Uploaded by SHSUOnlineTV on 13.07.2011

Let's talk about the critical path method. The critical path method is one
of two ways that you can
or one of two tools that you can use to identify the paths through
your project
The other way is called PERT
Program Evaluation and Review Technique.
the difference between Critical Path and PERT is that critical path uses one
time estimate
whereas PERT uses three time estimates so critical path is
more or less for when you're you're pretty sure about the durations that
the time it’s gonna take to do each task or each activity
whereas PERT is used in a more uncertain situation. You remember our discussion about uncertainty
and you can use these three time estimates to come up with something
called the expected time.
We're gonna start with the critical path method since it is the simplest
We're going to use a method that's a little different than in your book.
We're going to use this key.
This key if you'll notice in the center block that is uh that A
represents Activity
and down here D
represents Duration.
Whereas ES is Early Start. EF is Early Finish. LS is Late Start
and LF - Late Finish.
Over here we're going to have S which is equal to Slack Time.
You’ll notice this block right here where have the diagonal lines. All that is is a block
where you can write the description in of the activity if you choose to do so.
So let’s talk. Let’s get into the details of critical path.
When you're using the critical path method you need three pieces of 0:01:52.329,0:01:56.450 information: Activity, Predecessor, and Duration.
uh... You need to have the activities listed. You need to know which
activities are predecessors to other activities
and then you need to know the time that each duration will take.
In this instance, we're going to use
uh... weeks
as our unit of time.
So using this information, we can draw a Precedence Diagram
and if you look at the Precedence Diagram, you can see all of the paths that
go through
uh... our project and there are many different paths. This means that some
activities can be
done concurrently,
simultaneously uh... some activities though cannot be down that way;
they have to have the previous activity
completed before you can move on and so this
drawing this Precedence Diagram gives you a
pictorial view of what the project should look like.
We can use this diagram to go through and identify our tasks
or I’m sorry our paths.
For instance, we have
paths A-C-F
and -I.
We have path A-D-
H-J. Path A-D-G-
and J
and uh... path
E-H-J-B-F-I. So we have five paths through this project.
We can go through and we can use the information that we had for each one of
these activities
and we can identify what the critical path is.
So what is the critical path by definition?
Well, if you remember in class we talked about the critical path as being
that path
that if you had any delays on it would delay the entire project
that means that there is zero slack time associated
with the critical path.
Right now all the information we wanna know is which one is the critical path?
we can go through and we can add up each one of the activity times
and we can see that for a first path is eighteen weeks, our second nineteen,
third eighteen, fourth twenty-one, and fifth is fourteen.
So what does that mean to ask? Well what that means is that our critical path is
because it takes twenty-one weeks. That’s the longest duration of any path in
our project
and what that means is that these activities are not going to have any
slack time on them
and that is the path that we're going to monitor through our project.
So we're going to use this and use my boxes now
and uh
I've drawn out the network
and this is what it would look like with the boxes so the first thing that we’re
going to do is we're going to do something called a backwards
Excuse me, we're going to do a forward
(Dr. Z chuckles) uh... pass.
That means that we're going to move from left to right. In case y’all don’t remember
when you were in class I told you I was dyslexic
remember that. Alright
we're going to start with activity A
and if you remember a starting activity begins at time zero.
So our early start for activity A is going to be zero, the same thing
for activity B because if you remember
on our information activity B had no predecessors.
Okay so now we want to calculate what the early finish time is going to be.
To calculate early finish
we're going to take early start
and add
the duration
so zero plus five,
zero plus four
all right so we’ve we’ve done the first
to tasks.
Now we're looking at this diagram and we see out of activity A that we have
three arrows.
We don’t have to make any choice. We automatically know that the the early
start for each one of those activities is going to be five.
Again we're going to calculate the early finish
five-plus three is eight, five plus four is nine, five plus six is eleven.
Well now we get into a little bit of a dilemma because we see all of these arrows
going all different directions so we sorted out okay
for activity F
right here
we have two activities that feed into it
C and B.
