Critical Path Calculations

Quick reference

• 00:00 Hi, this is Ray Sheen.
• 00:04 I'd like to show you how to manually calculate critical path.
• 00:08 If you're planning to sit for the PMP exam, you will need to be able to do this.
• 00:12 Over the years, I've tried several manual techniques and
• 00:15 I've found this one works the best.
• 00:17 I start by creating a network diagram of all the project activities.
• 00:21 I represent each task with a box that looks like this.
• 00:24 The boxes are connected with arrows that show the predecessor and
• 00:27 successor relationships between the tasks.
• 00:30 Let me explain how each part of the box is determined or calculated.
• 00:34 The activity name or number is placed in the top section of the box.
• 00:38 The task duration estimate is in the center of the box.
• 00:41 Use consistent units for your estimates everything in days or weeks.
• 00:45 Now we're ready to start the critical path calculation.
• 00:49 For the very first task in the network, set the Early Start,
• 00:52 that is represented by the ES to zero.
• 00:54 This means we will start counting time when the first task starts.
• 00:58 Next, we add the duration to the early start to get the Early Finish or EF value.
• 01:03 Now we take this value for Early Finish and
• 01:05 we set that as the Early Start value for the next task in the network.
• 01:09 This indicates that the successor task can start as soon as
• 01:13 the predecessor task finishes.
• 01:15 We proceed all the way through the network, adding duration to
• 01:18 Early Start for each task to get the Early Finish and then setting the early start of
• 01:23 the successor task equal to the early finish of the predecessor task.
• 01:27 If there are multiple predecessor tasks,
• 01:30 you use the highest value of Early Finish to set the successor task Early Start.
• 01:34 This means that once the last of the predecessor tasks is complete,
• 01:38 the successor task can start.
• 01:40 After you have completed the entire project,
• 01:42 you have completed what is called the forward pass.
• 01:45 You may be able to recognize the critical path at this point.
• 01:48 However, the to calculate the amount of float for all of the tasks that are not on
• 01:52 the critical path you will need to do a what we call the backwards pass.
• 01:55 Let's look at that now.
• 01:57 For the last task, set the Late Finish,
• 01:59 the LF portion of the box equal to the value of Early Finish for that task.
• 02:05 This indicates that as soon as the task as done, we are done.
• 02:08 That is the latest time that the project will finish.
• 02:11 Now subtract the duration from the Late Finish to calculate the LS or Late Start.
• 02:17 The Late Start value for the last task is the Late Finish value for
• 02:21 the next to last task, the predecessor to the last task.
• 02:24 Continue subtracting the duration for the Late Finish for
• 02:28 each task to determine the Late Start and
• 02:30 then assigning that value to the Late Finish of the predecessor task.
• 02:34 If a task has multiple successor tasks,
• 02:36 you will need to use the smallest value of Late Start to set the Late Finish.
• 02:41 All of the predecessor tasks must be accounted for
• 02:44 when determining the Late Finish of a task.
• 02:47 Once you finish the backwards pass and
• 02:49 get back to the first task, the Late Start value should be zero.
• 02:53 If it is any other value, you did your math wrong.
• 02:56 Now we can calculate the Task Total Float.
• 02:59 Subtract the Early Finish value from the Late Finish value for each task.
• 03:04 Any task with a zero value for Task Total Float is a critical path task.
• 03:08 There will be at least one path and
• 03:10 possibly several paths through the project that are critical.
• 03:14 Let's go through an example.
• 03:15 In this example, there's a simple network of ten tasks.
• 03:18 The arrows show the predecessor and successor relationships and
• 03:22 the task durations are in the center of each task.
• 03:25 The units are in days.
• 03:26 The early start for the first task, Task A is set to zero.
• 03:30 We then calculate the forward pass.
• 03:32 The Task A early finish is 3.
• 03:34 Let's follow the top path first.
• 03:36 The Task B Early Start is 3 from Task A.
• 03:40 The Early Finish for Task B is 5.
• 03:42 The five goes over to Task D.
• 03:45 5 plus 4 is an Early Finish of 9 for Task D, then on to Task F 9 plus 3 is 12.
• 03:51 I will stop at that path and look at the bottom path next.
• 03:55 The Task C Early Start is 3 from Task A.
• 03:58 The Task C Early Finish is 3 plus 5, which is 8.
• 04:02 The 8 is the early start for Task E.
• 04:04 8 plus 8 is 16, which is the Early Finish for Task E.
• 04:08 Now Task G has one predecessor, so its early start comes from Task F and is 12.
• 04:14 12 plus 4 is 16.
• 04:16 Task H has two predecessors, so
• 04:18 we need to use the largest Early Finish of those two to set the Early Start.
• 04:23 Well, Task S is 12 and task E is 16, so we use 16.
• 04:27 16 and 6 is 22.
• 04:29 Task I has one predecessor, Task E.
• 04:32 So the early start for Task I is 16.
• 04:34 16 plus 2 is 18.
• 04:37 Finally, Task J has three predecessors.
• 04:39 Again, we need the largest value of Early Finish to set the Early Start.
• 04:44 Task G is 16, Task H is 22 and task I is 18, so we use 22.
• 04:49 Now 22 plus 4 is 26.
• 04:52 The project will take 26 days to complete.
• 04:55 Let's get ready for the backwards pass.
• 04:57 We set the latest finish value of Task J equal to the Early Finish value,
• 05:02 which is 26.
• 05:03 26 minus 4 is 22 for the late start value for Task J.
• 05:08 The 22 then is used for the late finish value for tasks G, H and I.
• 05:13 Task G is 22 minus 4, which is 18.
• 05:16 Task H is 22 minus 6, which is 16.
• 05:19 And task I is 22 minus 2, which is 20.
• 05:22 Task F has two successor tasks, G and H.
• 05:26 We must use the smaller of the two Late Start values for the Task F Late Finish.
• 05:30 In this case, the value from Task H of 16.
• 05:34 Let's look at Task E next.
• 05:36 It also has two successor tasks, H and I.
• 05:39 The smaller of the two Late Start values is 16, so
• 05:42 that is the Late Finish for Task E.
• 05:45 Continuing on with task E, 16 minus 8 is 8.
• 05:48 The 8 becomes the Late Finish for Task C and 8 minus 5 is 3.
• 05:53 Let's go back up to Task F.
• 05:54 16 minus 3 is 13.
• 05:57 The 13 becomes the Late Finish value for Task D.
• 06:00 13 minus 4 is 9.
• 06:02 The 9 becomes the Late Finish value for Task B and 9 minus 2 is 7.
• 06:06 Task A has two successor tasks, B and C.
• 06:09 The smallest Late Start value of those two is the 3 from Task C.
• 06:14 So with Task A, we have 3 minus 3, giving us 0.
• 06:18 We got back to zero, so we did our math correctly.
• 06:21 Now we can do the final calculation, which is for the Task Float.
• 06:25 This is done for
• 06:26 each task by subtracting the Early Finish value from the Late Finish value.
• 06:30 So the float value for Task A is zero, B is four, C is zero, D is four,
• 06:36 E is zero, F is four, G is six, H is zero, I is four and J is zero.
• 06:43 The critical path is obvious.
• 06:44 It is the path where each task has zero total float.
• 06:48 It is the path A, C, E, H, I.
• 06:52 And that is how we do manual calculations of critical path and task total flow

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