PMI RMP – MATH FORMULA GUIDE part 2

4. SCHEDULE NETWORK ANALYSIS AND CRITICAL PATH METHOD

Hi and welcome back again to a new lecture where we are going to discuss one of the most important topics in the project management in general the critical path method. In this lecture we will highlight the critical path technique, how to define the critical path on your project network diagram, how to find the early and late figures of the project activities in order to find out the flow associated with each project activity. Now, developed schedule process is about analyzing activity sequences, durations, resource requirements and schedule constraints to create a schedule model for project execution. And monitoring and controlling the critical path method is part of the developed schedule process. Critical path method is a technique that involves determining the longest duration path through the network diagonal.

The earliest and latest an activity can start and the earliest and latest an activity can be completed the early start, the late start, the early finish and the late finish of each activity. Now by developing your project schedule you will have these four steps. First of all, you would define the project tasks and the activities. Then you need to find out the duration of each activity. Then you will determine the dependencies within the sequence activities process. At the end you can identify your project critical path. Now, a project network diagram can be drawn using the precedence diagramming method or the PDM technique used for constructing a schedule model in which activities are represented by nodes and are graphically linked by one or more logical relationship to show the sequence in which activities are to be performed.

The project network diagram is the base or it’s the first step to find out or to determine the project critical path. Pure network diagram shows just dependencies logical relationships between the activities. If activity duration estimates are added to the diagram, it can also show the critical path if plotted against time. The network diagram is called a time scale schedule network diagram. This is an example of a simple network diagram of two activities. This arrow or this logical relationship means that once activity is completed or finished, activity B can start the PDM or the President’s diagramming methods, also called activity or note, where notes or boxes are used to represent activities as shown and arrows shows activity dependencies or relationships between the project activities.

Now, the critical path is an important tool for keeping your projects on track. Every network diagram has something called the critical path. It is the strength of activities that if you add up all durations is longer than any other path on the network, usually starts with the first activity in the network and ends with the last one shown on the network. So the critical path is the longest path in duration. Any delay on activities on the critical path will delay the whole project. This is why it’s called a critical path. The reason that the critical path is critical is that every single activity in the path must finish on time in order for the project to come in on time. The easiest way to find a critical path is to identify all paths through a network diagram and add the activity durations on each path.

The path with the longest duration is the critical path. This is the simplest way to find out the critical path on your project through the network diagram, find out all the paths, then calculate the duration of each path. The path with the longest duration is the critical path. Now what’s the flow? It’s an asset for the project. The flow it’s an asset for the project. It’s the amount of time an activity or a project can be delayed without delaying in the successor activity or the final date of the project. This is the flow, it’s the amount of time and activity or a project can be delayed. This is why it’s an asset for the project. What are the three main types of the float? First of all we have the total flow which is the amount of time and activity can be delayed without delaying the project in date or the project milestone.

This is what we called total fluid. The free fluid is the amount of time and activity can be delayed without delaying the early start date of successor activity. And the project float is the amount of time a project can be delayed without delaying the externally project completion date required by the customer, the contract or the senior management. This is the float. The amount of time and activity or a project can be delayed without delaying in the successful activity. Now here is a very important note. Activities on the critical path have zero flow. Any delay in the critical path activities will lead to a negative flow. So any activities located on the critical path have a zero flow. This is why it’s called the critical path because any delay on any activity located on the critical path will delay the whole project.

Now let’s dig deeper into the critical path method. This is the activity box model. This is how you will see the activity at this box here. The early start, the lead start, the early finish and the lead finish. Usually the activity name is written here. The duration here and the total flow is written here. Now how to find the flow of an activity equals the latest start minus the early start. The late start here, minus the early start here will give you the float or the late finish minus the early finish. This is will give you also the float. If an activity is located on the critical path the early start will be equal to the late start and the early finish will be equal to the late finish so that the float of this activity is zero because it’s located on the critical path. Now here are some general notes.

The first activity in the diagram or in the network diagram normally has an early start of zero. This is a rule project should never be left with a negative float. It should be compressed. You cannot leave your project schedule with a negative float of three or four months. It shall be compressed a forward pass. Forward pass means moving on. The network diagram from the beginning to the end through the network diagram is used to determine the early figures of activities. When I say the early figures, it means the early start and the early finish. You would perform a backward path end to beginning through the network diagram to determine the latest figures of activities, the late Spanish and the late start.

