For this time, let's go move forward to understand the backward pass calculations, And I highlighted here a quick example of only a three activities that we got from the previous example. And the key we expanded here a little bit, not to just have early start and early finish, but also to have a later start date and a late finish date of the activity as we can see from the key over on the top right. The only main connection between the forward pass calculation and the backward pass calculation is the early finish date. Which is the duration, the minimum duration of the project we have, which is day 18. And that number, we will take it to be the late finish date of the last activity. So again, I want to re-emphasize on this again. When you finish the forward pass calculation and you start doing the backward pass calculation, you always take the last activity. If you remember also even if you do have several of last activities, not only one activity. If you remember, I suggested for you to connect them all, in a previous module, to one node. And that node will be then the link between the forward and the backward pass. So luckily we have here just one activity at the end. So the early finish date for that activity G is equal to the late finish date of that same activity. With that being said, then we're going to go, similar to what we did with the forward, but now we're going to go backward and take the common cells. The late start date of activity G then will be late finish date of activity G minus the duration. So in this case will be 17. From mathematical point of view, which again I would not recommend for you to look just on mathematical. Always look at understanding the fundamentals out of it, is the late start date equal the late finish date minus the duration of that activity. So in our example here then if we want to go backward, the late start date of activity G will be equal to the late finish date of activity both E and F. So that will be 17, as well as this will be 17. Of course, if we want to go the same concept 17 minus 7 equal 10. And 17 minus 4 for activity F equal 13, which will give us the late start date for E equal 10, the late start date for activity F equal 13. The same as we did for the forward pass, let's highlight the last equation. If we have not just one activity like G, but other activities, and we're going backward, then the late finish date for the activities that going to be the predecessor's one will be the minimum of the late start dates of the successive ones. And we will go through an example and have this equation down here at the bottom to remind us with that mathematical approach. So as we said this is what we got from the forward pass calculations and we found all the top numbers, early start and the early finish. Let's go and find the late start and the late finish, which is the purpose and the objective of the backward pass calculations. To find the latest time to start and to finish activities without affecting the duration of the entire project. So we said 18, we'll take it as the same number from the early finish to the late finish and to find the late start of 17. For activity E, F and D, because they have only one successor which is G, we have all their late finishes to be equal to the late start of their successor, which will be 17 for all of them, the three here. So let's took the upper one and go to the levels afterward. So the latest start date for activity E will be 17 minus 7, which will be 10. For F, 17 minus 4, will be 13. And the last one activity D, 17 minus 13, which will be 4, the late start date for activity D. So let's go for activity B here. Activity B, we do have the one successor for it. So in this case, the late finish date for activity B equal the late start date for its successor. And the late finish date for activity C, we took 10, because if we want to look at the mathematical point of the view it's the minimum of the late start date of both activities, E and F. What if we chose 13 here, not 10? That's mean we are saying the latest finish date for activity C will then go three days after the latest start day, for one of its successors, which is activity E here. In this case, it will break the rule of the logical relationship and might affect the total duration of your project. So in this case, the late finish date will be 10. The minimum between the late start dates between E and F, 10 and 13 to be 10. 10 minus 6 to find the latest start date of activity C, which will be 4. The same thing will go to activity B of course, 10 minus 1. And then let's go the same exercise here. We have to find that late finish date of activity A, which will be the minimum of the late start date of B, C and D. 1, 4 and 4, which will be 1. And then 1 minus 1 to find the late start date of activity A to go back to 0. Here we go. We found that when we performed the forward and backward pass calculations to find the latest and the earliest dates without affecting the duration of the project. As well as from the forward pass calculations we found the minimum duration of the project to be executed. In this case here we have 18 days.
