP 1- original vertices with no arcs
STEP 2 - delete all arcs incident on A, B, C and redraw as shown
STEP 3 - repeat iteration
STEP 1- original vertices with no arcs
STEP 2 - delete all arcs incident on E and redraw as shown
STEP 3 - repeat iteration
STEP 1- original vertices with no arcs
STEP 2 - delete all arcs incident on D, G and redraw as shown
STEP 3 - repeat iteration
STEP 1- original vertices with no arcs
STEP 2 - delete all arcs incident on F and H and redraw as shown
STEP 3 - repeat iteration
STEP 1- original vertices with no arcs
STEP 2 - delete all arcs incident on I and redraw as shown
STEP 3 - STOP
Converting to a usable diagram
Proposed method
Now draw the
network diagram
using boxes
early start
time
duration
early finish
time
task number and/or name
late start
time
float
late finish
time
slack
Example
Duration
15
2
Task I
Task C
8
2
Task D
Task F
7
Task A
3
Task J
10
Task E
2
5
8
Task B
Task G
Task H
Finish
Critical Path
• Find the earliest possible start for each
activity, by going forwards through the
network.
• Secondly, the latest possible start time for
each activity is found by going backwards
through the network.
• Activities which have equal earliest and latest
start time are on the critical path.
Practice 1
4
3
Task 02
Task 03
5
Task 07
3
6
3
1
Task 01
Task 04
Task 05
Task 09
2
2
Task 06
Task 08
Practice 1
4
3
Task 02
Task 03
5
Task 07
0
3
6
3
1
Task 01
Task 04
Task 05
Task 09
2
2
Task 06
Task 08
Practice 1
4
3
Task 02
Task 03
5
Task 07
3
0 Task
3
01
6
3
1
Task 04
Task 05
Task 09
2
2
Task 06
Task 08
Practice 1
3
4
3
Task 02
Task 03
5
Task 07
3 3
0 Task
01
3
3
6
3
1
Task 04
Task 05
Task 09
2
2
Task 06
Task 08
Practice 1
3
4
7
Task 02
3
Task 03
5
Task 07
3 3
0 Task
01
3
6
9
Task 04
3
2
Task 06
5
3
1
Task 05
Task 09
2
Task 08
Practice 1
3
4
7
Task 02
7
3
Task 03
5
Task 07
3 3
0 Task
01
3
6
9
Task 04
3
2
Task 06
5
9
3
1
Task 05
Task 09
5
2
Task 08
Practice 1
3
4
7
Task 02
7
3
10
Task 03
5
Task 07
3 3
0 Task
01
3
6
9
Task 04
3
2
Task 06
9
3
12
1
Task 05
5
Task 09
5
2
Task 08
7
Practice 1
3
4
7
Task 02
7
3
Take the
largest value
10
Task 03
12
5
Task 07
3 3
0 Task
01
3
6
9
Task 04
3
2
Task 06
9
3
12
1
Task 05
5
Task 09
5
2
Task 08
7
Practice 1
3
4
7
Task 02
7
3
10
Task 03
12
5
17
Task 07
3 3
0 Task
01
3
6
9
Task 04
3
2
Task 06
9
3
12
1
Task 05
5
Task 09
5
2
Task 08
7
Practice 1
3
4
7
Task 02
7
3
Take the
largest value
10
Task 03
12
5
17
