Critical path method(cpm)

Critical Path Management…….
Work Smart Not Hard !!!

Critical path analysis
The critical path method (CPM), or critical path analysis (CPA), is
an algorithm for scheduling set of project activities It is commonly used in
conjunction with the program evaluation and review technique (PERT).
PERT chart for a project with five
milestones (10 through 50) and six
activities (A through F).
The project has two critical paths:
activities B and C, or A, D, and F –
giving a minimum project time of 7
months with fast tracking.
Activity E is sub-critical, and has a
float of 1 month.

The float
• With the network complete, you can now identify any idle time.
• This spare time is known as the float.
• Resources can be allocated to other duties during the float time.
• In this activity there is only one critical time - between tasks d and e,
where there are 5 floating hours.
• Float is calculated by:
Float = LFT – (EST - Duration)

Critical Path Method(CPM)
The essential technique for using CPM is to construct a model of the project
that includes the following:
1.A list of all activities required to complete the project (typically categorized
within a work breakdown structure),
2.The time (duration) that each activity will take to complete,
3.The dependencies between the activities and,
4.Logical end points such as milestones or deliverable items.
• Using these values, CPM calculates the longest path of planned activities
to logical end points or to the end of the project, and the earliest and latest
that each activity can start and finish without making the project longer.
• This process determines which activities are "critical" (i.e., on the longest
path) and which have "total float" (i.e., can be delayed without making the
project longer).

In project management, a critical path is the sequence of project network activities
which add up to the longest overall duration, regardless if that longest duration has
float or not.
This determines the shortest time possible to complete the project. There can be
'total float' (unused time) within the critical path.
• For example, if a project is testing a solar panel and task 'B' requires 'sunrise',
there could be a scheduling constraint on the testing activity so that it would not
start until the scheduled time for sunrise.
This might insert dead time (total float) into the schedule on the activities on that
path prior to the sunrise.
This path, with the constraint-generated total float would actually make the path
longer.

Task is an activity that needs to be accomplished within a defined period
of time or by a deadline to work towards work-related goals.
A task can be broken down into assignments which should also have a
defined start and end date or a deadline for completion.
One or more assignments on a task puts the task under execution.
Completion of all assignments on a specific task normally renders the
task completed. Tasks can be linked together to create dependencies.
Tasks completion generally requires the coordination of others.

A project can have several, parallel, near critical paths; and some or all of
the tasks could have 'free float' and/or 'total float'.
An additional parallel path through the network with the total durations
shorter than the critical path is called a sub-critical or non-critical path.
Activities on sub-critical paths have no drag, as they are not extending the
project's duration.
CPM analysis tools allow a user to select a logical end point in a project
and quickly identify its longest series of dependent activities (its longest
path). These tools can display the critical path (and near critical path
activities if desired) as a cascading waterfall that flows from the project's
start (or current status date) to the selected logical end point.

What is the Critical Path Method?
Every project has some core tasks that are crucial
to its completion.
Take something as simple as making an omelette.
A short recipe for making an omelette would look something like this:
1.Beat 2 eggs 2.Heat a pan, add butter/oil when hot 3.Pour in the beaten eggs and
cook for 5 minutes
There are several other tasks like seasoning the eggs with salt and pepper. Maybe
add some vegetables and some cheese. Perhaps you could flip it on the other side
so the eggs are fully cooked through.
However, these activities are in-addition to the three core steps in the recipe. Even if
you don’t perform them, you’ll still have an omelette.
On the other hand, if you forget to beat the eggs, or heat the pan, or cook the eggs,
you won’t have anything but a cold pan and two eggs.
Which is to say, the three steps in the recipe describe the critical tasks necessary to
make the omelette making project a success.

Example: if you’re building a house, you would have several task sequences as
follows:
The total time taken to complete the sequence along this critical path would give you an idea of
the project’s minimum duration.
You might undertake several task sequences simultaneously, but if there are any delays in the
critical path sequence, your project will suffer delays as well.

