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Want to learn everything about the Critical Path Method (CPM)? This video breaks down key terminologies, teaches you how to draw a network diagram, and walks you through two popular methods to calculate the critical path—the Plus-Minus-One Method and the Zero-Day Method while addressing the confusion for day counts using both methods. If you’re preparing for the PMP exam or managing complex projects, mastering CPM will help you optimize scheduling and meet deadlines with confidence.
Why Watch This Video?
CPM is an essential project scheduling technique that helps managers identify task dependencies, optimize timelines, and manage float efficiently. Whether you’re studying for the PMP exam or managing real-world projects, this step-by-step guide will ensure you fully understand the critical path concept.
In This Video:
- Key Terminologies: Precedence Diagramming Method (PDM), dependencies, float, lead, lag, and time-boxing
- Drawing a Network Diagram: Step-by-step guide using PDM to simplify the process
- Understanding the Critical Path: Identifying the longest sequence of dependent activities
- Float Calculation: Difference between Total Float and Free Float
- Two Critical Path Calculation Methods (Plus-Minus-One Method, Zero-Day Method)
- Forward and Backward Pass Calculations: Determining early start, early finish, late start, and late finish
Chapters
0:00 Intro
0:36 Term: Network Diagram
1:05 Term: Four Dependencies
3:05 Term: Critical Path
4:00 Term: Float
5:22 Term: Lead and Lag
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0:00
if you want to learn everything about
0:01
the critical path method this is the
0:03
video for you first we will cover the
0:06
key terminologies that you need to
0:08
master then we will draw a network
0:11
diagram together and show you a trick to
0:13
make the drawing easier finally we will
0:16
calculate the critical path using two
0:18
popular approaches the plus minus one
0:20
method and zero day method or you can
0:23
use the video timeline and skip to the
0:25
most relevant section by the end of the
0:28
video you will have a solid
0:30
understanding of the critical path
0:32
method if this sounds good to you let's
0:34
get started with the
0:36
terminologies first what is a network
0:39
diagram a network diagram is a visual
0:41
representation of project activities and
0:43
their dependencies it helps project
0:46
managers identify task sequences
0:48
overlaps and potential
0:50
delays precedence diagramming method is
0:53
the most commonly used method for
0:54
drawing the network diagram the
0:56
activities are represented as nodes or
0:58
boxes and arrows show their dependencies
1:01
we will go over drawing a network
1:03
diagram together
1:04
shortly next let's go over the four
1:07
types of dependencies dependencies
1:09
Define how tasks relate to each
1:11
other finish to start FS this is the
1:15
most common dependency which means task
1:18
one has to finish before task two can
1:20
start for example the student needs to
1:24
finish and hand in the exam before the
1:26
teacher can start grading it another
1:29
example is is that the workers have to
1:31
finish building the wall before the wall
1:33
can be
1:34
painted next start to start SS this
1:37
means task 2 cannot start until task one
1:40
starts but doesn't have to wait until
1:42
task one
1:43
finishes for example in a classroom the
1:47
professor has to begin the lecture
1:48
before students can start taking
1:50
notes another example is that writing
1:53
code has to start before starting code
1:55
review next finish to finish FF in this
1:59
dependency task two cannot finish until
2:01
task one
2:03
finishes for example a professor is
2:06
grading final exams and preparing
2:08
students report cards the professor has
2:11
to finish grading the final exams for
2:13
all students before finishing all the
2:15
students report
2:16
cards here is another example let's say
2:19
a company is assembling and inspecting
2:22
electronic devices before shipment in
2:25
this case all the assembly has to be
2:27
finished before the Quality Inspection
2:29
can be completed
2:31
finally start to finish SF this is the
2:34
least common dependency in this
2:36
dependency task two cannot finish until
2:39
task one
2:40
starts for example a university is
2:44
transitioning from an old library book
2:46
checkout system to a new digital system
2:48
in this case the new digital system has
2:50
to start functioning before shutting
2:52
down and finishing the Old
2:54
system another example is at a 24/7
2:57
security desk the night security guard
3:00
has to arrive and start his shift before
3:02
the morning security guard finishes
3:05
shift next let's talk about the critical
3:08
path method the critical path is the
3:11
longest sequence of dependent activities
3:13
