# Network Diagram for the PMP Exam

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Please click here to watch Cornelius Fichtner, PMP explain a number of PMP exam sample questions...

## Video Transcript

Hello and welcome to the Project Management Prepcast where we put you on the critical path to PMP exam success. I'm your instructor, Cornelius Fichtner. In this lesson, we cover the Network Diagram. We'll explain what it is and why it is so important for your project. We also explain the concept of the Critical Path and show you how to determine what it is. We discuss calculations like the forward pass and the backward pass as well as the early start, early finish, late start, late finish, and the float on your project. Let's get started.

Here are once again all the processes of project time management that you'll find in the PMBOK Guide and which we covered in previous lessons. The lesson right now focuses on the Network Diagram which is obviously not a process but a concept that you need to understand. The Project Schedule Network Diagram as the PMBOK Guide calls it officially, is first created as an output of sequence activities and then used as an input to develop schedule. In develop schedule, we then apply the Critical Path Method to the Network Diagram so that we can figure out when activities begin, when they end and how long our project will take. So for a quick review, the Critical Path method is a method that is used to estimating the minimum project duration and determine the amount of scheduling flexibility that we have on the logical network path within our schedule model. It can be easy when discussing the Critical Path method, to feel like you're trapped in a box, with the box being obviously our schedule. Early and late start and finish dates are calculated by means of either the forward pass or the backward pass. Your goal in using the Critical Path method is to find the longest path on your project schedule which at the same time is going to be the minimum project duration. You will do this with a forward pass which means that you will work your way forward through the schedule and calculate your early start dates and your early finish dates.

As a simple example, if you have three activities where activity A is 10 days long, activity B is five days long and activity C is three days long, then you can immediately see, ah, this is an 18-day long project. And you can also see that activity A starts on day 1 and because it's 10 days long, that means it ends on day 10. That again means B starts on the next day. B starts on day 11, it's five days long, it ends on day 15. And therefore, C starts on day 16, it's 3 days long and ends on day 18. But this is just a simple example. If you have hundreds of activities, it can get really complex because you will have paths that departed and other paths that come back into your main path. And once you have reached the end of your schedule, you are done the forward pass and you have determined the early and late start dates of all your activities. And now you're going to do the backward pass because you also want to determine the late start and late finish dates of all your activities. This forward pass and backward pass is an exercise in endurance, addition, and subtraction as well as being detail-oriented. Having project management software really makes this task easy. But on the PMP exam, you will not have software. You'll have a piece of paper and a pen and you must know how to apply the Critical Path method. In many sample tests, you will see a simple Network Diagram that will show maybe five to 10 activities and you will be ask to calculate the Critical Path by applying the Critical Path method.

Generally speaking, there are two types of Program Network Diagrams - ADM which stands for Arrow Diagramming Method and PDM which stands for Precedence Diagramming Method. The difference is quite simple. In a PDM diagram, Precedence Diagramming Method, your activities are displayed as boxes, or in this case here, circles, and these are connected with arrows. You must know this one for the PMP exam. In an ADM, that is the Arrow Diagramming Method example, your activities are arrows and the boxes or circles are just dummies. You can completely ignore the second one there, the ADM, on the PMP exam. So we will not mention it again here, only PDM is needed.

Let me show a couple of quick examples here of project network diagrams. And of course, the one that you will be most familiar with is this one here. Boxes and arrows, very easy to understand. Your project begins on the very left with the project start box and it ends on the very right with the project finish box. And in between your boxes and arrows representing the activities on your project as well as how everything flows. You also have burst nodes where after one activity, you suddenly have two or three arrows going away creating these bursting path. And then at some point, these paths they may converge again back into your main path. This is the type of schedule network diagram that you can expect to see in sample questions. But don't be surprised if you come across one that is just drawn with circles and arrows. It may be unusual to draw it like this but it's perfectly all right to use circles and arrows instead of boxes and arrows to draw your project's schedule network diagram.

