The Critical Path Method

In the field of project management there is a useful tool. Known as The Critical Path Method, it  that can used for planning any project that involves several tasks. You can use it to build a habitat on Mars or to bake several cakes. This is a useful tool.

  • CPM calculates the longest path of planned tasks to the end of the project.
  • The earliest and latest that each task can start and finish without making the project longer
  • Determines “critical” tasks (on the longest path). 
  • It prioritize activities for the effective management and to shorten the planned critical path of a project by pruning critical path activities

Here is an example.

Let us say you have a project and to complete the project you need to do several tasks (Task A to Task H).

Before you can draw the project network diagram of the CPM, here are the 3 stages you need to do.

Stage I 

  • Break project into tasks necessary for completion 
  • Determine sequential relationship of tasks 
  • Every task must have event to mark commencement – i.e. completion of preceding task 
  • Can tasks overlap? If it does, then these tasks can be done in parallel

Stage 2

Once you have done the above , put the tasks in an easy to understand form like the figure below.

   Figure 1


Stage 3

The proceed to put these tasks in the Task Identity Box (TIB)

   Figure 2


Definition of terms used

Early Start (ES) – the earliest the task can start

Early Finish ( EF) – is the earliest calculated time a task  can end

Late Start (LS) is the latest time a task can start without delaying the project

Late Finish (LF) latest time a task may be completed without delaying the project

Duration – is the time taken to complete the task

Slack or Float is the amount of time that a task in a project can be delayed without causing a delay to the project

Since you have 8 tasks, you must have 8 TIBs in your project network diagram and it should look like the figure below.

Figure 3

Once you have done the above, it is time to fill up the boxes with some numbers. Time for the Forward Pass and the Backward Pass.

The Forward Pass is used to move forward through the network and Backward Pass is the opposite.

Let us find the earliest time to start (EF) and to finish (EF) each task and to do that we use the forward pass

EF = ES + Duration

The project network should look like the figure below

Figure 4

After doing the forward pass, the next step is do the backward pass to find the latest start (LS) and latest finish (LF)  time.

As the name suggest we do the calculation going from front (the last TIB) to the back ( the first TIB)

For task H

Figure 5

Then we go backwards. Task H is dependent on two other tasks, G and E.


    Figure 6


Looking at TIB E, we can see that there is a slack/float  time of 7 days. This is from

Slack / Float = LF-EF

We can find the late start (LS) time by using

LS = LF – Duration

A point to note here is that the difference between Early Start and Late Start, must be the same as the difference between Early Finish and Late Finish


Exploring the TIB E backwards, we get

Figure 7

We can see that for TIB F,  the slack/float time is 8 and for TIB D the slack/float time is 7

For TIB B we get the LF time of 10, using the smallest ES value of the two tasks it precede. This is logical as task B must finish before the task with with the smaller value of LS, in this case task D can start. If task B late finish is 11 than this means task D will start on the 11 and finish one day later at 14 and affect task E which will eventually delay the project.

Doing the backward pass for task C and A, we get

 Figure 8


 The completed project network look like the figure below.

Figure 9

Total slack/float time of this project is the sum of all the individual tasks slack/float time, which in this case is 29 days.

Figure 10

The red arrow shown in the figure above shows the critical path of the project.

Critical Path Analysis is an effective and powerful method of assessing: 

  •          Tasks which must be carried out 
  •          Where parallel activity can be carried out 
  •          The shortest time in which a project can be completed 
  •          Resources needed to achieve a project 
  •         The sequence of activities, scheduling, and timings involved 
  •          Task priorities

So next time you have a project and find it difficult to cslculate the shortest time the project can be completed, try the CPM.