that must be finished on time to
3:15
complete the project this path
3:18
represents the shortest amount of time
3:19
needed to finish the work tasks on this
3:23
path have zero floats meaning any delay
3:25
on tasks in the critical path will
3:27
impact the Project's end date
3:30
a time box is used to represent an
3:32
activity at the center is the name of
3:35
the activity on the top are the early
3:38
start duration and early finish of the
3:40
activity at the bottom are the late
3:42
start total float and late finish of the
3:45
activity the start and finish represent
3:48
how early or late the activity can start
3:49
and finish those dates are determined
3:52
using the forward and backward path
3:54
which we will cover later in the video
3:56
the duration is how long the activity
3:58
takes to complete
4:00
next let's talk about float float also
4:04
known as slack is a general term
4:06
referring to the time at task can be
4:08
delayed without affecting the project
4:10
schedule there are two types of
4:13
floats total float is the maximum amount
4:16
of time a task can be delayed without
4:18
impacting the overall project completion
4:20
date this is the float represented in
4:22
the time box the formula to calculate
4:25
total float is total float equals late
4:29
start LS minus early start
4:32
ES or you can also calculate using total
4:36
float equals late finish LF minus early
4:39
finish
4:40
EF next let's talk about free float free
4:44
float is the delay allowed before it
4:46
affects the next dependent task the
4:49
formula for calculating free float is
4:52
free float equals the earliest start of
4:54
the next task minus the earliest finish
4:56
of the current
4:57
task again the key difference is that
5:00
total float impacts the project end date
5:02
whereas the free float impacts the next
5:05
dependent task float is essential for
5:07
scheduling flexibility and helps project
5:09
managers manage resources
5:11
efficiently while the total float and
5:14
free float for an activity are usually
5:16
the same they can be different which I
5:18
will illustrate as we go through a
5:19
critical path example later in the
5:22
video before we wrap up this section
5:25
another two terminologies that you will
5:27
hear often are the lead and lag let's
5:29
quickly cover them as they are quite
5:30
simple to understand lead allows the
5:33
successor or next activity to start
5:35
before the predecessor is fully complete
5:38
for example software testing starts 2
5:41
days before development is fully
5:43
finished this is a finished to start
5:45
relationship with a 2-day lead
5:48
represented by using FS minus 2 days
5:51
lead can offer useful insights if the
5:53
project manager needs to FastTrack the
5:55
project and compress the
5:57
schedule next lag is a delay between the
6:00
finish of one activity and the start of
6:02
the next
6:03
activity for example concrete pouring is
6:06
completed but a 3-day lag is required
6:09
for it to dry before construction can
6:11
continue this is also a finish to start
6:14
relationship but with 3day lag
6:16
represented using FS plus 3
6:19
days okay that wraps up the terminology
6:22
section we can now get into the fun part
6:25
of creating a network diagram using the
6:27
precedent diagramming method typically
6:30
the question will provide a table of
6:31
activities with predecessors and
6:34
durations here is a little trick that
6:36
will make it easier to draw the network
6:38
diagram for most people going from start
6:41
to finish is easier and comes more
6:43
naturally so instead of reading from
6:45
column 1 to column two you may find it
6:48
easier to read column two and then
6:51
column one going from the predecessor to
6:53
successor let's give it a try a has no
6:57
predecessor so let's write a
7:00
a is the predecessor of B and C so let's
7:02
draw arrows from A to B and C then B
7:06
goes to d c goes to both e and f d and e
7:12
both go to
7:13
g f and g go to
7:15
H there you go we just completed the
7:18
network diagram is that easier you can
7:22
also pause the video here and try the
7:24
traditional approach going from column 1
7:26
to column 2 to determine which approach
7:28
comes more naturally
7:30
if all you have to do is to figure out
7:32
the critical path and you have a simple
7:34
Network diagram you can figure it out by
7:37
adding the durations on the path the
7:39
path with the longest duration is the
7:41
critical path I am going to write the
7:44
duration on the network diagram we just
7:46
created let's calculate the duration of
7:49
each path we have three
7:51
paths the duration for the path a b d g
7:55
h = 3 + 4 + 8 + 1 + 2 =
8:01
18 the duration for the path AC G = 3 +
8:07
5 + 5 + 1 + 2 =
8:11
16 the duration for the path AC FH = 3 +
8:16
5 + 4 + 2 =
8:19
14 in our diagram a b d g h has the
8:23
longest duration and therefore it is the