And here are the two abbreviations that you have to be aware of when it comes to the project schedule network diagram - PDM as well as AON. You already heard about PDM. This stands for the Precedence Diagramming Method which is the technique used for constructing a schedule model in which activities are represented by nodes and are graphically linked by one or more logical relationships to show the sequence in which the activities are to be performed. And then AON stands for Activity On Node. This again means nothing more than the activities themselves are on the node. So if you take all the arrows that you have in your diagram, the place where the arrows meet, that is your node and there you include a box. And in this box, you will have your activity. So you place your activity on the node where your arrows meet. PDM -Precedence Diagramming Method and AON - Activity On Node.

Let us now move on towards working on the forward pass and backward pass. And your assignment on PMP exam sample questions on this kind is usually along the lines of that you've given a list of five to 10 activities. All of these have a start date and a duration and your task is to figure out in which order these activities will need to be executed and also what the float of these activities may be. So in your head, you're going to have to construct something like what you see on the screen here, With the activities following each other, some going in parallel and there on day five you see a red arrow, that would be the float that this particular activity has. And in order to do that, you're going to be needing a lot of information to calculate everything. And all this information is included in your node. Because remember, the node, that is your activity. So in the node information, you are going to have some kind of an activity name, you're going to find an activity duration, how long is this activity going to take. You're going to have to calculate the activity float. Well, we could start this activity 10 days late and the project would still finish on time. That's your float. You're going to have to calculate the early start, the early finish, the late start, as well as the late finish. And all of this information is going to be included in the box that represents the node and your activities on the project schedule network diagram.

Let's take a look at a couple of layouts of how you can graphically represent such a node, such a box, in your project schedule network diagram. The good news for our everyday lives as project managers is that modern software makes node calculations and layout quite simple. I mean, just open up your favorite scheduling tool, put in a few activities and it will automatically calculate everything for you and show you the node as well on your network diagram. Most often, there are two forms that you will see. The first one is the top down form where you have the activity ID at the top, and then there is the duration, the float as well as the early start, early finish, late start and late finish. That's what these abbreviations mean here, ES - early start, EF - early finish, and then you have of course, the late start and late finish. Or you could have a more horizontal format like this one here where you have the activity identification, the activity name is there in the center and you have the ES and EF at the top, and the LS, Float, and LF at the bottom. Here on the Prepcast and in the example that we're going to be working through, we are going to be using the top version right there on the right hand side. Because when you calculate a network diagram manually, when you do a forward pass and a backward pass, it is much easier to have the boxes arranged in this way because it goes from left to right and then from right to left. And you don't really have to think much where again is which box. So it helps purely graphically making things easier when you do a forward pass, goes from left to right at the top and a backward pass, goes from right to left at the bottom.

So we are trying to determine the amount of schedule flexibility or Float or Slack as it’s sometimes called in our schedule network. And we also want to know how it is measured and why is it important. So let's answer these questions by defining the two types of float that you may find in your project schedule network diagram. We have Free Float and Total Float. Total Float refers to the amount of time a schedule activity can be delayed from its early start date without delaying the project finish date or violating a schedule constraint. Where the Free Float refers to the amount of time a schedule activity can be delayed without delaying the early start date of an immediately following schedule activity or without also violating a schedule constraint. So Free Float means you're just looking at a single activity, how far towards the end of the schedule can I push this without changing an immediately following activity. And the Total Float means how far can I push this activity towards the end including pushing some that are coming afterwards without extending my schedule. So in other words, for total float, we're not just looking at one activity. We're pushing a group of activities usually towards the end of the project without extending the project because maybe a resource is not available right now and we have to push everything two weeks back.