Components of CPM:
The essential technique to construct a model of the project that includes the
following:
1.A list of all activities required to complete the project
2.The duration that each activity will take to complete,
3.The dependencies between the activities and,
4.Logical end points such as milestones or deliverable items.
Using these values, CPM calculates the longest path of planned activities to the
end of the project, and the earliest and latest that each activity can start and finish
without making the project longer.
This determines which activities are "critical" (i.e., on the longest path)

Critical Path Analysis
Nodes: Show the start and finish of a task
1 2
Node numbers showing order of
activities in the left hand semi-circle
of each node.
3
Earliest Start Time (EST)
5
Latest Finish Time (LFT)
A
3
B
5
Arrows
indicate the
order of the
tasks, the
letter above
shows the
order, the
time period
below the
arrow
The Critical Path

Nodes and activities
EST
LFT
Activity
paint wall
1 2
EST
LFTTime
3 hrs
The node shows the
physical start and
finish of an activity
The arrow shows us
the actual task
which is being
undertaken

Constructing the network
1 2
1 Start
the
project
2 The
first job
3 Finish
the job
4 Start the next activities

Building a network
1 2
3
4
5 Complete
tasks 3 &4
6 Start the next
activity once
both 3 & 4 are
complete

The completed diagram
7 Finish the job
1 2
3
4
5 6
Give each node a
number

Adding the information
a
b c
d e
f
1 2
3
4
5 6
Add the activities
and times
24
hrs
3 hrs 7 hrs
3 hrs 2 hrs
3 hrs

The earliest start times
a
b c
d e
f
1 2
3
4
5 6
Add the earliest
start times
0 24
24
hrs
3 hrs 7 hrs
3 hrs 2 hrs
3 hrs
27
27
34 37

The latest finishing times
a
b c
d e
f
1 2
3
4
5 6
Add the latest
finishing times
0 24
24
hrs
3 hrs 7 hrs
3 hrs 2 hrs
3 hrs
27
27
34
37
37
34
32
27
240

The critical path
a
b c
d e
f
1 2
3
4
5 6
0 24
24
hrs
3 hrs 7 hrs
3 hrs 2 hrs
3 hrs
27
27
34 37
3734
32
27
240
*
*
**
Critical
activities are
a, b, c, f.

Early Start(ES) and Early finish(EF):
Suppose you have a list of tasks as shown below

we'll try to find the earliest finish time for each activity.

Mark the Start Time (S) to the left and right of the first activity. Usually, this would be 0.
Now mark the Earliest Start (ES) time of each activity. This is given by the largest number to the right of the
activity's immediate predecessor (i.e. its Earliest Finish time, or EF).If the activity has two predecessors, the one
with the later EF time would give you the ES of the activity.

Activity-on-node diagram showing critical path schedule, along with total float and
critical path drag computations
In this diagram, Activities A, B, C, D, and E comprise the critical or longest
path, while Activities F, G, and H are off the critical path with floats of 15
days, 5 days, and 20 days respectively. Whereas activities that are off the
critical path have float and are therefore not delaying completion of the
project, those on the critical path will usually have critical path drag, i.e.,
they delay project completion.

The drag of a critical path activity can be computed using the following formula:
1.If a critical path activity has nothing in parallel, its drag is equal to its duration.
Thus A and E have drags of 10 days and 20 days respectively.
2.If a critical path activity has another activity in parallel, its drag is equal to
whichever is less: its duration or the total float of the parallel activity with the least
total float. Thus since B and C are both parallel to F (float of 15) and H (float of
20), B has a duration of 20 and drag of 15 (equal to F's float), while C has a
duration of only 5 days and thus drag of only 5. Activity D, with a duration of 10
days, is parallel to G (float of 5) and H (float of 20) and therefore its drag is equal
to 5, the float of G.
These results, including the drag computations, allow managers to prioritize
activities for the effective management of project completion, and to shorten the
planned critical path of a project by pruning critical path activities, by "fast
tracking" (i.e., performing more activities in parallel), and/or by "crashing the
critical path" (i.e., shortening the durations of critical path activities by
adding resources).

Find the Critical Path :
The critical path is the sequence of activities with the longest duration. A delay
in any of these activities will result in a delay for the whole project.