Now I want you to focus here. Now what are the steps you need to follow in order to find out the critical path of your project? Step number one, draw the network diagram as build a question sequence. There will be a sequence in the question. It might be a table, for example, that activity A will finish at an. Activity B will start when activity A and B finish, activity C will start and so on. This is the sequence described in the question. You need to follow carefully in order to draw the network diagram. The second step will be writing the duration of each activity above the activity box. The third step will be determining all paths of the network diagram from start to end. Whatever paths are available on the network diagram, you need to define them.

Oh, let’s assume we have the start here and the end here. You have a path from the start to end. You have another path here in the green line. You have the third path here in the black line and so on. Whatever you have passes, you need to define them all on the network diagram. The fourth step will be check the duration of each path. The longest is the project critical path. It’s okay to have more than one critical path. So these are the four steps you need in order to define the critical path on your project and find out the duration of this critical path. Now step number five, the second path in duration is the near critical path. You might face some questions in the exam asking you to find out the duration of the near critical path.

The duration of the near critical path is the second path and duration. Now step number six, start the forward path. First activity early start is zero and first activity early finish equals the early start of the activity plus the duration of this activity. Now starting a forward pass means starting from the start to the end on the network diagram in order to find out the early figures, the early start and the early finish. The first activity in the network diagram will have a zero early start. Let’s assume this is the start of your project and this is the first activity. The early start of the activity A will have zero figure and the early finish of activity A will be zero plus the duration of activity A. I hope it’s clear for you. The early start of the first activity will be zero.

The early finish will be the duration. If activity ad is assumed have a duration of three weeks then the early finish will be three weeks and the early start for the first activity is always zero. Now the early start of the following activity the successor activity equals the early finish of the predecessor activity. The activity early start equals its predecessor activity early finish unless there is a path convergence. So let’s assume we don’t have a path convergence. That simple. Forwarding pass or forward pass or performing a forward pass means moving from the start to A to B. The first activity early start at zero. The early finish equals zero plus the duration.

The early start of activity B is exactly the same early finish of activity A and the early finish of activity B equals the early starts activity B plus the duration of this activity and so on. You will find out the early figures of all the project activities. Now what will happen in case there is a path convergence? This is a normal situation from activity A to B the early finish equals the early start. Now there is a path convergence. This is what we call a path convergence. You have two activities A and B leading into activity C. So which early finish you will pick to have here for activity C? By sense I will pick the higher number if early finish of activity A is ten weeks and the early finish activity B is twelve weeks early start activity C will be twelve weeks.

You cannot put ten weeks here while the early finish activity B is twelve weeks. So from the early finish activity A and the early finish activity B you will pick the highest or the higher number and it will be the early start activity C. This is in case of there is a bad convergence. Now perform a backward path starting from the last activity. Last activity late finish equals the project duration and last activity late start equals the late finish minus the duration of this activity. Now this is the end of the project and let’s assume that the project duration is 25 weeks. 25 weeks will be the late finish of activity B and the latest of activity B will be the latest finish of activity B minus the duration of this activity and so on.

The late start activity B will be the late finish of activity A and you will keep moving backward to find out related figures of all the activities on the network diagram. The activity late finish equals the successor activity late start. This is what I’m talking about. The activity late finish equals the successor activity late start unless there is a path divergence. Now here is a normal case without a path divergence, late start of the successor equals the late finish of the predecessor activity. Now, in case there is a path divergence, you will take the late start of activity A or the late start of activity B. You will pick the lower number and put it here. So if it’s here six weeks and here it’s nine weeks, you will take here six weeks.

You cannot put here nine weeks and here six weeks. This is why you will pick the lower number. I hope it’s clear for you. Now we’ll have a few examples. Example number one, referring to the diagram below. What’s the float or the slack of activity two? This is a simple question, cricket, but simple as well. Now, this is the network diagram we have. We have two passes on this network diagram. Pass number one is activity one, activity three, activity four, activity five. The second path is activity one, activity two, activity five. These are the only two paths in this network diagram. Activity one, two, five, with total duration of 17 days. Activity 1345, with the total duration of 21 days.