8:25
critical path in other words this
8:28
project will need at least 18 days to
8:30
complete without any
8:32
delays let's move on to our next section
8:35
determine the critical path using the
8:37
time box and Float there are two popular
8:39
methods and we will go over both methods
8:42
and discuss which is better suited given
8:43
your situation for lack of better names
8:47
I will call the first approach the plus
8:48
minus one method and the second approach
8:51
the zero day method the plusus one
8:54
critical path method is more complicated
8:57
this is the method commonly taught in
8:59
the academic environment including the
9:01
project management Institute this
9:03
approach offers a better view of the
9:05
dates when a task finishes and the next
9:07
task starts use this method if you have
9:10
to show your work and the exact start
9:12
and end dates are important to save time
9:16
let me draw the network diagram again
9:18
with durations and activities in the
9:20
time
9:21
box what confuses many students is why
9:23
we need to plus and minus one when
9:25
counting the days instead of trying to
9:27
remember the formula let's think
9:29
logically and it will start to make
9:31
sense to make this Visual and easy we
9:34
are going back to our elementary school
9:36
days and using our hands to count the
9:39
days let's take a look at activity a
9:42
activity a takes 3 days to finish so we
9:45
are going to start working on day one
9:48
continue on day two and finish the work
9:50
at the end of day three therefore we
9:52
write down day one as the early start
9:55
and day three is the early finish since
9:57
it's already the end of day on day 3 the
10:00
next activities b and c will start on
10:02
day
10:03
four to get the early finish for
10:06
activity a by doing the math will be one
10:08
early start + 3 duration - 1 =
10:13
3 Let's do activity B next activity B
10:17
will start on day four and take four
10:19
days to finish so it will take day four
10:22
5 6 and 7 to finish the work so the
10:24
early finish is 7 and the next activity
10:27
begins on day 8 once you understand how
10:30
the days are accounted for the math will
10:33
make a lot of sense we are going to move
10:35
a bit more quickly by doing math from
10:37
this point for the forward
10:39
path the early finish for activity D is
10:43
8 + 8 - 1 =
10:45
15 before we can determine the dates for
10:48
activity G we will need to know the
10:51
early finish for activity E2 so we need
10:54
to go back and work on activity
10:57
C for activity C the early finish is 4 +
11:02
5 - 1 = 8 the next activities andf will
11:06
start on Day
11:07
N the early finish for activity e is
11:10
equal to 9 + 5 - 1 =
11:13
13 the early finish for activity f is
11:17
equal to 9 + 4 - 1 =
11:20
12 now we can come back to activity G
11:23
since both activities d and e have to
11:25
finish before working on activity G we
11:28
must pick the L latest early finish date
11:31
which is 15 from activity D so activity
11:34
G will start on day
11:36
16 since activity G only takes one day
11:39
to finish it will finish at the end of
11:41
the day on day
11:42
16 activity H will start on day 17 by
11:45
following the same logic from taking the
11:48
early finish from activity G and adding
11:50
one the early finish for activity H is
11:53
equal to 17 + 2 - 1 =
11:57
18 now that we have completed the
11:59
forward path we will work on the
12:01
backward path from activity
12:03
H first the late finish is 18 which is
12:06
carried over from the early finish
12:09
activity H takes 2 days to finish so we
12:11
need to count backward and it will take
12:13
day 18 and day 17 to do the work so the
12:16
late start is 17 or you can do the math
12:19
by 18 - 2 + 1 =
12:23
17 this means the late finish for
12:25
activities gnf will be day
12:28
16 at activity G only takes one day to
12:30
finish so we are still in day 16 for the
12:33
late start or you can do the math late
12:35
start is equal to 16 - 1 + 1 which is
12:39
16 for activity F the late start is 16 -
12:43
4 + 1 =
12:46
13 activity e has 15 as the late finish
12:50
the late start is 15 - 5 + 1 equal
12:54
11 activity D also has 15 as the late
12:57
finish the late start is 15 - 8 + 1 =
13:02
8 let's think about what the late finish
13:05
for activity C should be is it the
13:08
smaller number 11 from activity e or the
13:11
higher number 13 from activity F in this
13:14
case we need to pick the smaller number
13:16
going backward so activity C has to
13:19
finish on day 10 as the late finish so
13:21
that activity e can have a late start of
13:24
11 this means the late start for
13:26
activity C is 10 - 5 + 1 =
13:30
6 activity B has seven as the late
13:33
finish the late start is 7 - 4 + 1
13:37
equals 4 finally activity a will take
13:40
the smaller late start from activity B
13:43