Here are a few more facts to remember about Total Float. Total Float is the amount of scheduling flexibility that exists in the logical network paths within your schedule model. The Total Float can be positive which is based on a backward path that is calculated from a schedule constraint that is later than the early finish date that has been calculated during a forward pass calculation. It can be negative which is caused when a date in a constraint is violated by duration or by logic, or it can be zero which is always true on the critical path because it does not have any slack at all. And this is really the most important one to remember. The Critical Path always has zero float. Once the total float for a network path has been calculated, then the free float can also be determined.

I have a question for you that at first may sound strange. But if you start a project today, what number does that day get in your project schedule network diagram? So if you're starting today, are you starting on day zero or are you starting on day one? Do you think today is day zero or today is day one? Well, there are two schools of thought about this one here. However, here on the Prepcast, we are of the opinion that the correct answer is that your project starts on day one. This is not only our opinion but it is a generally accepted convention that is also used PMBOK Guide. Also frankly, when I begin working today, that's my first day on the project and not my zeroeth day. For the most modern scheduling software, when you open them, you don't actually start numbering the days. You start on a date, on a calendar date. And if you start your project on the first day of January, the software will tell you the project begins on January 1 and not on January 0. That is why in our following examples, all the formulas that you see, they take this as the basis. Our project starts on day one.

This slide at this table here is meant as a reference for you only. We're not going to spend too much time for it. The reason for this is that it's really just meant as a reference. Once you have worked your way through the upcoming minutes and looked at how we do a forward pass and then again, a backward pass, you can come back to this slide here and take a more in depth look at the four formulas that we're going to be using. So we just quickly go through these four formulas that you will need in the forward pass and backward pass calculation. So the early finish is calculated by taking the early start plus the duration and then you subtract one. The early start of an activity is calculated by taking the earliest finish of the predecessor activities and adding one to it. The late finish is calculated by taking the late start of a successor activity and subtracting one from it. And finally, the late start is calculated by taking the late finish of the current activity subtracting the duration and adding one. Okay, if all of these sounds confusing, don't worry. Once you have gone through the forward pass and backward pass with me, everything will make sense.

And here is the Network Diagram that we will be using in our example here and for which we are going to calculate the early start, early finish, late start and late finish as well as the float. You may just be able to make out there in Activity A that we have a start date of one and a duration of two but nothing else. And for all the other activities, you might be able to see that the boxes are empty except the one in the top center, which is the duration. So we're going to begin with activity A there. And what we're going to do is first, we are going to calculate everything in a forward manner. That's why we call this the forward pass. And in the forward pass, we fill in the top half of each of these boxes, the top half of each of these nodes. And once we have arrived at the end, we're going to turn around and calculate the backward pass. And that would then of course give us the bottom half of each of these boxes of each of these nodes. In the coming slides, we are going to zoom in to those areas of our network diagram that interests us for that particular moment. So I'm zooming in right now here on Activity A, B and C because we want to begin by calculating the early finish date of Activity A. How do we do this? Quite simple. As you can see in Activity A, we already have the start date of one and we have a duration of two. So what we want to do is we want to calculate the early finish date which is in the box at the top right here in the node. And we do this by taking the formula that I've shown you a little while back and I said that the early finish date is the early start plus the duration minus one. And so in our example here, the early start is one and the duration is two. So one plus two equals three minus one, we end up with two. So why do we again subtract the number one from these numbers as we calculate them? Well, let me explain it to you because it's really just a mathematical need because our project starts on day one.

