So similar to what we did in activity on node. I also want to highlight what we call a key for your diagram. If you remember before we did the forward and the backward past calculation. We'll highlight the key to highlight what is the latest start, the late finish, the early start, and the early finish. For the activity on arrow, it also there, usually the key would look similar to the following. Where you have here the activity name, and here you have the activity duration. And for the numbering, as we just mentioned, we have i here and we have j here. And we will have the early start and the early finish of the activity on top of the arrows, as we can see here. And the late start and the late finish in the bottom of the arrows as we can see here. Then for later in the forward pass calculations, we would highlight on the early start to say the time T1, which is the early start of the activities. So, whenever will you have so many activities coming for the same node, you want to find what is the earliest time possible to reach that node, and the same will go to this one here as T2. Now when we do the backward pass calculations you want to find the latest duration, or the latest time that activity reaches, or start there. And we will cover it through a calculations for later, where it highlight also a time, four let's say, and here, time three. And we will go through an example with the numbers to identify all that, and why all this is important. So going back to our example, let's perform a forward pass calculations which highlight the following. If you remember, the main objective for a froward pass calculations is to identify and determine that early start and the early finish. The early start and early finish time possible for each activity in your project. And also to identify what is the earliest time of each node, which is, I refer to as T1 and T2 in the previous discussion. And here, I highlighted the mathematical equations, but usually I like you to understand it, not memorize it. So, the early start for activity i, would be the latest early finish of all the predecessors of activity i. It's exactly the same concept of activity unknown. So, the early finish, in this case, would be the early start of the activity plus the duration of that activity. As for the backward pass calculations, the objective, which is also similar to the activity on node, to find and determine the late start and the late finish of each construction activity. But adding to that to identify the latest time of each node. Again, the two equations, quickly here, that I would love for you to understand not to memorize, here as well, that the late finish of activity i would be the earliest late start of all the successors of that activity. And if you want to do, or calculate the latest start, would be the late finish of the activity minus the duration of that activity to give you the latest stat of that activity. So, let's do the forward and the backward pass calculation. And what I'm going to do, I'm going to draw the diagram quickly for you here starting. One here and then we have the following, and then we have activity here. I believe we have A, B and C, and then we have F here with another node. And we have a dummy activity. And we have another dummy activity here and activity E, this one activity D. And then we have Activity G and Activity H. And we said we have a dummy activity here. And we have the last activities of K. We have. J and we have the last one here which is activity I. The durations were 3 days, 2 days, 1 day. We have a 3 days here, we have 3 days here, we have H3, we have 5, we have the 4, we have J1, and we have K2, and that's our project. So for the forward and the backward pass calculations, let's forget not to, not forget to number them as we did before. 2, 3, 4. We have 5, we have 6 here, 7. 8, we have 9. And we have 10 here. And we might be missing A dummy activity here. So with that, we did not finish, we did not miss anything. So for the forward pass calculations, for the fist three activities, A, B, and C, we start with the project with one. As I explained to you in that activity on node, you can start also with 0, but I always like you to, in that activity on arrow, both are fine. But I start with a 1here, which will be the earliest time that node in time is going to start, in this case, the early start time for A, B and C would be also equal to that first day. We have 1, 1 and 1. If you remember the key, we said if we look at D here, here is the early start, early finish, late start and late finish. So to go through activity A for example, that late start or, I'm sorry, the early finish, if this is the early start, the early finish we're going to put it here is 1 plus 3 equal 4. Then the B, the early finish would be 1 plus 2 equal 3. For C, the early finish would be 1 plus 1 equal 2. So, node 2 is the point in time, or that event in time, when activity A finishes, would be day number 4. So this is the earliest time and activity 2 can reach, which is 4 here. Now for activity or node 3, you have only one activity which is 3. And for node 4 you have the number 2 here, so you have 3 and you have 2. So, node 2 is the point in time in the project we reach it when we are on the fourth day. So the earliest date to start for the following activities which is D and E, would be also the end of the day 4 which here will be 4, 4D and 4 For E. In this case, the early finish for D will be 4 plus 4 equal 8 and for E, the duration of 4 here The early finish of E was 4 plus 4 equal 8. What about a node 3 here? The node 3 also, they have 2 dummy activities, then the same concept of what we move forward with node 2, would be then here 3, and here's 3. So the dummy activity in the definition, we gave that, does not need any time, it doesn't have any time duration for it or resources used in it. So, the 3 will move towards here as a 3 to take it to node number 5. The same 3 for this dummy activity will go from 3 to 3 here as the early start and the early finish. So with that, let's go with activity F, 2 here, the early start. The 8 4 F and the early finish will be 2 plus 3, which will equal to 5 So if you have, let's work on this node here. If you have a node where you have two activities coming to it, the dummy activity represent Activity B. So it shows that two predecessors of I are F and B. So the early finish for B is a 3, the early finish of F is 5. So the node in time when both finishes would be here, the earliest will arrive is day number 5, which is the maximum between all the early finishes of the activities reaching that specific node. So we have here, As five. So, let's go for node number 5 here, the same. We have node 5 connected to two predecessors activities of E and B, both finishes E at 8, B at 3. The maximum number would be 8, which it says that, what's the earliest we can reach to that point in time would be at day number 8. So that would be 8. So for G and H, the early start dates for them would be 8. For G and 8 for H, so the early finish for G is 8 plus 5 is 13. And H, the early finish would be 8 plus 3, which equal 11. In this case, node number 7, the earliest date to reach it would be day 13. As for node number 8. 13 because this is a dummy activity, we can move the 13 here, 13 here. So node number 8, we will reach it in a point of time when we finish G and H. Which G only finishes in 13, day number 13, H at day number 11. So the earliest it will reach node 8 would be 13, so let's have it as 13 here. So because the earliest for 8 is 13, then we have the earliest start for K is also 13. For the dummy here is also 13, 13 which will leave us for node number nine. The earliest time to reach this node would be maximum of 13 and 8 is 13. Which will go to the earliest date for J, which is also 13 here, and that early finish for J is 13 plus 1 is 14. And the early finish for K is 13 plus 2 is 15. Which will leave us with I here, the early start 5, 5 plus 3 equal to 8 then would leave us that with the duration of the project of 15 days for the project. The maximum between the early finishes of all the activities is 15 here. So that will be the end of our forward pass calculations and we identify from that that early start, the early finish of all that construction activities, as well as, the duration of the entire project, which is 15 days. In matter of fact, once you start the project with day number 1 in this case, the duration of the project will be 15 minus that 1 which will be 14 days. If you start with 0 there, this number then, it will give you 14. So, that will be the forward pass calculations