so the late finish is three for activity
13:45
a the late start is 3 - 3 + 1 = 1 now
13:50
that we have completed the backward path
13:52
we can fill in the total float for each
13:54
of the
13:55
activities if you remember there are two
13:57
ways to calculate the total float you
14:00
can get total Float by either doing late
14:02
start minus early start or late finish
14:05
minus early
14:06
finish you should get the same result if
14:10
not this means you didn't put in the
14:11
dates correctly somewhere and it is a
14:14
good sanity check so the total float for
14:17
activity a is 1 - 1 = 0 the total float
14:22
for activity B is 4 - 4 = 0 the total
14:27
float for activity C is 6 - 4 = 2 the
14:31
total float for activity D is 8 - 8 = 0
14:36
the total float for activity e is 11 - 9
14:39
= 2 the total float for activity f is 13
14:44
- 9 =
14:46
4 the total float for activity G is 16 -
14:50
16 = 0 the total float for activity H is
14:54
17 -7 = 0 the critical path path is the
14:59
path that has zero total float so that
15:02
will be the path with activity AB b d g
15:05
h now let's talk about free float
15:09
remember free float is the delay allowed
15:11
before it affects the next dependent
15:13
task you calculate by taking the
15:15
earliest start of the next activity
15:17
minus the earliest finish of the current
15:20
activity let's calculate the free float
15:23
for activity a together the earliest
15:25
start of the next activities from B and
15:27
C is four and the earliest finish of the
15:30
current activity a is three keep in mind
15:33
that we also need to adjust the date by
15:35
one therefore the free float for
15:38
activity a is 4 - 3 - 1 = 0 the free
15:43
float for activity B is 8 - 7 - 1 = to 0
15:48
the free float for activity C is 9 - 8 -
15:52
1 = to zero the free float for activity
15:56
D is 16 - 15 - 1 equal to 0 the free
16:01
float for activity e is 16 -3 - 1 = to 2
16:07
the free float for activity f is 17 - 12
16:10
- 1 = to 4 the free float for activity G
16:14
is 17 - 16 - 1 equal
16:18
to0 there is no activity after activity
16:21
H so activity H has no free float or
16:24
free float is effectively
16:26
zero you can see total float and free
16:29
float are the same most of the time
16:31
except for activity C where it has two
16:34
for total float but zero for free float
16:38
if activity C is delayed by one day it
16:40
will impact the early start date for
16:42
activity andf although the project
16:45
completion date is not
16:47
impacted here is another question let's
16:50
go back and take a look at activity C
16:52
and which both have two total floats
16:55
does this mean we can slack off 2 days
16:57
or 4 days in total without imp acting
16:59
the project timeline if you want pause
17:01
the video here and think about it let's
17:04
say Activity C was delayed for 2 days so
17:07
the duration is 7 instead of 5 the early
17:10
finish will change from 8 to 10 and the
17:13
late start becomes 10 - 7 - 1 equal to 4
17:17
so activity C has zero total
17:19
float let's look at activity e now the
17:23
early start will be 11 instead of 9 and
17:26
the early finish becomes 11 + 5 5 - 1
17:29
equal to 15 you can see that activity e
17:33
also has zero
17:34
float as you can see the path a c e g h
17:38
only has room for two days to slack off
17:40
not four and now you have two critical
17:44
paths activity F will also be impacted
17:47
and cut the total float from 4 days to 2
17:49
days this wraps up everything I want to
17:52
cover for the plus minus1 critical path
17:54
method next I will go over the zero day
17:57
method this approach is easier because
18:00
you do not need to plus or minus a day
18:02
when calculating the start and end date
18:05
using the forward and backward path you
18:07
can get the same result for the critical
18:09
path and Float values with less effort
18:12
let's take a minute to fully understand
18:14
how to count the dates using this
18:16
approach so the math will come naturally
18:18
and make
18:19
sense remember in the earlier plusus one
18:22
approach we assumed all tasks finish at
18:25
the end of the day and the next task
18:27
starts in the next morning
18:29
however what happens if the task usually
18:31
finishes by noon and the next task
18:33
usually begins in the afternoon of the
18:35
same day in this case zero day method
18:39
may represent the dates better to begin
18:42
let me draw the time box again with all
18:44
the durations here is a timeline
18:47
starting from zero using this approach
18:49
you count the days when you go from one
18:51
day to the next to keep it simple let's
18:55
assume that all activities finish at
18:57
noon and the next activity starts in the
19:00
afternoon of the same day let's use
19:03
activity a as an
19:05
example activity a takes 3 days to
19:08
finish activity a starts at noon on Day
19:11
