Critical Path Method

When I was preparing my PMP exam, it was tough for me to understand this CPM concept. I watched tons of videos and read blogs, but nothing was working for me. Eventually, after a hard practice, I cracked the way out.

Today, I am going to discuss the easiest of the methods to understand concepts. If you are going for a PMP exam, then make sure to draw the network diagram always as there may be more than one questions relating to that network. But if you got a network diagram already in question, then you just need to visualize and crack the questions.

You may also like: PERT & CPM.

Moreover, in a project management life, the understanding of critical path is the primary area to be discussed on daily, weekly and monthly meetings. That’s why to understand every concept is quite remarkable.

Let’s see how to get a network diagram from the given table or conditions.

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What is Critical Path?

On any network diagram, if you see a path met with below conditions, then it is a Critical Path.

  1. The longest path in the complete network diagram
  2. The path with the shortest duration to complete a project.

There are some conditions like every activity should be connected. See if you find if more are mentioned on given data.

How to Find Critical Path?

To find a critical path on any project or given conditions you need to follow the below steps;

Step – 1: Construct a network diagram.

Step – 2: Determine the Project Completion time.

Step – 3: Perform Forward and Backword pass (Not necessary every time!)

Step – 4: Calculate the float.

Step – 5: Mark the Critical path with zero float activities.

How to Draw a Network Diagram?

First of all, we need data in tabular form or in any proper format;

Activities NameABCDEEG
PredecessorAA, BDC, EE
Time (Days)79128955

Now, read it and see all the conditions to implement during a draw. If you are doing it on a plain paper, then make sure to use boxed and right angles. This will avoid you to mess around the things and logics.

Below is the standard representation of terms. You can go for your understanding, but it must be consistent and logical. PMBOK does not constraint it anyways. For float, I will put on top of the box that you will see in our network diagram.How to represent an activity on network diagrams

First of all, let see the technologies we will use in it;

  •  Early Start – ES
  • Early Finish – EF

we will get by using  forward pass, and then

  • Late  Start – LS
  • Late  Finish – LF

we will get by using a backward pass.

Then we will calculate the float that will help to find a critical path.

First of all, I put all the activities as per given condition on our table. I have also applied the logic as you can see.

How to plot activities with logic ate CPM

Forward Pass in CPM

Now, we will calculate forward pass. for this you can start with 0 0r 1. There is no condition, but in PMBOK they took 1. This is logical as my first day on any project should be 1, not the 0 days. Still, some school thoughts agree to start with 0. Like they have zero semesters in a college 🙂

I will explain below how I have calculated the forward pass.

Forward pass on a network diagram

From the start, I put 1 and added 7 and then minus one and hence the formula is like

  • Early Start (ES) = Early Finish of predecessor activity + 1
  • Early Finish (EF) = Activity Time + Early Start of Activity – 1

I did the same keeping in view the logics as shown in as per arrowheads. Hope I am clear till now. If you feel any nag comment below and I am happy to answer.

Backward Pass in CPM

The next step is to calculate the Backward pass. it is the same as forward pass, but this time we need to keep in view the below formulas;

  • Late Start (LS) = Late Finish of Activity – Activity Time + 1
  • Late Finish (LF) = Late Start of Successor Activity – 1

Backward pass calculations in a CPM

Float calculation in CPM

This one the most natural part in CPM but the most important one. it helps to locate the critical path in a particular network.

Below are the simple formulas to calculate float;

  • Total float for an Activity  = LS of Activity – ES of Activity
  • Total float for an Activity  = LF of Activity – LF of Activity

You can apply any, and the answer will be the same. If not, then you are doing something wrong.

Float Calculation in CPM

Locating the CPM

You need to find all the activities with zero float, or we also call it slack.

In our network diagram, there are different paths like;

  1. Start – ACF – Finish
  2. Start – BDEG – Finish
  3. Start – AEG – Finish
  4. Start – AEF – Finish
  5. Start – BDEF – Finish

But we have to look for a path having all the activities with zero float on. In our diagram, Activities BDEF are with zero floats, and hence this is the critical path. This is the longest path also with 32 days. Rest is less, you can calculate by your own.

Critical Path on a CPM

That is how you can calculate a critical path. But as I said earlier, you need not go for forwarding and backward path in most of the PMP  exam. Just calculate the longest path from activities durations and check all the possible paths in glace and hopefully, you will get it right or else you can calculate this method – Practice it hard and let me know in comments if I can add more on it.

Zero-Day Start | Method

If you belong to other schools of thought then you will get a final shape like below picture;

CPM zero start method

Final Words

I have explained this with a bit complex diagram so that if you get a hard question, still you can calculate it easily. I got a question that to estimate free float and total float on a particular activity and I just found out that this activity is on a critical path and hence I select the answer as zero.

You will get a plain paper and a lead pencil during your PMP exam and make sure to draw boxes for activities and join them with straight and right-angle lines so that you don’t mess up there.

Good Luck! Any question or you found any mistake – comment, please.

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