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Critical Path Method (CPM) charts are similar to PERT charts and are sometimes known as PERT/CPM. In a CPM chart, the critical path is indicated. A critical path consists that set of dependent tasks (each depend on the preceding one) which together take the longest time to complete. Although it is not normally done, a CPM chart can define multiple, equally critical paths. Tasks which fall on the critical path should be noted in some way, so that they may be given special attention. One way is to draw critical path tasks with a double line instead of a single line. 

Tasks which fall on the critical path should receive special attention by both the project manager and the personnel assigned to them. The critical path for any given method may shift as the project progresses; this can happen when tasks are completed either behind or ahead of schedule, causing other tasks which may still be on schedule to fall on the new critical path.

Around 1957 the Critical Path method (CPM) was developed to assist in the building and maintenance of chemical plants at du Pont.

Critical path analysis (CPA) is used to organize and plan projects so they are completed on time and within budget. The project is structured so tasks that are dependant on each other are identified so that critical tasks can be identified.

CPA is similar to PERT but uses a deterministic model, ie. the duration of the activities and their cost are know with certainty.

Our first step is to decide what our tasks are, which tasks depend on which and how long they will each take. 

Once we have defined the relationship between the tasks and their duration we can derive two number for each task:

• The earliest starting time for the task (EST). Starting from the earliest (starting) task in the project, the EST of the task is the EST of the preceding (dependant) task plus the previous one’s duration. This is calculated for each task. 

• The latest starting time for the task (LST). Starting with the last task in the project, the LST of the preceding task is the LST of the task minus its duration. This is calculated for each task.  

The difference between these two numbers is the float of each task is its float.

This approach can then be used to identify critical tasks (to the project).

These are tasks that, by definition, cannot be delayed or take longer than their estimate without impacting the time the overall project will take. There is no slack (or float) in them.

These tasks give the critical path. Other tasks in the project can be delayed or take longer without affecting the duration of the project (providing they remain within their float). 

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