Zero continues to noon on day one and
19:14
this counts as one day of work between
19:16
noon on day one and day two counts is
19:18
the second day and the noon between day
19:21
two and day three counts is the third
19:23
day so activity a starts on Day Zero and
19:27
finishes on day three as the early
19:29
finish using math it is simply 0 + 3 = 3
19:34
at this point you may wonder do I have
19:36
to start the timeline from Day Zero or
19:38
can I start from day one you can but
19:41
starting from day Zero has two benefits
19:43
first it's easier and less confusing
19:46
second the dates for early finish and
19:48
late finish for the activities will
19:49
match those using the plus minus one
19:52
approach let's get back and continue the
19:54
forward
19:55
path activities b and c will start from
19:58
the tail end of day three as their early
20:01
start activity B takes 4 days to finish
20:04
so it will start on day three and finish
20:06
during day s to calculate the early
20:09
finish for activity B is simply 3 + 4 =
20:13
7 as you can see it's a simple math
20:15
addition without plus and minus between
20:18
activities let's move forward a bit more
20:21
quickly early finish for activity C is 3
20:25
+ 5 = 8 early finish for activity D is 7
20:30
+ 8 =
20:31
15 early finish for activity e is 8 + 5
20:35
=
20:36
13 early finish for activity f is 8 + 4
20:41
=
20:42
12 activity G needs to take the higher
20:45
early finish from activity D so it is 15
20:48
+ 1 =
20:50
16 activity H needs to take the higher
20:53
early finish from activity G so it is 16
20:56
+ 2 = 18
20:59
doing the backward path is easy with
21:01
simple subtraction starting from
21:03
activity
21:04
H first let's carry over 18 the early
21:08
finish to late finish the late start is
21:11
18 - 2 =
21:13
16 then copy 16 to the late finish for
21:17
activities G and F the late start for
21:20
activity G is 16 - 1 =
21:23
15 the late start for activity f is 16 -
21:27
4 =
21:29
12 the late start for activity e is 15 -
21:33
5 = 10 the late start for activity D is
21:37
15 - 8 = 7 for activity C the late
21:42
finish is the smaller value from
21:44
activity e which is 10 so the late start
21:47
for activity C is 10 - 5 = 5 the late
21:52
start for activity b is 7 - 4 = 3 for
21:57
activity a the late finish is the
21:59
smaller value from activity B so the
22:02
late start for activity a is 3 - 3 =
22:06
0 finally let's fill in the total float
22:09
for each
22:10
activity again you can calculate total
22:13
Float by doing late start minus early
22:15
start or late finish minus early
22:18
finish the total float for activity a is
22:21
0 - 0 =
22:23
0 activity B is 3 - 3 = 0 activity C is
22:29
5 - 3 = 2 activity D is 7 - 7 = 0
22:35
activity e is 10 - 8 = 2 activity f is
22:39
12 - 8 = 4 activity G is 15 - 15 equal 0
22:45
activity H is 16 - 16 = 0 to calculate
22:51
the free float you can simply take the
22:53
earliest start of the next activity
22:55
minus the earliest finish of the current
22:57
activity with without making minus 1 day
23:00
adjustments so the free float for
23:02
activity a is 3 - 3 = 0 the free float
23:07
for activity b is 7 - 7 = 0 activity C
23:12
is 8 - 8 = 0 activity D is 15 - 15 = 0
23:18
activity e is 15 - 13 = 2 activity f is
23:23
16 - 12 = 4 activity G is 16 - 16 =
23:29
zero activity H has no free float or
23:32
effectively zero since this is the last
23:34
activity as you can see you get the same
23:37
result for total float and free float
23:39
whether you use the plus minus one or
23:41
zero day critical path method we went
23:44
over the zero day critical path method
23:47
quickly since it's simpler but feel free
23:49
to pause rewatch or leave a comment if
23:52
you have any
23:53
questions this wraps up our
23:55
comprehensive coverage of the critical
23:57
path method we went over all the
24:00
essential terminologies drew a network
24:02
diagram using the Precedence diagramming
24:05
method and covered two popular
24:07
approaches to the critical path method
24:10
hopefully this video gives you
24:11
confidence and a clear understanding of
24:13
the critical path
24:14
method if you found this video helpful
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in helping you understand the critical
24:18
path method please give a thumb up your
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support is greatly
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appreciated also don't forget to
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insights for even more res ources check
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aspirin. if you have any questions
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please leave a comment below thanks for
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watching and I'll see you in the next
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