It means that the critical path is the second path, with the duration of 21 days, this path. So all these activities have a float of zero. The question is asking about activity too. So if the duration of the upper activity is 17 days and the duration of the lower activity is 21 days, so the flow activity two will be four days. If activity two was delayed by one or two or three or even four days, there will be no effect on the project and your project will not be delayed. So activity two flow is four days. Another example here your project includes the following dependencies what’s the critical path duration and what is the flow of activities B, D and E. This table shows the dependencies between all the project activities. We have start dafe, GBHC and end.

You have the predecessor activity of each and you have the duration of each activity. You need to start by drawing the network diagram. So first of all you have the start, then activity D and activity A. Both are after the start. So here is the start. Here is activity D with four weeks duration. And here is activity A with six weeks duration. Then you have activity F after activity D and A with seven weeks duration. Then activity E with eight weeks duration after activity B, then activity G after completion of activities E and F with a duration of five weeks. Then activity B with a duration of five weeks. Activity H with a duration of seven weeks. Activity C with a duration of eight weeks. And at the end you have the end of the project. So this is the network, the gram you have of your project.

How many paths? This is the second step. We are done with the first step. We have the network, the Gram. What are the paths you have? First of all, you have start deghcn. This is path number one. Then you have start dfg HC. And this is path number two. Then you have start, AFB. And this is path number three. Then you have start afghc. And this is path number four. And the fifth path will be Start Dfbn. So the project dip diagram includes five paths. You need to find out the duration of each path. The first path will be D-E-G-H-C with a duration of 32 weeks. The second part will be DFB with a duration of 16 weeks. The third path will be Dfghc with a duration of 31 weeks. The fourth path will be AFB with a duration of 18 weeks.

And the last path will be Afgh with a duration of 33 weeks. So this is the project critical path Start Afghc, end with the longest duration of 33 weeks. What’s the project near the critical path? It’s the first one. Start D-E-G hcn to the duration of 32 weeks. Now, the second question is asking about the float of activities BD and E-B-D and E are almost located on the critical path. So we need to find out the early figures and the late figures by performing a forward and backward path to determine these figures and then find out that activity is fluent. Now, by performing a forward pass, we have the start here. The first activity early start is zero and the early finish is the early start plus the duration of this activity.

So the early finish here is four. The same for activity A, it’s zero here, zero plus six. We have six weeks. Then we have activity F with a path convergence. If there are two activities leading into one activity, so we will pick the higher number, it’s four or six, we will take six. So the early start of activity F is six. Six plus seven. The early finish is 13. Four, you will bring the four here. Four plus eight, you will have twelve. Again here we have a path convergence, twelve or 13 for sure. You will take the higher number 13 weeks. Then we have 13 here and 1313 plus 518, 18 early finished activity G. It’s the same with the early start activity edge for the duration of seven weeks. Seven plus 18, 25, 25 here.

We will take it to activity C, 25 plus 833. So this is the critical path of the project, 33 weeks. Now we define the early figures of all the project activities. We want to perform a backport path in order to find out the late finish and the late start of all the project activities. Now, without any calculations for all activities located on the critical path Afgh C, you will just copy these numbers and put them here into the late figures because the flow would equals the late start minus the early start which is zero for all activities on the critical path. So 25 will be 25 as well and 33 will be 33 as well. Now for activity B, it’s the last, as I mentioned before, few minutes. The late finish of the last activity in the network diagram will have the duration of the project.

So it’s 33. 33 minus five will have 28 weeks. For activities H and G we will just copy the numbers because they are located on the critical path. And for activity E you will take the number here, copy it here, 13 minus E to give you five weeks for activity F located on the critical path you would have the same numbers. The early figures equals the late figures. Now for activity B there is a path divergence, it’s leading into two activities so it’s either five or six. While performing a backward path will take the lower number, so it will be five here. For activity A it’s on the critical path. So we have a zero float. I hope it’s clear for you till now, now we want to find out the flu activity B, it’s 33 -18 15 weeks for activity D, it’s five minus four one week.