Task 07
3 3
0 Task
01
3
6
9
Task 04
3
2
Task 06
9
3
12
1
Task 05
5
Task 09
5
2
Task 08
7
Forward pass complete
3
4
7
7
Task 02
3
10
Task 03
12 5
17
Task 07
0
3
3
3
Task 01
6
9
Task 04
3
2
Task 06
9
3
12
17
Task 05
5
1
18
Task 09
5
2
7
Task 08
Duration = 18
Backward pass
3
4
7
7
Task 02
3
10
Task 03
12 5
17
Task 07
0
3
3
3
Task 01
6
9
Task 04
9
3
12
17
Task 05
1
18
Task 09
18
3
2
Task 06
5
5
2
Task 08
7
3
4
7
7
Task 02
3
10
Task 03
12 5
17
Task 07
0
3
3
3
Task 01
6
9
Task 04
9
3
12
17
Task 05
1
Task 09
17 0
3
2
Task 06
5
18
5
2
7
Task 08
Float
18
3
4
7
7
Task 02
3
10
Task 03
12 5
17
Task 07
0
3
3
3
Task 01
6
9
Task 04
9
3
12
17
Task 05
17
1
Task 09
17 0
3
2
Task 06
5
18
5
2
7
Task 08
17
18
3
4
7
7
Task 02
3
10
Task 03
12 5
17
Task 07
0
3
3
3
Task 01
6
9
Task 04
9
3
12
12
0
17
Task 05
17
1
Task 09
17 0
3
2
Task 06
5
18
2
5
7
Task 08
15
10 17
18
3
4
7
7
Task 02
5
2
3
10
Task 03
9
9
12
2
12 5
17
Task 07
0
3
3
3
Task 01
6
9
9
Task 04
12
12
0
17
Task 05
3
0
9
3
2
5
Task 06
13 10
3
15
9
0
17
1
18
Task 09
12
17 0
2
5
7
Task 08
15
10 17
18
Forward pass complete
Take the
smallest
3
4
7
7
Task 02
5
2
3
10
Task 03
9
9
12
2
12 5
17
Task 07
0
3
3
3
Task 01
6
9
9
Task 04
12
12
0
17
Task 05
3
0
9
3
2
5
Task 06
13 10
3
15
9
0
17
1
18
Task 09
12
17 0
2
5
7
Task 08
15
10 17
18
Critical Path – float = 0
3
4
7
7
Task 02
5
2
3
10
Task 03
9
9
2
12
12 5
17
Task 07
0
3
3
3
Task 01
0
0
6
9
9
Task 04
3
12
12 0
17
Task 05
3
0
9
3
2
5
Task 06
13 10
3
9
0
1
18
Task 09
12
17 0
5
2
7
Task 08
15
17
15 10 17
18
Your turn
2
15
Task I
Task C
8
2
Task D
Task F
7
Task A
3
Task J
10
Task E
2
5
8
Task B
Task G
Task H
Finish
Example 1 – Forward pass
0
2
15
Task I
Task C
0
8
2
Task D
Task F
7
Task A
3
Task J
10
Task E
0
2
5
8
Task B
Task G
Task H
Finish
Example 1 – Forward pass
0
2
15 15
Task I
Task C
0
7
8
2
Task D
Task F
7
Task A
3
Task J
10
Task E
0
2
Task B
2
5
8
Task G
Task H
Finish
Example 1 – Take the largest value
0
?
15 15
Task I
Task C
0
7
2
8
2
Task D
Task F
7
Task A
3
7
Task J
10
Task E
0
2
Task B
2
5
8
Task G
Task H
Finish
Example 1 – Take the largest value
0
?
15 15
Task I
Task C
8
2
Task D
Task F
17
0
7
2
7
Task A
3
7
Task J
10 17
Task E
0
2
Task B
2
17
5
8
Task G
Task H
Finish
Example 1 – Take the largest value
0
?
15 15
Task I
Task C
8
17
25
Task D
0
7
2
2
Task F
7
Task A
3
7
Task J
10 17
Task E
0
2
Task B
2
17
5
Task G
22
8
Task H
Finish
Example 1 – Take the largest value
0
?