Float Determination
Float is the amount of time an activity can slip(wait) before it causes your project to be delayed. Float is
sometimes referred to as slack.
Figuring out the float :You will start with the activities on the critical path. Each of those activities has a float of
zero. If any of those activities slips, the project will be delayed.
Then you take the next longest path. Subtract it's duration from the duration of the critical path. That's the float
for each of the activities on that path.
If an activity is on two paths, it's float will be based on the longer path that it belongs to.
Using the critical path diagram from the previous section,
Activities 2, 3, and 4 are on the critical path so they have a float
of zero.
The next longest path is Activities 1, 3, and 4. Since Activities 3
and 4 are also on the critical path, their float will remain as zero.
For any remaining activities, in this case Activity 1, the float will
be the duration of the critical path minus the duration of this
path. 14 - 12 = 2. So Activity 1 has a float of 2.
The next longest path is Activities 2 and 5. Activity 2 is on the
critical path so it will have a float of zero. Activity 5 has a float of
14 - 9, which is 5. So as long as Activity 5 doesn't slip more than 5
days, it won't cause a delay to the project.

Early Start & Early Finish Calculation
The Critical Path Method includes a technique called the Forward Pass which is used to determine the
earliest date an activity can start and the earliest date it can finish.
Starting with the critical path, the Early Start (ES) of the first activity is one. The Early Finish (EF) of an activity
is its ES plus its duration minus one. Using our earlier example, Activity 2 is the first activity on the critical
path: ES = 1, EF = 1 + 5 -1 = 5.
You then move to the next activity in the path,
in this case Activity 3. Its ES is the previous
activity's EF + 1. Activity 3 ES = 5 + 1 = 6. Its EF is
calculated the same as before: EF = 6 + 7 - 1 =
12.
If an activity has more than one predecessor, to
calculate its ES you will use the activity with the
latest EF.

Late Start & Late Finish Calculation
The Backward Pass is a Critical Path Method technique you can use to determine the latest
date an activity can start and the latest date it can finish before it delays the project.
You'll start once again with the critical path, but this time you'll begin from the last activity
in the path. The Late Finish (LF) for the last activity in every path is the same as the last
activity's EF in the critical path. The Late Start (LS) is the
LF - duration + 1.
In our example, Activity 4 is the last activity on the critical path. Its LF is the same as its EF,
which is 14. To calculate the LS, subtract its duration from its LF and add one. LS = 14 - 2 + 1
= 13.
You then move on to the next activity in the path. Its LF is determined by subtracting one
from the previous activity's LS. In our example, the next Activity in the critical path is
Activity 3. Its LF is equal to Activity 4 LS - 1. Activity 3 LF = 13 -1 = 12. It's LS is calculated the
same as before by subtracting its duration from the LF and adding one. Activity 3 LS = 12 - 7
+ 1 = 6.
You will continue in this manner moving along each path filling in LF and LS for activities
that don't have it already filled in.

Calculate ES and EF and the critical path

Step – 1 : Calculate the total number of paths and their duration.
The path with longest duration is the critical path. Description of all the paths in
mentioned below.
•First path is Start (S) – A – D – E – End (E’) the duration of this path is 16 weeks
•The second path is S – A – E – G – E’ the duration of which is also equal to 16
weeks
•The third path is S – B – C – E – G – E’ the duration of this path is 22 weeks
•Fourth path is S – B – F – G – E’ the duration of this path is equal to 20 weeks
The longest path in the network above is S-B-C-E-G-E’ with a duration of 22
weeks.
Hence, path S-B-C-E-G-E’ is the critical path of the above schedule network
diagram.

Calculate Early Start and Early Finish of activities on Critical Path:
First Node
There are two conventions for critical path analysis. The convention
used for solving CPM example problem is that the project starts on
day one. Another convention for CPM analysis states that the project
starts on day zero. We will stick to the convention indicated in
PMBOK, which states that, the project starts on day 1. Hence ES of
first activity B on critical path is 1.
•EF = ES + Activity Duration – 1
•EF of Activity B = 1 + 6 – 1 = 6
Node B
•ES = EF of first node + 1 = 6 + 1 = 7
•EF = ES + Activity Duration -1 = 7 + 4 – 1 = 10
Repeat the above step till you reach the last node

Critical path schedules will...
•Help you identify the activities that must be completed on time in order to
complete the whole project on time.
•Show you which tasks can be delayed and for how long without impacting
the overall project schedule.
•Calculate the minimum amount of time it will take to complete the project.
•Tell you the earliest and latest dates each activity can start on in order to
maintain the schedule.
The Critical Path Method has four key elements...
•Critical Path Analysis
•Float Determination
•Early Start & Early Finish Calculation
•Late Start & Late Finish Calculation
The Critical Path Method (CPM) can help you keep your projects on track

Critical path method(cpm)

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