We have to make a choice. You see that we have
an early finish of eight for activity C and an early finish of four
for activity B.
Remember by definition
the the path
all of the activities have to be complete
all the predecessor activities have to be complete
before the new activity can begin
that means that we have to choose the highest of the two.
So we’re going to choose eight for our early start for activity F.
For activity G,
we only have one predecessor which is D so we don't have to make any choice.
So for activity
G we're going to have nine as our early start.
For activity H,
we have activity
and activity E
that feed into H.
So we have to look at those early finish times and we have to determine which one
is going to be our early start for activity H.
uh... activity D has a
uh... early finish of nine and activity E has an early finish of eleven.
We're going to choose the higher of the two
which is going to be
eleven plus six is seventeen,
nine plus five is fourteen,
and eight plus four is twelve.
So now we need to come over here to activity
activity I.
Activity I we have no choice we know our early start is twelve.
Twelve plus six is eighteen.
For activity j, we have to choose between the early
finish for activity
G and activity H.
H has the larger number so we're going to select a larger number
for our early start for J.
So seventeen plus four is twenty-one.
If you'll remember when we looked at are uh... each path individually
the path that we selected
had a uh... duration at twenty-one weeks for the critical path.
Well that doesn't really give us a whole lot of information. We still don't have any
more information than what we had
when we just went through it and identified all the paths and added up the
slack time.
So, what we to do now is something called the backwards pass.
When we’re beginning our backwards pass we’re gonna start with the late finish.
Now in order to calculate
our late start, we're going to take our late
and subtract are duration,
but we have to get started on this; we have two ending activities and
I know when you were in class you probably never saw this because all of
the ones that we did
had just one ending activity.
When you have to ending activities, you have to select between the two times so
for activity J, which is an ending activity, it is twenty-one weeks and for
activity I
it is eighteen weeks.
Well for both of these activities, we’re going to going to use twenty-one to
start our backwards pass because remember
twenty-one weeks
equals the duration of the project.
Everything has to be completed in twenty-one weeks.
now what we're going to do is we're going to calculate
the late start for activity J;
twenty-one minus four
is seventeen.
For I,
minus six
is fifteen.
So we're going to take seventeen and we're going to transfer that into
activity H and G
as the late finish
and we're going to transfer fifteen
for activity F as the late finish.
Seventeen minus six is eleven.
Seventeen minus five is twelve.
Fifteen minus for is eleven.
So now we've got to be a little bit careful 'cause we're back in that
situation where we have multiple arrows
uh... coming in and out of activities.
So let's start with activity E.
Activity E
we have
You see where it comes backwards here.
So we're going to take
eleven and transfer it down here. We don't have to make a decision; we know
it's gonna be eleven.
Eleven minus six is five.
For activity D
well now we've got to make a decision because we have
two arrows coming backwards.
Now remember
this is a backwards pass that means that our rules have been reversed
so at this point we're going to look at those
late start times and we're going to choose the lowest
of the two.
So in this case, we're going to choose
eleven. 0:11:47.170,0:11:51.760 Eleven minus for is seven.
So for activity C,
we have one activity
which is F.
You see the arrow right here,
so we're going to transfer eleven up here for the late finish.
Eleven minus three is eight. Okay.
So for activity B
we don't have to make a decision because the only arrow that we have
is the arrow leading to activity F
so we know that that is going to be eleven.
Eleven minus four is seven.
For activity A; however, we have to make a decision.
We see that we have activity C, D, and E
that and uh... are
come after activity A
so we need to choose the lowest
of the
late start times
for our late start for activity A
and that happens to be five.
minus five is zero.
We still don't have a lot of information. We can look at this and we probably
could off the top of our heads identify the critical path because we
know by definition that it’s gonna be the activities that have zero slack,
but now that's what this little box is for right here
used to calculate slack
and to calculate slack
we can do it one of two ways.
We can calculate slack
looking at the late finish
the early finish
we can look at the
late start minus
the early start.
Either formula you use
you should come up with the same answer.
