Critical Path Calculations

Quick reference

• 00:05 Hi, I'm Ray Sheen.
• 00:06 I'd to show you how to manually calculate critical path.
• 00:09 Now if you're planning to sit for
• 00:11 the PNP exam, you will need to be able to do this calculation.
• 00:16 Over the years I've tried several manual techniques and
• 00:20 I have found that this approach works best.
• 00:23 I start off by creating a network diagram of all the project activities.
• 00:27 I represent each task with a box that looks like this.
• 00:31 The boxes are connected with the arrows that show their predecessor and
• 00:34 successor relationships between the task.
• 00:37 I get that right from the network diagram.
• 00:39 Now let me explain how each part of the box is determined or calculated.
• 00:43 The activity name or number is placed in the top section of the box.
• 00:47 The task duration estimate is in the center of the box.
• 00:50 The duration estimate is determined using the appropriate estimating techniques.
• 00:55 Use consistent units for estimates.
• 00:57 Everything in days or weeks.
• 00:59 Now we are ready to start the critical path calculation.
• 01:02 For the very first task in the network,
• 01:04 set the early start that is represented by the ES to zero.
• 01:08 This means we will start counting our critical path time
• 01:11 when the first task starts.
• 01:13 Next we add the duration to the early start and get the early finish or
• 01:17 EF value.
• 01:19 Now we take this value for early finish, and
• 01:22 we set that as the early start value for the next task in the network.
• 01:26 This indicates that the successor task can start
• 01:29 as soon as the predecessor task finishes.
• 01:32 We now proceed all the way through the network, adding durations to early start
• 01:36 for each task, to get the early finish for that task and then setting the early start
• 01:41 as the successor task equal to the early finish of the predecessor task.
• 01:45 If there are multiple predecessor tasks, you need to use the highest value of early
• 01:50 finish to set the successor task early start.
• 01:53 This means that once the last of the predecessor tasks is complete,
• 01:57 then the successor task can start.
• 02:00 Once you've completed the entire project,
• 02:02 you completed what's called the forward pass.
• 02:04 You may be able to recognize critical path at this point.
• 02:08 However to calculate the amount of flow for all the tasks that are not other
• 02:11 critical path, you will need to do what we call the backwards pass.
• 02:15 Let's look at how that works.
• 02:17 For the last task set the late finish, the LF portion of the box,
• 02:21 equal to the value of the early finish for that last task.
• 02:25 This indicates as soon as the last task is done we are done,
• 02:29 that is the latest time when the project will finish.
• 02:33 Now subtract the duration from that late finish, to calculate the late start or
• 02:37 LS value.
• 02:39 The late start value for the last task is the latest finish value for
• 02:43 the next to the last task, the predecessor to that last task.
• 02:47 Continue to subtract the duration from the late finish for
• 02:50 each task to determine the late start.
• 02:52 And then assigning that value to late finish of the predecessor task.
• 02:56 If a task have multiple successor tasks, you'll need to
• 03:00 use the smallest value of late start to set the late finish for that task.
• 03:06 All the predecessor task must have been accounted for
• 03:08 when determining the late finish of a task.
• 03:11 Once you've finished the backwards pass and get back to the original task,
• 03:15 the late start value for that first task should be zero.
• 03:18 If it's any other value, you've done your math wrong somewhere.
• 03:21 Now we can calculate the task total float,
• 03:24 subtract the early finish value from the late finish value for each task.
• 03:28 Any task with a zero value for task total float is a critical path task.
• 03:33 There will be at least one path and
• 03:36 possibly several paths to the project that are critical.
• 03:40 Let's go through an example.
• 03:41 In this example, there is a simple network of ten tasks.
• 03:45 The arrows show the predecessor and successor relationships and
• 03:48 the task durations are in the center of each task box, the units are in days.
• 03:53 The early start for the first task, task A is set to 0.
• 03:57 We then calculate the forward pass.
• 04:00 The task A early finish is 3, let's follow the top path first.
• 04:05 The task B early start is 3 from task A, and the early finish is 5.
• 04:10 The 5 goes over to task D, plus 4 is an early finish of 9 for task D.
• 04:16 Then on to task F, 9 and 3 is 12.
• 04:19 I'll stop at this stop path and look at the bottom path next.
• 04:23 The task C early start is from task A and that's 3.
• 04:26 The task C early finish is 3 plus 5, which is 8.
• 04:30 The 8 is the early start for task E.
• 04:33 8 plus 8 is 16, which is the early finish for task E.
• 04:38 Now, task G has just one predecessor, so
• 04:40 its early start comes from task F and is 12.
• 04:43 12 plus 4, 16.
• 04:46 Task H has two predecessors, so
• 04:48 we'll need to use the largest early finish of those two tasks to set the early start.
• 04:53 Task F is 12, task E is 16, so we use 16.
• 04:58 16 and 6 is 22.
• 05:00 Task I has one predecessor, which is task E.
• 05:04 So the early start for task I is 16.
• 05:06 16 plus 2 is 18.
• 05:08 Finally, task J has three predecessors.
• 05:11 Again, we need the largest value of early finish to set the early start.
• 05:16 Well G is 16, and H is 22, and I is 18.
• 05:19 So we use the 22.
• 05:21 Now 22 plus 4 is 26, the project will take 26 days to complete.
• 05:26 Let's get ready for the backwards path.
• 05:28 We set the latest finished value of task J equal to
• 05:31 the early finished value which is 26.
• 05:33 26 minus 4 is 22, for the late start value for task J.
• 05:38 The 22 is then used for the late finish value for task G, H, and I.
• 05:43 Task G is 22 minus 4 which is 18, task H is 22 minus 6 which is 16,
• 05:49 and task I is 22 minus 2 which is 20.
• 05:54 Task F has two successor values, G and H.
• 05:58 We must use the smaller of the two late start values for the task F late finish.
• 06:03 In this case, that's the value from task H of 16.
• 06:06 Let's look at task E next.
• 06:09 It also has two successor tasks, H and I.
• 06:12 The smaller of the two late start values is 16, so
• 06:14 that is the late finish value for task E.
• 06:17 Continuing on with task E, 16 minus 8 is 8.
• 06:20 The 8 becomes the late finish value for task C.
• 06:24 8 minus 5 is 3.
• 06:25 Let's go back up to task F now.
• 06:28 16 minus 13 is 3.
• 06:30 The 13 becomes the late finish value for task D.
• 06:33 13 minus 4 is 9.
• 06:35 The 9 becomes the late finish value for task B, and 9 minus 2 is 7.
• 06:40 Task A has two successive tasks, B and C.
• 06:44 The smallest late start value of those two is 3 from task C.
• 06:48 So, with task A we have 3 minus 3 giving us a zero for the late start.
• 06:54 Phew.
• 06:55 We got back to zero so, we did our math correctly.
• 06:59 Now, we can do the final calculation which is for the task to over float.
• 07:03 This is done for
• 07:03 each task by subtracting the early finish value from the late finish value.
• 07:08 So the total flow for task A is 0, task B is 4,
• 07:12 task C is 0, task D is 4, task E is 0, task F is 4.
• 07:17 Task G is 6, task H is 0, task I is 4, and task J is 0.
• 07:22 The critical path is obvious.
• 07:25 It is the path where each task has zero total float.
• 07:28 A, C, E, H, J.
• 07:31 And that's how we do manual calculations of critical path and task total float.
• 07:37 Your project management software will do these calculations for you, but
• 07:41 it's helpful to understand how they work.
• 07:43 And remember, if you change the network or
• 07:46 change an estimate all that math has to be redone.

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