And for activity E it’s 13 minus twelve, it is one week as well. Another example here, given the network diagram below, what is the float of activity A? Okay, again, it’s a pretty simple question. You just need to be aware of the tracks. The first step, the network diagram is given here. So we don’t need to draw any network diagram, we need to define all the paths available on this network. So the first path will be Start A-B-C and the second path will be Start A-D-C. And the third path will be Start A-D-G. And the fourth path will be E-F-G. And the fifth will be Start E-D-G and number six will be star E-D-C-N. So in this network diagram we have six paths. As shown here, the path with the highest duration will be the critical path.

Now this is not the question, the question is asking about the flow of activity A. So how to find out the flow of activity A without wasting time and finding out the early and late figures of all the project activities. Now, the critical path activities all have a zero float. So activities Ed and C have a zero float. Let’s refer to the second part here the path contains start A-B-C and with a duration of twelve days. Now if the float of activities D and C is zero and there is a difference of two days between this path and this path. So for how many days can activity A be delayed without delaying the successful activity? It’s two, because this path twelve days duration and this path have 14 days duration d and C are activities in common between the two paths and D and C have zero float.

So the two days float of this path are all within activity A. So activity A float or slack is two days. The last example we have here given, the following portion of the network diagram was delayed finished activity F. So we have this portion of the network diagram and the question is asking about the late finish of activity F. Now this is the activity box model. The question is asked about the late finish of activity F. The late finish activity F equals the late start of activity G or activity H. There is a path divergence here so you will pick the lower number. So it’s eleven days for activity F. The late finish for activity should be 17 or eleven. As mentioned earlier, we select the lower number by performing the backward path in case there are path divergence.

I hope it’s a clear now for the critical path it’s very important, very important actually for the exam it’s very important as well for your practical life. Conclusion the first step will be to determine the critical path. Carefully write the duration of each activity above the activity box. Start the forward path to determine the early figures give attention of convergence. If two activities are leading to one activity, the early start of the successor is the higher of early finishes of the predecessor. Fill all late figures of critical path activities. As float is zero, it’s the same of early figures. Start the path forward path to determine the remaining late figures give an attention of the divergence. Consider all paths that flow backwards into an activity.

The late finish of predecessor is the lower late start of both successors. Any question is asking about flow to an activity on the critical path. The answer is very directly. I mentioned this step in my exam. Actually in my PmP exam I think there was a large network of the drum and the question asked about the float of an activity located on the critical path. So once you determine that this activity the question is asking about is located in the critical path, you just need to check the zero answer. All activities on the critical path have a zero float without performing a forward path and a backward path. Another small topic in the schedule network analysis will be the schedule compression techniques.

Sometimes you need to compress the schedule to meet customer satisfaction or due to an instruction of senior management. The main objective of this is to compress schedule without affecting the project scope. So what are the schedule accomplishing techniques? You will have the fast tracking. Fast tracking means executing critical path activities in parallel instead of series as planned. You must give attention to dependencies while performing fast tracking. Usually fast tracking increase the rest of the project. In this method you will perform activities in parallel if possible. This depends on the dependencies between the activities. The second tool is the crashing. Crashing means adding or adjusting resources in order to compress the schedule while maintaining the project scope.

It trades time for many so crashing trades time for many by adding resources to the project activities to finish the work earlier. Now, for the math purposes, here is an example of the crashing you are supposed to do schedule accomplishment for your project. Your team brought you this information the project had a negative float of three months so the float is minus three. What are the activities you will crash to save three months in the project and how much it would cost to crash the project? So as per the table, there are four activities mentioned fjknl the original duration of each activity is stated as well let’s take an example of activity J the duration is 14 months the crash duration is twelve months and the time saving will be two months 14 minus twelve. The original cost of the activity is $10,000.

If you will perform crashing, the cost will become $14,000 so the extra crashing cost will be $4,000 for two months saving so it’s $2,000 per month. The same for activities KN and L. So how to compress the schedule by three months without stating in the question that you should look for the activities with a minimum crash? Of course, you should think of this by yourself the three months can be reduced by two here and one here or here but the crashing of one month of activity K will cost you $9,000 while for activities J and N it’s $2,000 per month and $1,000 per month. So the best choice will be crashing activities J and N as the cost of crashing of activity J is $4,000 and to reduce two months as per the table and for or activity and it’s 1000 to recuse one month so total compressed duration three months.