Critical path method

1. CRITICAL PATH METHOD
Prepared by:- Guide by:-
T.N. Manasiya (216262306003) Y.T. Rana sir
P.N. Chauhan (216260306002) F.A. Mukhi sir
A.R. Bhariyani (216260306007)
Course Name :- Construction Project Management
Course Code :- 4360603
Branch :- civil (6th)
College :- Government Polytechnic Palanpur
University :- Gujarat Technological University

2. COURSE OUTCOMES
a) Describe construction project management and roles of various
construction agencies.
b) Explain contracts and tendering process
c) Develop the CPM and PERT network of various construction activities.
d) Show leadership skills required to manage various construction
resources and achieve targets.
e) Apply safety measures and legal aspects at various construction works.

3. CRITICAL PATH METHOD
 The critical path of a network is the longest path in the network and the
duration of this path gives the duration or completion time of the project.
Critical path joins all those activities which are critical. In case of PERT
technique the critical path joins the events having zero or minimum
slacks while in CPM technique the critical path joins all critical activities
which have total float equal to zero. The activities which have total float
as zero, control the project duration and form continuous chain starting
from first node and ending at the last node.
 From the above discussion, following points can be concluded.

4. 1. Critical path starts from the initial event and ends at the last event of the network. All
events and activities lying along the critical path are critical for the completion of the
project.
2. In PERT technique, the critical path passes through all those events whose slack is
zero. Although it is a necessary condition, but it is not sufficient. In this case though
events may be critical, but the activity joining them may not be critical. Thus for
determining the critical path total float concept is more useful, as it provides both the
necessary and sufficient condition for the activity to be critical. This explains the basic
difference in approach for determining the critical path through PERT and CPM
techniques. Thus the concept of de- trimming the critical path by CPM technique (Total
float = zero) is more rational.
3. There can be more than one critical path in a network. Depending upon the total float
value, degree of criticality can be assigned to a particular path.
4. Critical activities have no flexibilities in their start time or finish time.

5. BASIC RULES FOR PREPARING CPM
NETWORK
The following network rules are noteworthy:
1. In a network there must be only single initial node. Initial node has only
one outgoing arrow.
2. A network can have only one final node and the final node will have
only incoming arrows.
3. No activity can start until its tail event has occurred.
4. An event cannot occur until all the activities leading to it are completed.

6. 8
4
5
6
7
Concrete foundation
2
Procure aggregate
Install concrete mixer
Procure cement
5
4
1
RULE 4
5. An event cannot occur twice, i.e. there cannot be any network path looping
back to previously occurred event. Network shown in Fig is incorrect.
1 2
3
6
5
4
Incorrect figure

7. 6. There must not be any dead end left except the find node. Final node has
only incoming arrows. There must be only single final node. Thus, the
network shown in Fig. is wrong because there are two final Nodes.
5
1 2
4
3
Incorrect network
7. Any arrow should represent singular situation, i.e. individuality and
separate entity must be maintained in a network. Particular arrow can
emanate from a single event only. Thus, the network shown in Fig. is wrong
since activity P has two arrows.

8. P
A
D
S
C
B Q
R
P
Incorrect network
8. The number of arrows should be equal to the number of activities in the
project.
9. The network should be drawn in such a way that all activities are
completed to reach the end objective.
10. A ‘dummy activity’ is introduced in the network either to show
dependency or to avoid duplicate numbering of activities.

9. ‘Erect beams’ can be taken up only when both ‘concrete pier’ and ‘precast
beams’ are completed. Dummy activity 2-3 shows this dependency and also
avoids duplicate numbering of activities.
2
Precast beams
4 3
8 Dummy activities
Dummy activity
2
1 4
Concrete pier Erect beams
11. Logic of network should always be maintained, i.e. arrow heads point
correct way to indicate the true control situation.
12. It is usual practice to show the time flow from left to right.