This is a really good
check point for you
uh... because you know that if you've got something off where you don't come
up with the same slack time using either of these formulas
then you've done something wrong
in in your diagram.
So let's go through and calculate slack time.
For activity A,
we're going to use uh...
late start minus early start. So zero minus zero, it's going to be zero.
Now let's check out here
five minus five
is zero as well, so we know were correct.
For activity B, seven minus zero is going to be seven
and we can check here
eleven minus four is seven.
We're going to go through and calculate the slack for each one of these activities.
Now we can be easily identify the critical path
and now we know which activities have slack time and which activities don’t.
If you’ll think back, we identified the critical path
path previously, we said that it was A-E-H and J.
If you look at A-E-H and J, you see that each one of those activities have
zero slack time.
The rest of them
all have slack.
What does slack mean?
Well that means that for activity B,
we can actually wait seven weeks before we start that activity
and so we've got some leeway in there.
What if we had valuable resources allocated to activity B?
Well, now for seven weeks we can free up those resources; we can use them in other
parts of this project or we could use them on another project
uh... this gives us a way to analyze our project and start trying to figure
out how we can allocate those resources
and it also helps us in the budgeting process that we've talked about
So that's the critical path method.
uh... As we we started out talking I told you there was a second method it’s
PERT. Program Evaluation and Review Technique.
PERT uses three time estimates.
It uses a time estimate that is called A, that is the Optimistic Time.
The optimistic time
that's when you know how how
in life we think uh...
people as having these sunny dispositions everything goes right
there's never a down day and
here we look at them like they’re crazy. Well, that's what optimistic time is.
You’re thinking nothing in the world is going to go wrong, everything's gonna go
right and
this is the best time that we can complete that task in, okay.
Not really the way to look at it,
but we're going to soften that some with our formula in just a few moments.
The letter B
represents the Pessimistic Time.
Pessimistic time - that's when everything is going to go wrong.
Nothing in the world goes right.
This task
this is the longest time that we can possibly think of that this task
would take
given the fact that everything is going to go wrong
and then we have time M.
You know in life we know that it's not always gonna be the very best
and it's not always going to going to be the very worst.
It's going to be somewhere in the middle and that's what M represents; that's
the most likely time.
So we have those three time estimates that we have to deal with
and so when we look
at how we're going to deal with those, we need to have some information, obviously.
We have to know what the activities are
and what
the uh
optimistic time is, the pessimistic time and the most likely. Now you'll notice
that this
chart is laid out differently than I presented the time estimates and that's
I’ve laid out the chart and most
books will lay out the chart
the way that you're going to use the formula
okay so
uh... we have all of our time estimates here so let's just calculate a couple of
them real quick okay.
We have
our formula for expected time
You’ll notice and we have a column here, right here,
for expected time.
Well, our formula is
optimistic time plus
four times
the most likely time. Now why would most likely time
have a way to four?
Well, that's because it is the most likely to occur
so we're going to weight that time more than the other two time estimates.
You'll see that the pessimistic time only has a weight of one
as does the optimistic time
so we're going to add all of those up
and then we're going to divide by six. Why six? Because we have six weights.
Remember that we have an unseen one here
and an unseen one here so one plus four plus one
six. It's always going to be six. It's constant. It will never change.
So for our activity A, we can substitute in
our time estimates
uh... we have a…I’m sorry an optimistic time of one plus four times
the most likely time which was two plus
the pessimistic time of three
and we divide - that adds up to twelve – and we divide that by six and we
come up with two so now for our
chart we can come back here
and we can simply fill in two.
Let's do one more.
is the uh... optimistic time plus four times the most likely time of three for
activity B
plus four which is the pessimistic time
that's going to add up to eighteen we're going to divide that by six and so
expected time for activity B is three.
Everybody understand that? I'm sure you do. I know you don't want me to go
through each and every one
so let's just fill in our chart.
So now we have the expected time.
We need some other information that we want to know what the variance of each
activity is going to be.
We have a formula for the variants we can use.
The formula is the pessimistic time minus the optimistic time
divided by six and then we're going to square that.