15 15
Task I
Task C
8
17
25
Task D
0
7
2
2
25
Task F
7
Task A
3
7
Task J
10 17
Task E
0
2
Task B
2
17
5
Task G
22
22
8
Task H
Finish
Example 1 – Minimum 32
0
27
15 15
8
17
25
Task D
7
29
Task I
Task C
0
2
2
25
27
Task F
7
Task A
29
7
3
32
Task J
10 17
Task E
0
2
Task B
2
17
5
Task G
22
22
8
Task H
30
32
Finish
Example 1 – Backward pass
0
27
15 15
8
17
25
Task D
7
29
Task I
Task C
0
2
2
25
27
Task F
7
Task A
29
7
3
32
Task J
10 17
Task E
0
2
Task B
2
17
5
Task G
22
22
8
Task H
30
32
Finish
32
Example 1 – Take lowest value
0
27
15 15
8
17
25
Task D
7
29
Task I
Task C
0
2
2
25
27
Task F
7
Task A
29
7
2
Task B
2
32
Task J
10 17
2
9
Task E
0
3
17
5
22
22
Task G
8
2
32
30
Task H
24
0
32
32
Finish
32
Example 1 – Take lowest value
0
27
15 15
27 0
8
17
25
Task D
7
29
Task I
Task C
0
2
2
25
29
27
Task F
7
Task A
29
7
2
Task B
2
32
Task J
10 17
2
9
Task E
0
3
17
5
22
22
Task G
8
2
32
30
Task H
24
0
32
32
Finish
32
Example 1 – Take lowest value
0
27
15 15
27 0
8
17
25
Task D
7
2
25
7
25 0
27
27
29
7
Task B
2
3
32
Task J
10 17
2
9
Task E
2
29
Task F
Task A
0
29
Task I
Task C
0
2
17
5
22
22
Task G
8
2
32
30
Task H
24
0
32
32
Finish
32
Example 1 – Take lowest value
0
27
15 15
27 0
8
17
25
Task D
7
7
17 0
Task A
2
25
7
Task F
25
25 0
27
Task B
2
3
32
Task J
10 17
2
9
Task E
2
29
27
29
0
29
Task I
Task C
0
2
17
5
22
22
Task G
19 2
8
24
2
32
30
Task H
24
0
32
32
Finish
32
Example 1 – Take lowest value
0
27
15 15
27 0
8
17
25
Task D
7
7
17
Task A
0
2
25
7
Task F
25
25 0
27
2
2
0
3
32
Task J
10 17
2
9
Task E
7
29
27
29
0
29
Task I
Task C
0
2
17
17
Task B
5
22
22
Task G
19
2
8
24
2
32
30
Task H
24
0
32
32
Finish
32
Example 1 – Take lowest value
27
15 15
0
27 0
27
8
17
25
Task D
0
7
7
17
Task A
0
0
0
2
25
Task F
25
25 0
27
29
2
2
0
2
9
17
17
Task B
5
5
5
22
22
Task G
7
3
32
Task J
10 17
Task E
7
29
27
7
7
0
29
Task I
Task C
12 12
2
19
2
8
24
2
32
30
Task H
24
0
32
32
Finish
32
Example 1 – Critical Path – zero float
27
15 15
0
27 0
27
8
17
25
Task D
0
7
7
17
Task A
0
0
0
2
25
Task F
25
25 0
27
29
2
2
0
2
9
17
17
Task B
5
5
5
22
22
Task G
7
3
32
Task J
10 17
Task E
7
29
27
7
7
0
29
Task I
Task C
12 12
2
19
2
8
24
2
32
30
Task H
24
0
32
32
Finish
32
Example 1 – Critical Path – A-E-D-F-I-J
27
15 15
0
27 0
27
8
17
25
Task D
0
7
7
17
Task A
0
0
0
2
25
Task F
25
25 0
27
29
2
2
0
2
9
17
17
Task B
5
5
5
22
22
Task G
7
3
32
Task J
10 17
Task E
7
29
27
7
7
0
29
Task I
Task C
12 12
2
19
2
8
24
2
32
30
Task H
24
0
32
32
Finish
32
Using the outputs
• Gantt Charts
• optimising the schedule
Gantt: Critical path in red
Gantt: Critical path in red
Scheduling: Move the critical path along the top
Now fit the other activities like a puzzle
Now fit the other activities like a puzzle
Schedule
Any delay on the critical path causes a delay in
the entire project
There is a 2-day float on the non-critical path
Definitions
• Critical Path Those activities that can not over run
without effecting the total length of the project, are
those where the EST = LFT (Total float = 0).
• Total Float LFT of the activity- the duration- EST of the
activity. This shows how much ´slack´ there is on a
particular route of the network. If the total float is 0
then an activity lies on the critical path.
• Free Float EST of the next activity – Duration – EST of
this activity. This shows the ´slack´ on an individual
activity before it delays the start of the next activity.
• EES = Earliest early start time
• LLF = latest late finish time
Free float: The amount of time that a schedule
activity can be delayed without delaying the
early start date of any immediately following
schedule activities.
Free Float = EESsuccessor – EF
• EES = Earliest early start time
• LLF = latest late finish time
Independent float is that portion of the total
float within which an activity can be delayed for
start without affecting the float of the preceding
activities.
Independent Float = EESsuccessor-LLFpredecessor-duration