10. Advantages and Disadvantages of Critical Path
Method
Advantages:
1. The inter-relationship and sequence of performance of various activities
of work are clear from the network.
2. The sequence of operations to be followed at site is decided by logical
thinking.
3. There is no possibilities of overlapping of the activities.
4. Proper co-ordination of activities is maintained.
5. If something goes wrong with the planning of project it can be easily
identified and corrective measures can be taken.

11. 6. It helps in preparing the most economical time table for all the
operations of the project.
7. It assists in the selection of the best combination of equipment and
Labour so as to finish up the project in time.
8. It eliminates the idle period and hence reduces the project time and cost.
9. The engineer in charge can direct idle labour from one activity to
another.
10.It rationalises construction costing and financing.
11. It makes the most economical use of the available resources i.e. labour,
equipment, finance etc.

12. Disadvantages:
1. It is very expensive.
2. Experience and skill is required for preparing a network.
3. If the assumptions made in planning a project does not comes true, there
will be delay in the project.

13. Example of critical path method :-
 The following activities are to be performed in a project. Draw a
network diagram and determine ‘Critical path’ and total time to complete
the project.
Activity Nodes Duration( days)
A 1 – 2 4
B 1 – 3 5
C 2 – 3 3
D 2 – 4 6
E 3 – 4 8

14. Solution:-
First of all draw the network diagram.
1
0
4
3
2
15
7
4
0
4
7
15
4
8
5
3
6
B
A
E
C
TE
TL
D
Computation of TE :
Starting from event -1 and proceed towards right.
TE = TE of tail event + time duration of preceding activity.
For the first event, TE = 0
 TE1 = 0
 TE2 = TE1 + 4 = 0 + 4 = 4

15. TE3 = TE1 + 5 = 0 + 5 = 5 Taking larger value,
= TE2 + 3 = 4 + 3 = 7  TE3 = 7
TE4 = TE2 + 6 = 4 + 6 = 10 Taking larger value,
= TE3 + 8 = 7 + 8 = 15  TE4 = 15
Computation of TL : ∆
Starting from event - 4 and proceed towards left.
TL = TL of head event - time duration of succeeding activity.
For the last event, TL = TE
 TL4 = 15
TL3 = TL4 - 8 = 15 - 8 = 7
TL2 = TL3 - 3 = 7 - 3 = 4
TL1 = TL2 - 4 = 4 - 4 = 0 Taking smaller value,
= TL3 - 5 = 7 - 5 = 2  TL1 = 0

16. Calculation of EST : Calculation of EFT :
EST = TE of tail event of activity EST = TE of tail event of activity + D
activity A, EST = 0 activity A, EFT = 0 + 4 = 4
activity B, EST = 0 activity B, EFT = 0 + 5 = 5
activity C, EST = 4 activity C, EFT = 4 + 3 = 7
activity D, EST = 4 activity D, EFT = 4 + 6 = 10
activity E, EST = 7 activity E, EFT = 7 + 8 = 15

17. Calculation of LFT : Calculation of EFT :
LFT = TL of head event of activity EST = TE of tail event of activity - D
activity A, LFT = 4 activity A, EFT = 4 - 4 = 0
activity B, LFT = 7 activity B, EFT = 7 - 5 = 2
activity C, LFT = 7 activity C, EFT = 7 - 3 = 4
activity D, LFT = 15 activity D, EFT = 15 - 6 = 9
activity E, LFT = 15 activity E, EFT = 15 - 8 = 7
CALULATION OF (TF ) :
TF = LST – EST
OR
TF = LFT – EFT
Activity TF
A 0 – 0 = 0
B 2 – 0 = 2
C 4 – 4 = 0
D 9 – 4 = 5
E 7 – 7 = 0

18. The above calculations are shown in the table below :
Activity Duration EST EFT LST LFT TF Remarks
A 4 0 4 0 4 0 critical activity
B 5 0 5 2 7 2 -
C 3 4 7 4 7 0 critical activity
D 6 4 10 9 15 5 -
E 8 7 15 7 15 0 critical activity
 Critical Path : A - C – E
Total time for completion of project : 4 + 3 + 8 = 15 days

19. Thank you