Let me show this to you in a some more different graphical format here. So what we have right now is we have two activities. The first activity starts on day one and it's two days long and of course it finishes at the end of day two. And then the second activity begins on the morning of day three, it takes three days and it ends on day five. Well, hopefully on day five at three o'clock because day five is Friday and I like to go home early on Friday. Okay. So we have these two activities and they fill the whole week. Purely from a visual point of view, it's quite easy for us to understand and say, okay, activity - the first one begins on Monday at eight o'clock, takes two days, it finishes Tuesday evening around five o'clock. And the other one is three days long so it has to end Friday around between three and five o'clock. Very simple in this visual format. But now let's do this mathematically. All right. So the first activity, if we just said that the activity begins on day one, and the duration is two days long, then it suddenly ends on day three because one plus two equals three. But wait, that's not correct because it ends on day two because we can see right there above, it says two days, it ends on day two. Therefore, we have to say that our first activity here starts on day one, it takes two days and now, we must subtract one in order to just purely mathematically end up with the correct end date. And it's the same for our second activity. This one starts on day three and it's three days long. Therefore, it ends on day six mathematically. But if we calculate this correctly, if we do subtract the one, then once again, it ends on the correct day which is day five, Friday, hopefully at around three o'clock so we can go home early. So this minus one that we're using here right now and also a plus one when we do the backward pass is a mathematical necessity so that you end up with the correct numbers because our convention says that the project we're working on starts on day one and not on day zero.

So after this excursion into mathematics, let's return to our project schedule network diagram here with Activity A, B, and C and continue with our forward pass. We have already calculated early finish date for Activity A and we calculated this as being two. The next thing we're going to want to do is we want to figure out the early start date of Activity B and Activity C. And it's easy to see if your Activity A ends on day two at five o'clock. Logically, Activity B and Activity C, well, they're going to be starting on the next day plus one. Therefore, Activity B will be able to begin on day three and also Activity C will be able to start at the earliest on day three. All right. Now we can continue to move on to the right. And we're now going to calculate the early finish date both of Activity B and C with the formulas that we have looked at before. So in activity B's case, it's going to be three plus four equals seven minus one is six. And for activity C, it's three plus six equals nine minus one equals eight. There you go. We have now calculated the early start and the early finish dates for activities A, B, and C.

And we are now going to continue with the forward pass from Activity B to Activity D and also from Activity C to Activity E. And we're going to first want to determine the early start date of Activity D and E. And it's easy to see how this is done. You take the early finish date of Activity B which is six and you add one to it. So at the top, that will give you seven and at the bottom for the Activity C, your early finish date is eight, you add one to it. And so the early start date for Activity E becomes nine. Next, we can now calculate the early finish dates. Again, our simple formula at the top for Activity D is seven plus three equals ten minus one equals nine. And at the bottom, nine plus six equals fifteen minus one is fourteen for our early finish date. So from this moment on forward, if your schedule network continues likes this which is one activity after the other, it's really a simple mechanical procedure of taking the numbers, adding one, adding up the early start date with the duration subtracting one and going on like this throughout your network. But there are a couple of rules that you have to be aware of.

The first area that may cause a little bit of a headache at first is the question of what do you do if you have merging paths? When two paths that were separate converge back to into a single path like we see right here. As you can see, Activity D is followed by Activity F, but Activity E is also followed by Activity F. So which of the two early finish dates here will we have to use to determine the early start date of Activity F? Are we going to take nine plus one equals ten at the top or are we going to take 14 plus one equals 15? Well, the rule is quite simple. Because Activity F has two predecessors, Activity D and Activity E, you always take the largest early finish date. So in this case, we are not going to use the early finish date of Activity D which is nine. Instead, we are going to take the early finish date of Activity E which is 14. So fourteen plus one equals 15. That is our early start date for Activity F, right. And now, we can calculate the early finish date simply by saying 15 plus six is 21 minus one equals 20.

Another area of concern is that you are going to have to make sure is that you read your network diagram correctly. Take a look here between Activity E and Activity G. There is no connector. The predecessor activity for G is C and not E. So when you want to calculate the early start date for Activity G, make sure that you use the correct number. In this particular case, you have to use the early finish date from Activity C which is eight plus one which of course will end up with nine as the early start date for Activity G. If you haven't seen that missing connector there, you might have used 14 from Activity E and then suddenly, Activity G starts on day 15 which would be incorrect. And now, of course, we can go ahead and we can calculate the early finish date, nine plus four equals 13 minus one is 12.

