Hello everyone. For this module we would be covering the forward and the backward pass calculations or what we referred to sometimes as the CPM, critical path method scheduling procedure, CPM forward calculations, and the CPM backward pass calculations. The forward pass process determines the following. The earliest dates from the start and the finish of each construction activity you do have in your project, and this is one. The second also determines the minimum duration of your construction projects. This is the two main things that we generate and calculate from the CPM or the Forward Pass Procedure in the scheduling technique here. The backward pass process, on the other hand, determines the latest dates from the latest to start and the latest finish of each construction activity or task that can be performed but without increasing the construction projects minimum duration that had been identified in the first Forward Pass calculation, or the first step of the CPM scheduling procedure calculations. So, lets go through an example here, from the Forward Pass calculation. If you do remember, we covered in another module what we call the key for your diagram. In this aspect, we have the key here which is showing in the square the activity name. Let's say A, B, or C, concrete pouring erecting steels, or taking the forms and so on. And below it we will have the duration in days or in weeks or in months. And for the time being, for this specific example, we will highlight only the ES and the EF in our key for this diagram, which is referring to the Early start date, ES and the EF is the Early finish date. So this have an example here. Let's assume this is part of a diagram, of an activity on node diagram which highlighting the A as the first activity, we can start in our project and the successors of activity A will be activity C and activity D. In the forward past calculations when you start the process, you always start with the first number of the earliest start date of the first activity you have in your project. My recommendation always to start this number with zero. Some softwares, they actually give you the option to start from either zero or one. That's why you can also start with one if you like and some softwares even have it by default to start by one and then move forward the calculations. So it's up to you which one you want to start with. But for the sake of our course we will highlight the zero as the starting early start of the first activity you have in your project or the examples that we want to go through. So as we can see here, the early start date of activity A is 0. And once we given the duration of the activity in this example we have one day. In this case, we will have the early finish date of activity A is 1, and the equation, if you want to look from a mathematical point of view, the early finish of the activity in the forward pass calculation is equal to the early start of that activity which is, in this case, we have zero plus the duration, in this case we have one day for activity A which will give us one. I always recommend to everyone not to memorize these mathematical equations. I highly recommend for you to understand the flow of how you build the Forward Pass calculations, even though you have a lot of softwares out there, like Microsoft Project, like Primavera P6 that can do the calculations for you, but it is very important to understand the concepts and the foundations behind that, so as to be able to read it, to be able to understand where it came from. So, that been said then we will move forward with the calculations from the forward pass. We look at what is the early start of the successors' activities after we moved from the first activity. So we have to take the early finish of activity A to be equal to the early start of its successor activities which will have 1 here and also the same will go for activity D. So once we understand then, what is the early start date for activity C and D, we will then have to look at the duration of activity C and activity D and then from that, we will find the early finish of both activities, which in this case for activity C the early finish will be the early start which is 1+6, which will equal to 7, and the same go for activity D. If we have duration is 13, then the early finish for activity D will be early start of 1 plus the duration of 13, which will all well to be 14 days, the early finish of Activity D. So in this example, what we highlighting is that relationship between the activities of finish to start which is the traditional relationship that I explained in the previous modules, that I highlighted, that most of schedulers we have, they do prefer to follow the traditional module here, the traditional relationship, I'm sorry, in this example. So that will held correctly if we have this specific relationship. Also, another point I want to highlight in the forward pass calculation is what if we do have not just one activity like A that C is the successor for? So let's say for example, we have another activity here called activity B. And also it has a relationship between B and C, which is finish to start. In this case, the early start date for activity C will be the maximum number between all the early finish dates of the activities that predecessor or before that activity. Which again, I don't want to highlight just a mathematical equation, we're going to go through an exercise here to understand it better. So let's have, for example, this project, very simple small project. And I highlighted the last command that I put which is the early start equal the maximum of the early finish of all the activities. I will go from the beginning. This perform a forward pass calculations. The first activity again is activity A, so we'll start by the assumption, we'll start by zero. So, the early start date for A is 0 and the early finish date of activity A is 1 which is 0 plus 1 equal 1. In this case the successors activities of activity A will be B, C and D and the early start for each of these activities will be the same as the early finish of the predecessor A which would be one. So, early start for B one, early start for C one and early finish early start for D is one. What's that mean that when activity A we finish with that activity and we finished it in the end of the first day, the second day we can start with the following activities. So let's go from top to bottom, to do the calculations. In this case, activity B, we have the early start of one, then the early finish will be one plus nine, then it give us ten. Activity C will going to give us one plus six equal seven. And activity D will give us early finish day of 14 which is 13 plus one. What about activity E here? In activity E, if you notice we do have two predecessors for activity E which is activity B and activity C. So the relationship it shows that when both activities B and C will finish, then we can start with activity E. So without looking at the equation in the corner here, just think about it. That's mean, if I want to say the early start date for activity E is equal to seven not 10 then, that will not satisfied the relationship that we have in our project here. Because if the early start date of E equals 7, that's mean the activity B will intersect of its relation with E. So, I have to wait until the relationship of both are correct and finish both activities which will have the date of 10 to then start with activity E. So in this case, activity C even if we finish it at day number 7, we still have three days, kind of a buffer, to wait until we finish with activity B to start activity E. And that number, we will talk about it for later module that focusing on the floats. So that been said, then if you notice if we want to look at it from a mathematical point of view, the early start date for activity E is the maximum early finish date of the predecessors, which is 7 and 10 and we'll take 10. So in this case, the early finish date for activity E will be 10 plus 7 equals 17. And then, we will go to the following activity F here which has only one predecessor which is activity C here. This case we have the early start date for activity F is equal to the early finish date of the predecessor activity of 7. And then the early finish date for activity F will be 7 plus 4 to equal 11. So again, similar to what we did with activity E above here, let's try to finalize the end of the project, the last activity in the project which is activity G. The early start date for that activity will be the maximum number between all the predecessors activities their early finish date. Which in this aspect would be 17 because we waiting for activity E and F and G to finish all three to start with activity G, so the last one will finish is activity E, then the early start date for activity G will be 17, then the early finish date for activity G will be 18. So, if you remember in the beginning of the introduction of this module, I highlighted that the forward past calculations, it will calculate or determine the earliest time and the earliest time we start an activity, and the earliest time we finish an activity without kind of effecting the duration of the project. Second, is we highlight that minimum duration of the construction project. So in this case, what do you think the minimum duration of the project here? In this case, it will be that early finish date of the last activity we have, which is 18. So the duration of our project would be 18 days. So these are the two aspects we determine when we look at the forward task calculations.