So what have we done so far, in terms of planning our project? Well, first we scoped our project. How did we do this? We used a work breakdown structure. In the example of the startup project, this was the work breakdown structure that we came up with. A header task, a summary task, and eight lower level tasks. The next step in planning our project was to come up with the precedence relationship. Which tasks are dependent on others? And how are they dependent on them? We came up with the following list. We recognized that fundraising depended on the creative work. That marketing depended on the creative and developing a strategy. Sales similarly depended on the creative and the strategy. Finance depended on the marketing and the sales, and HR depended on the fundraising and on the sales. In order to now move on and establish how long our project will take, what is the schedule, and when is the completion date for our project? We need to think very carefully about the durations of each of the individual tasks. For instance, in the case of our startup example, we might think about the following, or we might come up with the following duration, estimations in weeks for each one of our tasks. We assume that creative might take us five weeks. Strategy will take us two weeks to develop. The IT might take four weeks to put in place. Fundraising is a long activity that will take us four weeks. Marketing will take us five, sales will take us two weeks. And hopefully, with finance and HR, we will be done within two and one weeks. But actually thinking about these durations and coming up with these weekly estimates is not an easy task. It takes a lot of practice, and there are a lot of problems and a lot of difficulties when we come to think about our estimates. Let's list a few of those challenges that come up with thinking about the project activity durations. One of the most notorious struggles that individuals have when they think about how long a task will take in a project is something called Parkinson's Law, made publicly known by work by Cyril Parkinson in the 1950s. What Parkinson's Law tells us is that, if we plan for an activity to take a certain amount of weeks, be sure that the work will fill up that entire duration. If we give somebody four weeks to complete their task, they will take the entire four weeks to complete their task. And so we think, when we think about task durations, sometimes we might find ourselves asking or building upon historical patterns in which individuals used up the entire duration of the task or the entire time that was allotted to them when they actually completed the task. As opposed to really knowing what the work required. A second challenge that probably most of you can sympathize with is a phenomenon known as the Student's Syndrome. What the Student's Syndrome says is that I give you four weeks to complete a task, you are like to not even start working on that task until the very last minute. Like students, we procrastinate. We postpone our work. And therefore, even if we think that a task might only take two days, but we give you two weeks to do it, you will actually only work towards the end of that duration. Again, it makes it harder for us to really get a good sense of how long a certain piece of work might need or might require when we plan up front. Individuals are notorious for being overconfident. And so if you ask them how long something will take them, they are likely to be very sure of themselves. And actually report something is probably shorter than it will turn out to be in reality. Other biases that individuals suffer from are anchoring and confirmation. If I ask you how long a task will take and I'll say, hey will this, this following task take you two or three weeks? Well, I anchored you around those numbers. And you're not likely to suddenly tell me, oh, actually you're way off, it's going to take me eight, eight weeks to complete. And so, by having a conversation, we sometimes anchor ourselves and we sometimes like to confirm historical patterns. And so if we estimated a task in the past to take on two weeks, we might report that going forward. And so there are many challenges to coming up with proper task duration, durations and estimates for what those durations will be. Which of course is the underlying basis in our, in coming up with a overall project duration. But let's for a moment assume that we did our due diligence and we spent some time correcting for these phenomena. And we came up with good individual path durations, or estimates for the durations. Our network diagram might look like this. We have the exact same layout of our tasks. We have our start. We have our end. And we wrote underneath each one of the names of the tasks, we wrote the estimated duration that we came up with. Five weeks for creative, four weeks for IT, similar to what we saw in the table format before. How long will this actual project take, from start to end? What is our expected completion date? Well, it might not be too hard to find the longest path. If we look at all the different combinations and look at all the different possible paths along the tree, we might be able to see that the longest it will take us will be a path that goes from the start through the creative, through the sales, finance to the end of the project. A total of 12 weeks. But imagine that you have a much compli, more complex