2. CPM
• The critical path method (CPM) is a
technique which is used for planning
and coordinating large project.
• A critical path in project management
is the longest sequence of activities
that must be finished on time in order
for the entire project to be complete.
• Application area are construction
project such as bridges, building,
dams , canals etc.
3. Objectives of CPM
1) Complete the job at the earliest to
avoid rising cost.
2) Ensure logical discipline in
planning, scheduling and
controlling projects.
3) Encourage more long range and
detailed planning of projects.
4) Provide management with
periodic reports as the project
progress.
5) Identify the most critical element
of the plan.
4. Procedure to Drawing a CPM
Network
Structure Analysis:
Draw up list of Activities
Draft of Structure /Network
Numbering of Events
Time Analysis:
Assessment of the duration of the Activities.
Progressive time Calculation (Forward Pass &
Backward Pass)
Assessment of the Critical Path
Assessment of the Float/ Slack
5. Forward Pass
(Progressive Computation)
Forward Pass used to compute
Earliest Event Time.
Sequence of activity start from left
to right of the network.
It usually start with zero (first
activity) i.e. ES (Earliest start) to
EF (earliest finish)
Zero be the staring time for the
Project.
6. Backward Pass
(Retrogressive Computation)
Backward Pass used to calculate
latest Event Time.
Sequence of activity start from
Right to left right of the network.
For finding event consider E = L
7. Assessment of Critical Path
In every network EE = LE
Or Earliest time of event (EE) = Latest time of event (LE)
An activity is said to b critical, if the total float (TFij) for any activity is zero.
Critical path Condition
• ESi = LFi
• ESj = LFj
• ESj-ESi= LFj-LFi= tij
8. Assessment of Float/Slack
Slack/ Float:
It is the time by which occurrence of an event can be delayed. It
is denoted as “S”
[S= L-E ]of the event
It is other wisely known as allowable slippage for a path.
The Slack analysis is done for each activity path to identify the
sub critical path.
It is of two types;
1. Event Slack
2. Activity Slack
9. Event Slack
• Event slack is the difference between latest event
time and earliest event time.
• Event Slack= LE- EE
= Latest event time- Earliest event time
10. Activity Slack
Activity Slack= (LEA- ESA)-D
where; LEA = latest ending time
ESA = earliest starting time
D = Duration of the activities
In network (CPM), three types of activity slacks or foat are identified;
Total Float/Slack: it is the difference between maximum available to
perform the activity and activity duration.
(TF)ij = LEj - EEi -D
Free Float/Slack: it is the time by which completion of an activity can be
delay without delaying its immediate succession.
(FF)ij = EEj - EEi -D
Independent Float/Slack: it is the portion of total float within which an
activity can be delay for start with effecting the float of preceding
activity.
(IF)ij = EEj - LEi -D
11. Example-1
• A project schedule has the following characteristics;
• Construct Network Diagram.
• Compute the earliest event time and latest event time.
• Determine the critical path and total project duration.
• Compute the total and free float for each activity.
Activity 1-2 1-3 2-4 3-4 3-5 4-9 5-6 5-7 6-8 7-8 8-10 9-10
Time (Days) 4 1 1 1 6 5 4 8 1 2 5 7
20. PERT
• Program (Project) Evaluation and Review Technique (PERT)
is an activity to understand the planning, arranging,
scheduling, coordinating and governing of a project.
• This program helps to understand the technique of a study
taken to complete a project, identify the least and
minimum time taken to complete the whole project.
• PERT was developed in the 1950s, with the aim of the cost
and time of a project.
21.
22. How to make PERT Chart?
Recognize particular projects and milestones.
Decide the precise sequence of the project.
Create a network diagram.
Determine the time needed for each project activity.
Manage the critical path.
Update the PERT chart as the project progresses.
23. PERT
PERT is a probabilistic method, where the activity times are
represented by probability distribution. This distribution of
activity is based on three different time estimate made for each
activity, which are as follows;
• Optimistic time estimate
• Most likely time estimate
• Pessimistic time estimate
24. PERT
Optimistic time estimate:
• This is the fastest time an activity can be
completed. For this, the assumption is made that
all the necessary resources are available and all
predecessor activities are completed as planned.
Most likely time estimate:
• Most of the times, project managers are asked
only to submit one estimate. In that case, this is
the estimate that goes to the upper
management.
Pessimistic time estimate:
• This is the maximum time required to complete
an activity. In this case, it is assumed that many
things go wrong related to the activity. A lot of
rework and resource unavailability are assumed
when this estimation is derived.
25. Calculation of PERT
Expected Completion Time (te) =
𝑡𝑜+4𝑡𝑚+𝑡𝑝
6
Possible Variance of the Activity 𝜎 2 = {
𝑡𝑝−𝑡𝑜
6
}2
Where;
Optimistic time estimate (to)
Most likely time estimate (tm)
Pessimistic time estimate (tp)
26. Example
• The following table shows the job of a network along with
their time estimates
Activity Estimated Duration (Weeks)
Optimistic
time (to)
Most Likely
time (tm)
Pessimistic
time (tp)
1-2 1 7 13
1-6 2 5 14
2-3 2 14 26
2-4 2 5 8
3-5 7 10 19
4-5 5 5 17
6-7 5 8 29
5-8 3 3 9
7-8 8 17 32
1) Draw the Project Network
2) Find the expected duration and
variance of each activity.
3) Calculate the earliest and latest
occurrence of each event.
4) Calculate the variance and standard
deviation of project length.
5) Find the probability of the project
completing in 40 days.
31. Example
Critical path = 1-2-3-5-8
So, Total project duration
=7+14+11+4=36 Weeks
Project length variance (σ2)= 4+16+4+1= 25
Project length standard deviation (σ) = 5 weeks
32. Calculation of Standard Normal Variable
𝑍 =
𝑇𝑠 − 𝑇𝑒
σ
Where,
Ts= Schedule time to complete the project
Te= Normal expected project length
σ =expected standard deviation of the project length
The probability that the project will be complete in 40
days is given by P (Z ≤ D )
So D =
𝑇𝑠−𝑇𝑒
σ
= 0.8
P (Z ≤ 0.8) = 0.7881 or 87.81% (Ans)