We have almost reached the end of our network diagram. So what we need to do now is finish our forward pass and then begin our journey onto the backward pass. So the first thing we need to do is calculate the early start of activity H. And we have a converging path here. Two paths merge together, Activity F and Activity G. And we have learned that if we have a situation like this, we take the larger of the two early finish dates which is of course the one at the top. 20 is larger than 12, so we take 20. We add one and we come up with the early start date of 21 for Activity H. Now, we can go ahead and we can calculate the early finish date for Activity H. Of course, 21 plus five is 26 minus one is 25. That is our early finish date. This is now the end of our forward pass and we can begin the backwards journey. And to do this, we simply copy the number 25 right there from the early finish date down into the late finish date. And now, we begin the journey backwards at the bottom from right to left. And of course, what we now want to do is we want to calculate the late start which is the box at the bottom left right there. And the formula for this is that the late start is the late finish minus duration plus one. Or in our case here, we have 25 minus five plus one equals 21. In this particular case here, both the early start and the late start are the same as well as our early finish and late finish are the same, 21 is 21, 25 is 25. And what you can also see right now, there is one box, one part of our node here that is still empty. And that is of course our float, the box in the middle at the bottom there. The Float is calculated simply by subtracting the two numbers right here. Subtracting late start and early start and in our particular case, the float for this last activity is zero. That means in order for our project to end on day 25, this activity must start on day 21 or we will go beyond our scheduled end date of 25. So this activity here has zero flexibility. We cannot move this activity a day late or else it will end on day 26.

All right. So we have begun our journey backwards towards the start of the project and we have already calculated the late start and late finish as well as the float on our final Activity H. Next, we are going to have to determine the late finish of both our Activity F and Activity G. And we do this pretty much the same way as we have done this for the forward pass. So, the late start of Activity H is 21. That is the latest when this activity has to start in order for us not to miss the deadline. That means of course that both Activity F and Activity G, they must finish no later than the day before so that we can start Activity H on day 21. That means they must finish on day 20. So we take day 21 and we subtract one from that number. And we end up with a late finish of Activity F of 20 and a late finish of Activity G, also 20. And now it's really just a question of continuing to apply our formulas. So let's calculate the late start for these two activities. At the top, we take our late finish of 20 minus the duration of six which is 14 plus one and we have 15. At the bottom, we take our late finish of 20 minus the duration of four that ends up being 16 plus one equals 17 as the late start for Activity G. And now let's go ahead and also calculate the float for these two activities. At the top, we have 15 minus 15, that ends up being a float of zero. And at the bottom, we have 17 minus nine, that gives us a float of eight. So this means that Activity G can start on any day between day nine and day 17. And we will still be able to start Activity H in due time so that we can finish our project on day 25. That's what the float means of eight for Activity G. We have eight days to shift this activity forwards and backwards on the schedule.

Let's continue our journey here on the backward pass and we are going to calculate the late finish and late start as well as float of Activity D and E. But before I do that, let's not forget that Activity E and Activity G are not connected. Activity D and Activity E are followed by Activity F. Therefore, we have to take the late start from Activity F which is 15 in order to determine the late finish of Activity D and Activity E. And of course, we know Activity F, the late start is 15, that means D and E must end on the day before. So they must end on 15 minus one equals 14. That is quite a simple calculation really. From here, we now go and we want to calculate the late start. At the top, the late finish of 14 minus the duration of three is 11 plus one equals 12. And at the bottom for Activity E, we have the late finish of 14 minus the duration of six equals eight plus one equals nine. As I've said, these are really simple calculations that you can do in your head. But on the PMP exam, you may choose to use the built-in calculator and calculate them out by tapping them into the onscreen calculator. Because sometimes, one plus one in the heat of the exam turns out to be 12. And then of course, your activity network diagram looks a bit wrong. All right. So we’ve got the late finish and the late starts calculated. Let's also look at the floats that we have here. At the top, Activity D, we have an early start of seven and a late start of 12, so 12 minus seven, that gives us a float of five days. So this activity can be started up to five days late and we can still finish our project on time. And at the bottom, of course, you can instantly see that the early start and the late start are the same, they are nine. Therefore, our float is zero.