and a much larger project to analyze. With millions of parallel, mil, millions, maybe millions is an exaggeration. With hundreds of tasks, and many, many combining paths. What will be your project duration? Are you going to sit down and list all the possible paths, from start to finish, to come up with the longest one? Let me introduce a systematic way that was developed in the 1950's that allows us to identify the project completion date. How, meaning, how long the project will take, and will allow us to identify more information about our project that will turn out to be very useful as we think about our project and plan it properly. Follow me with the next few steps. What we're going to do, is we're going to look at the project and we're going to schedule everything as soon as we can. We're going to work from left to right and think about how, when a, a task will start and when will it end, if we schedule everything to start as soon as we can. Once we're completed and we've gone through our entire project from left to right, scheduling everything as soon as we can, we're going to come back from right to left, we're going to unravel everything. And say, when is the latest everything could start? If everything had to be delayed, when could the latest, when would the latest be in order to not change our overall project duration? That will reveal a lot of crucial information for us. Let me take you through this. In order to do that I'm going to change the pen and I'm going to work with our early start and our early finish, I'm going to work in an orange color. So if we start the project immediately, we can start at time zero. So, the start task, we know, is a dummy task. So it's doesn't take us long. It doesn't have any duration of its own. So it finishes its start at time zero. If we are at time zero, we can actually immediately smart as soon as possible, the IT task, the strategy, and the creative. So, the three of these tasks can start as soon as possible at time zero. And on the left hand side here you see some indication as to what these numbers are. The top left, I'm writing the earliest start. Now if the IT started at times zero, since it takes me four weeks to complete, the earliest I can finish it will be at time four. Similarly the task associated with the strategy, since it takes me two weeks to complete, it will end at time two. And the creative, in a similar way, I can add five weeks, which is its duration, and I will end at time five. Now moving forward with our project, since I completed the strategy and the creative, I can start my marketing task. The two predecessors for marketing have actually completed. When had they com, been completed? Well creative is the later of the two, and so the earliest that my marketing task can start will be at time five. Therefore, since it takes two weeks to complete, it will be finished at time seven. In a similar way, my sales activity can start at the earliest at time five and it will be completed at time ten. Finally, my fundraising only depends on my creative, and, therefore, it can start at time five, and since it takes four weeks to complete, it will be finished by time nine. Moving along, we have two more tasks to complete in order to come up with our project completion time. Our finance task depends on marketing, and on sales. Since sales is the later of the two, the earliest my finance can start will be in week ten. Adding two weeks for its duration, it will be completed at time 12. The HR activities depend on sales and fundraising. They can too start at time 10, and they will complete it it will be completed at time 11. And therefore, if I look now at my end task, my project completion, the earliest my project can be completed will be at time 12. 12 is the duration of my project if everything is scheduled as early as possible. So we've now found that it will take us 12 weeks at the minimum, 12 weeks, to complete this project. That is the longest path, that is the longest path in our, in our project, in our network diagram. The next step is to actually unravel everything from right to left. We are going to go back in time and say well, what is the latest we can start? How much can we push some of the activities and still not impact that total duration of 12 weeks? In order to do that, we're going to mark on the bottom of each one of our tasks, the late start, and, the late start and the late finish. Let me walk you through the example, and in order to make it clear that we're talking now on late starts, I'm going to change my pen to a color blue. So we've completed the project at, after 12 weeks. This implies that, at the very latest, the HR task will be finished, we would not want it to be finish past 12 weeks. Which means at the latest it would need to start at time 11. Since it takes us one week to complete. Similarly, the finance, at the latest, we want to finish at time 12 in order to not postpone our entire project. And therefore it would at the latest have to start at time 10. Moving back in our tree, we can now, we now know that the IT task at the very latest we would like it to finish at time 12, since all it's feeding into is our final completion of the project. And therefore, if at the very latest it were to start, that would have to be at time eight in order for the four weeks to be completed on time. Moving back through our network, we see that the marketing task