So if we uh...
just do activities A and B, we can see that
the pessimistic time of 3 minues the optimistic time of one
divided by six, so two divided by six squared is going to equal
point one one.
uh... For activity B,
the pessimistic time of four
so two divided by six
square it
and we're going to again have point one one.
So we're just going to fill in
our chart
okay so now we’ve got
uh... the expected time
we've got the variances of the activities
and so now we're gonna make some basic assumptions
about our
project. We're going to assume that our critical path
for this project is A-
and H.
What we want to know is we want to know what the project variance is.
Well, I know y’all didn’t think you were gonna have stats again, well
this is terrible but you’re gonna have them, but it's not as bad as it was when you were
in statistics.
What we're going to do is we’re going to calculate our project variance. Project
variance is denoted
as the following
and all it is it is the sum
the variances
the critical path.
So we can go back to our chart now and we can figure out what that is.
It's point one one plus point one
one plus
one plus
one point seven eight plus point one one
that's going to give us a total of three point one one
So we know that our project variance is
two point one one,
or I’m sorry three point one one.
We need another bit of information. We need to know what the standard deviation is
so in order to get the standard deviation we're going to take the square
root of the project variance
and that is going to be
one point
seven six.
So, one point seven six, Dr. Z what does that mean?
Well, what that means is that our project,
the time, the direction of our project
is going to be plus or minus
one point seven six weeks.
Now that's a piece of valuable information isn't it.
We can do a lot with that information.
We know
we could be in trouble.
It depends on what this project is.
In this case, this project is a compliance project.
It is a project where the company has to put in an
uh... air filtration system; otherwise, the E.P.A._ is going to shut them down.
They have to do it
within sixteen weeks
so now that plus or minus one point seven six weeks becomes a whole
different picture doesn't it?
Because if they are over
by one point seven six weeks their going to shut their company down.
They are not going to be able to do business, they're going to lose money
until the project is complete
and then you've got to get people out there to inspect it so it could be far
longer than one point seven six weeks if they're going to be shut down, so we want
to avoid that.
Well, the first question out of your boss’s mouth is now is going to be
what is the likelihood that we're going to be finished by this time
and most of the time we give them as SWAG answer. I'm hoping everybody knows what's
SWAG stands for.
Okay, so I'm not sure I should say it and let it be recorded.
(Dr. Z chuckles) So look it up on the internet
and uh...
uh... we're going to figure out what the probability of this happening is.
You know we’re… we have uh... assumed this and we're going to assume one other
bit of information and that is that the project duration
is fifteen weeks,
So, we have all of this information so now we want to know what the probability
of finishing this project is
you know have having it done by that sixteenth week.
Well, we need something called a Z-score.
You remember those from
Well, it's not as difficult either
as it was in statistics.
What we're going to do is we're going to
use a very simple formula:
Z is equal to
due date
minus expected
date divided by
the uh
project standard deviation.
So we said we had a due date of sixteen weeks.
Our project direction,
we expect to have it done in fifteen weeks and we know that a project
standard deviation is one point seven six weeks.
So when we calculate this we come up with a Z-score
of point five seven.
Now what does that mean?
Well, it doesn't mean anything until you use a normal distribution table.
On a normal distribution table,
you can come and you can find
the five
the point five on the side on the left hand side
and the point zero seven.
Where they meet
is at point
seven one five seven.
What that means to you is that there's a seventy one point
five seven percent probability
that you will finish this project by the sixteenth week.
Are you worried?
You should be. Your boss should be worried
because that also means that you have over twenty eight percent probability of not
being finished on time.
So, pretty scary stuff,
but the point that I would like to make is now rather than giving your boss a
SWAG answer, you know,
and I’m guilty of that. The boss will come and say, “Well, what's the likelihood that we're
going to be finished with
uh... the information for that new class you're putting on line by
August and I'll say
oh it’s
ninety nine percent.
Well, now I don't just have to guess,
I can go back and I can calculate that
and I can tell my boss based on the numbers
I can tell you that
there is less than a seventy two percent probability that we will be finished on
Great stuff! (The End)