We are now coming to the situation where on our backward pass, we have a converging path where two activities, Activity E and Activity G, suddenly lead back into the same one there, Activity C, as you can see. And by the way, yes, I did cheat a little bit here on this slide with the layout by moving Activity G below Activity E so that you can see it more easily. In the forward pass, we learned that if you have two predecessors, you will take the larger early finish date to calculate the early start date. Now, as we are going backwards, you are going to do it exactly the other way around. So, instead of taking the larger, you take the smaller. So that means, if you look at this graphically here, we have a late start date for Activity E of nine and we have a late start date of Activity G of 17. We have just learned we're going to take the smaller of these two, that means we are going to take the number nine. And of course, if Activity E has to start on day nine, in order for us to finish our project on time, Activity C must end on the day before. That means it must end on day eight. That's quite logical. And now we can go ahead and we can calculate the late start of Activity C simply eight minus the duration of six equals two plus one, that gives us a late start of three. Now, we can also instantly see our float is going to be zero because three minus three is zero. This means this activity has no schedule flexibility. It must start on day three or else our schedule will change.

We have almost arrived at the very start again of our network diagram. And I've gone ahead and I have calculated the late start float and late finish dates for our Activity B. As you can see, it has a float of five. Let's now finish this off and also calculate the late finish float and late start for our first activity, Activity A, the three boxes in the node that are still uncalculated here. So we have a converging path going backward. And at the top, we have a late start of eight and a late start of three at the bottom in our Activity C. And we have learned, we use the smaller of these two, so we take three and we move that over to Activity A. Of course, we have to first subtract one which means we end up with a late finish of two for Activity A. Then we calculate the late start for Activity A, two minus the duration of two equals zero. Well, we can't begin our work on day zero so we have to add one, two minus two equals zero plus one equals one. And you can again instantly compare early start and late start and you see that they are the same, therefore, it is zero. Our float is zero. Your first activity must begin on day one; otherwise, you may not be able to complete your project on time.

And here is the completed network diagram, early finish dates, late finish dates, floats, late starts, early starts, all calculated for you via the forward pass and backward pass. My recommendation is go through the previous slides a few times. Follow me along as I'm going through the forward pass and backward pass. Take another look at the formulas that I've shown you in the table earlier so that you can get an understanding and a gut feeling of what it is that you have to do. And of course, it's also very important for you to understand when you have to add one and when you have to subtract one in regards to the bursting and converging paths and when you have to take the larger of the two numbers and when do you have to take the smaller of the two numbers in order to calculate either early start or late finish on the successor or predecessor activities. The example that we have just gone through is of roughly the same complexity that you can expect to find in exam sample questions. Most of them have about five to 10 of these nodes, of these activities here that you may have to calculate in order to figure out the answers.

Let's review. The network diagram is a graphical representation of your project schedule. And by the way, the PMBOK Guide officially calls it the Project Schedule Network Diagram. It's usually shown as boxes and arrows, and the boxes are called nodes. And that's why we also call it the Activity On Node diagram, the AON diagram. It helps you determine the critical path on your project which is of course the longest path in your project. And this is created through the application of the forward pass, the backward pass, and by doing that, you calculate the early start, early finish, the late start, and late finish, as well as the float for each of your activities. And of course, even though you can do this, with a push of a button in your software that you're using right now, on the day of your PMP exam, you are going to have to be able to do this with a pen and a piece of paper.

And this concludes our look at the Project Schedule Network Diagram. So it's time for Justine to say, stay happy. And I say, until next time.