at the latest could finish at time ten, and therefore at the very latest, it would have to start at eight. Our sales feeds into both HR and our finance activity. In order to ensure that it delivers what it needs to deliver to each one of those tasks, it must complete by ten, since the finance task is dependent upon it, and therefore it had to start at week five, at the very latest. Similarly, our fundraising at the very latest, can finish at 11, and therefore it had to start at seven. Creative work, since it feeds into marketing, sales and fundraising, must be completed by week five in order to support the sales activity, and therefore would've had to start immediately at time zero. Strategy however, since it feeds into marketing and sales, will have to again be completed at time five, but therefore it could start at the very latest at time three. And if we mark our start activity with 00, since a du, it's a dummy ta, task to represent the start of the, project, we have completed the entire set of calculations. We have early start times, and we have late start times for each one of our activities. And what's so important is that this systematic approach of calculating early starts and early finishes, and then sweeping backwards calculating late finishes and late starts. What did it give us? What information can we learn from this? Well, what's interesting is that we see that for some of the activities, there is a gap. Meaning that for some, not for all of our activities, does the Early Start equal the Late Start. Or Early Finish equal the Late Finish. And in those cases where there is a gap between our Early Start and our Late Start, that is slack, meaning the task can move. More importantly, perhaps, is that for some of the tasks in our network, there is no slack. My Early Start equals my Late Start. These activities, for which this is correct, for which this holds, in which our early start equals our late start, or similarly, our early finish equals our late finish, these are our critical activities. These activities highlighted in red on my slide are my critical path. They must start at the time that we desi, designated to them. They must end at the time that we designated to them. Otherwise there will be a delay to my project. The other activities in which there is slack, those activities will be our leverage. We can postpone starting them. We can discuss when we might want to do that and when we may not want to do that. However, it is critical to know that the critical activities in our critical path is what tells us and indicates to us when we're going to finish our project, and what is our completion time, and where we want to focus our attention in order to ensure that we meet our completion time. There's going to other uses for the critical path activities as we move forward, and how we plan and how we trade off, cost versus time. And so, summarizing what we've learned about the critical path. The critical path is the longest chain, the longest path of activities in our network. It is, sometimes people call it the makespan. That's typically how it's referred to in academic literature. Any delay to any of those activities on our critical path will ensure a delay to your project completion time. It seemed a little bit tedious and perhaps it took us a few, a little while to walk through that network diagram. And of course, if a project is much bigger, with many more tasks, it might take you even longer to calculate the early start and the early finish, the late start and the late finish, to identify your critical path and your project completion. The good news is that there are plenty, plenty of tools out there to help you come up with those calculations, and in fact, they're so good, and they're well-programmed, that they will calculate the critical path for you. They will run through the calculations and identify the early start and the early finish, the late start and the late finish, depending on the precedence relations that you've defined. A tool, one of those tools is Microsoft Project, there are plenty more out there, that we will mention throughout the course, here, the screenshot that you're seeing on the screen is from MS Project, for our specific example of the startup project. Here's another example, of course, this is overwhelming in terms of the detail. I'm sure you can't see that much on the screen. It just gives you a sense of how many tasks you can include in a project plan, and what I do think you are able to see is that there is a red path highlighted in the Gantt chart in front of us. Those are the critical activities. That is the critical path. It is visual. It is accessible. And if you want to, you can zoom in and just focus on those critical paths. Most of the tools these days will allow you to filter and to focus your attention on those atta, tasks that you know you have to complete on time in order to meet the project duration. Software tools will also allow you to automate and to look at the network diagram in a fairly accessible way and customize it to your liking. The screen in front of us takes the entire project that we've seen appear and fo, per, presents it in a network diagram format. Check out some videos that I've prepared associated with how to execute on these steps in MS Project. The next step is to think about whether we want to schedule tasks as early as possible or as late as possible.