Alright welcome back in this video. We will be doing two examples on how to draw CPM network diagrams by hand. So, first of all, let’s just do the first project we have up here. We have a table of dependencies, but right away, we can draw on activity a as our first activity. We have our activity on the arrow between two nodes, so we’re good to go for now. Next up we have activities B and C. These both depend on a so we can have an arrow coming off for B and an arrow coming off for C. Then next up we have activity D, it depends on activity B. So let’s draw an arrow coming off of B. Then next we have activities E and F. They both depend on C. So I’m going to suggest what, if we draw like this, then when we went to draw activity G on here in order to get all of the correct predecessors, we’d have to draw it like this. Now this has the correct predecessor relationships. We need de and F to happen before to finish before G can start, and this is correct. We have the easiest. One to see is e. Write leads into this point where E is done and G begins, and then D leads into this point. Where D is done, but it’s connected with this dummy activity that actually has no time or duration, it’s not an actual activity. It just shows that we have to continue this on. So D must finish before G can start same for. F. F must finish before G. Can start but the way that I’ve drawn this there’s two dummy activities. We actually want to minimize the amount of dummy activities that we’re using and so there’s a way that we can draw this, where we’ll only use one instead of two so I’ll just erase it, and it will look like this so now, what we’ve done is: we’ve Reduced the entire network diagram to only have one dummy activity and we still have all the correct predecessors for G right. So it D leads into this point where G can start a leads into this point and then F by extension of this dummy leads into this point. So F needs to also be done before. G can start. So next we have to do is just draw an activity H and then the last thing we need to do is we need to number each node in a way that every arrow points from a lower number to a higher number. So I would do it this way. This way we can use these numbers as, what’s called a unique IJ number, to identify our activities as an alternative to using their name. For example, a is i J number would be one to be. Zj number would be two three e would be four six and if you notice, every single arrow is always pointing from a lower number to a higher number and if that’s correct or if that’s the case, then you know you’ve done it correctly. Alright. So, let’s move on to the next example here, because this one is done for the next example. We have activities a and B or both of the very beginning of the project because they have no predecessor, but one of the limitations of the CPM network diagram is that you can only start on one node and you can only end on one node. So, first of all, we’ll have to draw a single node with arrows coming off for both activities, a and B all right. So next up we have activities C and D. Both depend on a so we can have an arrow coming off for C and an arrow coming off for D. Then next up we have activity E, it depends on B. So let’s go ahead and draw an arrow coming off of B. Then we have activity F. It depends on D, so, let’s just let’s try this out: let’s just draw another arrow coming off of D and then lastly, we would have an activity G and this predecessors are b and c, so we’re going to need to come off of c and then connect To B to this node with the dummy, but this is going to leave us with three nodes at the end of our project. If we wanted, we could draw on dummy variables connecting F to G and E to G or to this. This node at the end of G, but then we’re just introducing extra dummies that we don’t need. So the best way to do this actually is to, instead of drawing F to its own node, just bring F down to the same node. The G ends on and then bring the node that ends on same node. The G ends on just like this, so now we have our project ending on one single node, so that rule is satisfied. And lastly, we will just number our nodes and as long as all of the nodes are numbered in a way that each arrow points from a lower number to a higher number, we’ve done it correctly. So if we just check, we have the a2 leading to four five leading to six etc, one leading to three. So we’ve done this correctly and there you go. There’S two different examples for how to draw a CPM network diagram.