 Hi, I'm RYRIZH and in this video, we will continue to talk about time planning. In this video, we will focus on the calculation of the critical path and the calculation of the slacks of a project. Just to wrap up, let's talk where we start. Everything starts from WBS, the work breakdown structure, which is a hierarchical description of the work that has to be done to complete the project. And where the lift nodes, the lowest level, are work packages. The lowest level, when assigned the time and cost, together with the necessary resources, people and material, and individual responsibility for their accomplishment, defines a work package. From the WBS, we can make the estimation of effort in person-month, person-day, or person-hour, which will be more suitable for the project. And based on the effort, we can calculate the duration and based on the effort, we can calculate the cost, as we will see in a different video. OK, based on the duration, we have each task and the precedences of those tasks, we can build the precedence diagram. So in this video, we will learn how to calculate the critical path. And based on calculations made on the project's network, the critical path method allows us to know the following. The start and then times of each node, the critical and non-critical activities, and the days off, free and full, for the activities. OK, the critical path. Let's focus on the critical path. In a network, paths represent sequences of ordered activities. Critical activities are those that when delayed cause a delay in the project completion date. The critical path is the one that connects the project's critical activities. Just to recap, OK, when we have a precedence diagram, we have the ID of the task, OK, the estimation of the duration here, OK. Then we have the earliest start time, the earliest finish time, the latest start time, the latest finish time, and the slack, OK. Let's see how can we reach these times and the critical path. To determine the earliest start time and the earliest finish time, OK, we start by calculating the earliest start time of an activity. Which is equal to the highest value of the earliest hand date among all activities arriving at that node. As we will see in the next picture, the node D. The earliest start time of an activity and the earliest hand time of an activity are determined from a procedure towards the start to the end of network. So we calculate for each node these values, the earliest start time and the earliest finish time, OK, based the earliest start time, the highest value of the earliest hand date among all activities arriving at node. And we can calculate the earliest finish time by the earliest start time plus duration all minus one unit. As we will see in the next slide, as you can see here, OK, activity D, OK, performs after A and B and A and C. After finishing activity A, we have activity B and activity C. They can occur in parallel, but D can only start when B and C finish. So to calculate the earliest start time of D, OK, as we can see, we have activity A and duration of activity A is one. So the earliest start time of A is one and in the next unit of time, it finishes. So it occupies only one unit of time, so it starts in the same unit of time. OK, B starts in the second unit of time as well as C, but B as a duration of three units of time. So in the fourth unit of time, it ends. On the other hand, C as a duration of two units of time and it finished in the third unit of time. So for D, OK, D will start in the fifth unit of time. Why? Because B and C must finish. And as B is the longest activity that depends on D, OK, D can only start when B and C finish. So D can only start in the fifth unit of time that is after the fourth unit of time. Just to note that a time unit is subtracted here to account for the fact that the activity starts at the beginning of a time unit, hour day and so on, and ends at the end of a time unit. In other words, an activity that lasts for one day and starts at the beginning of the day starts and ends on the same day. So the time window between the earliest start time and the latest finish time, OK, is where the completion of the task must occur and the resources to perform the task must be allocated. As we can see here, as we will see later, sorry, the difference between the latest finish time and the earliest finish time is this slack where we can slide the task. So let's see how now can we calculate the latest finish time. The latest finish time of an activity that enters a given node is equal to the smallest of the latest start times of all activities that leave that node. So we will see, as we will see in the node C of the next slide. So we start tracking the diagram from the beginning to the end to calculate the earliest times, OK, from left to the right of the diagram. And we do the opposite way to calculate the latest finish time and the latest start times, OK. The latest activity and time and the latest activity start time are determined from a network and to start procedure. So we start to calculate from the end to the start. As we can see here, OK, we have node C. And to calculate the latest finish time, we can see that C as a relationship from D and E, and the smallest latest start time, OK, is from D. So if the latest time time is in the fifth unit of time, OK, as we can see here, OK, the latest finish time of C, can only be in the fourth unit of time, because if it starts after that, it will have an impact on the other nodes, OK. So, and how can we calculate the latest start time is the latest finish time, as you can see here. Last duration of the task and then we had one unit. So 4 minus 2 plus 1 gives 3. And we can calculate it here just to recap from the smallest number that comes from LST. And in this case, it's tasks D and E and the smallest number is 5. So the previous unit of time should be 4. And you having LFT, we can calculate LST. With all these values, EST, EFT, LFT and LST, OK, it is possible to calculate the slacks. The slack time of an activity is the value of the delay expressed in time units that can be tolerated in conclusion of activity, OK. But just to be clear, rest periods, like holidays, week and so on, are not considered part of the slack, OK. So, how can you calculate the slack is the latest finish time minus the earliest finish time, OK. This is the sliding window that you can use to move the beginning of the task without a delay in the project, OK. The critical path, as you can see here, is composed by the sequence of the tasks where slack is 0, OK. Why? As you can see, if we don't have any slack, any, any, but any delay in one of these tasks, OK, delays the project, OK. So, what is the duration of the critical path of this project? We can sum here the duration of A, B, D and F, OK, 4, 9, 10, 11, 12. So, the critical path is 12 units of time, OK. As we can see here, any delay in this sequence of tasks delays the project. Complimenting the critical path, we should also define milestones and calendars. Milestones are dates where requirements must be met and goals must be achieved. Are control points that you put in the project in order to make a checkup and guarantee that everything is done until that point, OK. Calendars, identify the time periods in which work can be done, OK. Project calendars affect all the resources and resource calendars affect specific resources on the resource of the tasks and can affect the duration of the tasks, OK. In this video, we talk about critical path, about milestones and calendars.