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Critical Path Calculations

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About this lesson

Critical Path calculations are the method used to determine the critical path within a project.

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Quick reference

Critical Path Calculations

Critical Path calculations are the method used to determine the critical path within a project.

When to use

Normally, the critical path will be calculated by project management software once the project network diagram and task duration estimates have been entered into the software.  However, sometimes it is necessary to conduct the calculations manually.  Also, if you intend to sit for the PMP exam, you must be able to calculate critical path manually.  I believe the method shown below is the easiest and most straightforward of the manual techniques.

Instructions

  1. Create a project network diagram with all tasks.   I create a box (as shown below) for each task in the network and draw arrows between boxes to show the relationships.                                                    
  2. Estimate task duration for all tasks and put the duration in the center portion of the box.  I strongly recommend that you use consistent units.
  3. Starting with the first task in the network, set the Early Start (ES) equal to zero.
  4. Add the Duration to ES to calculate Early Finish (EF) for the first task in the network.
  5. The value of EF for the first task is the value of ES for the next task in the network, just follow the relationship arrow(s).
  6. Continue to the end of the project adding a task duration to each task’s ES to determine that task’s EF.  If a task has multiple input arrows, use the highest value of EF from predecessor tasks to set the ES.  You have now completed the “forward pass.”  The critical path may be obvious to you at this time, but you need to do the next steps to determine the task total float.
  7. For the final task or milestone in the network, set the value for Latest Finish (LF) equal to the value of EF for that task.
  8. Subtract the Duration from LF to calculate the Latest Start (LS) for that last task or milestone.
  9. The value pf LS for the last task is the value of LF for the next to last task, follow the arrow backwards.
  10. Continue subtracting the task duration from the LF for a task to determine the LS for that task until you have reached the beginning of the project.   This is referred to as the backwards pass.  If there are multiple arrows flowing back into a task, use the lowest value of LS from successor task to set the LF for that task.  The final value for LS that you calculate (which would be for the first task in the project) should equal zero.  If not you have made a mistake.
  11. Subtract the EF from LF for each task to determine the Task Total Float.
  12. Tasks with zero Float are on the critical path.

 

An example is shown below:

 

 

 

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  • 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.

Lesson notes are only available for subscribers.

Float, Slack, Buffer
6m:04s
Project Budget
6m:03s

PMI, PMP, CAPM and PMBOK are registered marks of the Project Management Institute, Inc.

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