Critical Path Method (CPM)
Redoy Masum Meraz
Lecturer
Department of Mechanical Engineering
Chittagong University of Engineering &
Technology
Project
A project is a planned set of interrelated tasks to be executed
over a fixed period and within certain costs and other
limitations.
Any unique endeavor with specific objectives
With multiple activities
With defined precedent relationships
With a specific time period for completion
Meraz
Industrial Management & Laws
ME459
Project Management
The
process
of
planning,
organizing,
analyzing,
implementing, and controlling a project to ensure the best
possible use of resources.
used to deliver something of value to people, such as
developing software for an improved business process,
constructing a building, or expanding sales into a new
geographic market.
Meraz
Industrial Management & Laws
ME459
Network Analysis
1. Define the project and prepare the work
breakdown structure.
2. Develop the relationships among the activities.
3. Draw the network connecting all the activities.
4. Assign time to each activity.
5. Compute the longest time path through the
network.
Meraz
Industrial Management & Laws
ME459
CPM
If the duration of each activity is known with certainty, then
the critical path method (CPM) can be used to determine
the length of time required to complete a project.
Can be used to determine how long each activity in the
project can be delayed without delaying the completion of
the project.
Meraz
Industrial Management & Laws
ME459
 The early event time for node i, represented by ET(i),
is the earliest time at which the event corresponding
to node i can occur.
 The late event time for node i, represented by LT(i),
is the latest time at which the event corresponding
to node i can occur without delaying the completion
of the project.
Meraz
Industrial Management & Laws
ME459
ET(1)=0
ET(3)=6
ET(4)=8
ET(5)=10
 ET (3)  8  14

ET (6)  max  ET (4)  4  12
 ET (5)  3  13

ET(6)=14
Meraz
Industrial Management & Laws
ME459
LT(5) =24
LT(6) =26
LT(7) = 28
Meraz
Industrial Management & Laws
ME459
Total Float is the amount of time that an activity can
be delayed from its early start date without delaying
the project finish date and denoted by TF(i,j).
TF(i,j)=LT(j)-ET(i)-tij
Meraz
Industrial Management & Laws
ME459


Any activity with a total float of zero is a
critical activity.
A Path from node 1 to the finish node that
consists entirely of critical activities is called
a critical path.
Meraz
Industrial Management & Laws
ME459
Draw a project network, determine the critical
path, find the total float for each activity, and
find the free float for each activity.
Meraz
Industrial Management & Laws
ME459
Meraz
Industrial Management & Laws
ME459
 Activity A: TF(1,3)=LT(3)-ET(1)-6=3
 Activity D: TF(3,4)=LT(4)-ET(3)-7=0
 Activity C: TF(3,5)=LT(5)-ET(3)-8=9
 Activity E: TF(4,5)=LT(5)-ET(4)-10=0
 Activity F: TF(5,6)=LT(6)-ET(5)-12=0
 Activity Dummy: TF(2,3)=LT(3)-ET(2)-0=0
Meraz
Industrial Management & Laws
ME459
Meraz
Industrial Management & Laws
ME459
The free float of the activity corresponding to arc (i, j),
denoted by FF(i, j), is the amount by which the starting
time of the activity corresponding to arc (i, j) (or the
duration of the activity) can be delayed without delaying
the start of any later activity beyond its earliest possible
starting time.
FF(i, j) =ET( j)-ET(i)-tij
Meraz
Industrial Management & Laws
ME459
 Activity B: FF(1,2)=ET(2)-ET(1)-9=0
 Activity A: FF(1,3)=ET(3)-ET(1)-6=3
 Activity D: FF(3,4)=ET(4)-ET(3)-7=0
 Activity C: FF(3,5)=ET(5)-ET(3)-8=9
 Activity E: FF(4,5)=ET(5)-ET(4)-10=0
 Activity F: FF(5,6)=ET(6)-ET(5)-12=0
 Activity Dummy: FF(2,3)=ET(3)-ET(2)-0=0
Meraz
Industrial Management & Laws
ME459