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PMEducation
CRITICAL PATH METHOD (CPM)
TUTORIAL
Project Steps
Click on any photo to get to a project step
This method will show you how to construct a schedule in the Critical Path Diagram form. A Critical Path Diagram (CPD) shows project duration, Activity Durations, and the logical sequencing between Activities. It is an excellent tool for planning and reporting your time plan. Computer programs are available to create CPD's, but being able to draw one by hand is the best way to understand how they work.
There are various conventions for CPD symbols, legends, and starting dates. What follows is a simple stepbystep method that never fails if you follow it carefully. Caution ! do not jump ahead, but follow each step, stepbystep to ensure success. An example is shown on this Power Point, and it follows these steps:
1) Start with your Activity list. Here is where you have inserted Activity attributes such as Activity name, predecessors, successors, and durations.
2) Draw an Activity box for the first Activity. Each Activity box contains 7 compartments.
3) Insert the Activity number and the Duration in the Activity box.
4) Draw the same number of lines from the Activity box as there are successors. You will find successors on the Activity List. The line length is in no way related to the duration.
5) Move down the Activity list to the very next Activity. Do not skip and do not leave any Activities out.
6) Draw an Activity box for that Activity at the end of the line from its predecessor.
7) Repeat steps 3, 4, 5, 6 until you run out of Activities.
8) Now we will begin to fill in the other 5 compartments in each Activity box. Start at Day 0 for the first Activity(ies), unless there is a delayed start. Think of this as being the end of the day before you begin (like Christmas Eve!). Insert all the Earliest Finish (EF) dates by adding the duration of each Activity to its predecessor's EF date. This working from LEFT to RIGHT is sometimes called a forward pass.
9) In doing a forward pass, when you come to a converging junction in (lines coming together, from left to right), pick the biggest EF at the junction to calculate the successor. This is because all the Activities at the junction need to be completed before you can move on to the next Activity.
10) The EF of the last Activity is the end date of the project.
11) You will have noted that your project contains parallel paths. Calculate the total duration for each path separately. The longest path is called the Critical Path and it is the length of time leading to the end date of the project. The other paths are called NonCritical Paths, and they have some room for delays without affecting the project end date. This "room for delays" is called path slack and is calculated as the arithmetic difference in path length compared to the Critical Path length.
12) Since the paths take different lengths of time, those Activities on the NonCritical paths (NonCritical Activities) have flexible start and finish times. That is up to some point, they could start later and finish later, and still not affect the total project end date.
13) We already calculated the EF for each Activity in Step 8, 9 and 10. Now we will calculate the Earliest Start for each Activity. Follow carefully as this can be tricky. On the Critical Path and going from LEFT to RIGHT (forward pass), calculate the ES for each Activity on the Critical path. The ES for your first Activity (ies) is 0. The ES for each following Activity is just the EF of the preceeding Activity.
14) Still on the Critical path but this time going from RIGHT to LEFT (sometimes called backward pass), calculate latest finishes and starts (LF and LS) as follows. Start with the last Activity having LF=EF because it is critical. Next subtract from the LF the duration of the last Activity to get the LS for the last Activity. Note the LF of each Activity is just the LS of the successor Activity. Note: As you progress backwards through the Critical path you will observe that the Early dates equal the Late dates, because on the Critical path there is no path slack.
15) Next we will calculate the Earliest Start (ES) dates for Activities not on the Critical path (Noncritical Activities). Go from LEFT to RIGHT and starting at the launching point off the Critical path, insert the ES for each Activity. Remember: the ES for each Activity is just the EF of the preceeding Activity. As in Step 9, in doing this forward pass, when you come to a converging junction (lines coming together, from left to right), pick the biggest EF at the junction to calculate the successor.Stop when you get back to the Critical path.
16) Finally we will calculate the Latest dates for Activities not on the Critical path (Noncritical Activities). Go from RIGHT to LEFT and notice the LS of the successor Critical Activity. This will equal the LF of the last noncritical Activity (ies).In this backward pass, when you come to a converging junction pick the smallest LS at the junction to calculate its predecessor.
17) Then subtract the duration of that last noncritical Activity to get the LS for that Activity.
18) Continue calculating backward from LF's to LS's by subtracting durations as you go back. Stop when you get back to the Critical path. Repeat, calculating LF's and LS's on the other noncritical paths.
You should now have ES, EF, LS, LF, durations and Activity name (or number) filled in for every Activity on your Critical Path Diagram.
19) The last step to completing your CPM diagram is to calculate Total Float (TF) for each Activity. Total Float is the amount of time that an Activity can be delayed, from its Earliest Start, without delaying the project completion date.The formula is TF = LFEF.
Let's use this CPM diagram to learn more about the project. You will want to print out the last slide of the Power Point, to refer to. We already know the project duration which could not be determined from the Activity list alone. We also now know the Critical path and the Path Slack for the noncritical paths. Try these Questions and Answers:
Q1) On which path could you afford to have some slippage in dates?
A1) Path B has the most path Slack so could afford to slip a bit.
Q2) How much slippage could Path B afford.
A2) Path B Activities could slip (2114=) 7 days without affecting the project finish date. Note this is also equal to the Total Float on Path B.
Q3) Can Path A allow some slippage?
A3) Yes Path A can allow 3 days of slippage, the TF of Path A, without affecting the finish date.
Q4) If we have available skilled resources from Path A (or B) where should we put them.
Q4) Apply surplus resources to the Critical path, Path C.
Q5) What happens to the finish date if Activity 7 takes 10 days instead of 6 days, but starts at the ES of day 4.
A5) It will finish on Day 14, thereby using up all the Total Float plus one more day. Then Activity 8 will start on Day 14 and end on Day 15. This will affect the end date of the project which will become Day 22 instead of Day 21. In fact the Critical path would become path A, instead of path C. We see then, a project will finish later by the number of days any Total Float is exceeded. Total Float is a measure of how tightly the Activity is tied to the finish date.
Q6) What happens to the finish date if Activity 6 takes 6 days longer than planned.
A6) No change to the finish date because the additional duration (6 days) is within the Activity's Total Float (7 days).
Q7) What happens to the finish date if we save a day on Activity 4 but lose it on Activity 10.
A7) No change. Both Activities are on the Critical path.
Q8) What happens to the finish date if we save 2 days on Activity 7 and lose one day on Activity 9.
A8) The project will take one day longer and finish on Day 22. Saving time on a noncritical path does not reduce the overall project duration. Only by saving time on the Critical path can we shorten the project duration.
Q9) What is the latest that Activity 6 can start without affecting the project finish date.
A9) Day 13, the Latest Start (LS) for that Activity.
Q10) If Activity 5 starts on day 11, what is the latest that Activity 6 can start without affecting the project finish date.
A10) The latest Activity 6 can start without affecting the project finish date is Day 13, its LS. The start of one Activity does not affect the Latest Start of another. LS is simply the latest that Activity can start without affecting the finish date. Remember, the CPM is best as a planning tool, not a history recording tool.
Q11) What happens to the finish date if Activity 10 takes 3 days.
A11) Adds 2 days to Critical Path. Project ends 2 days later, on Day 23
As a review, here is a video showing how to make a CPM diagram. You will note some differences in this video. For example the Activity box has only 6 compartments (missing Total Float). He goes fast so pause often to see each step.

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