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Critical Path Analysis

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Overview

The Critical Path Method (CPM) is a project management methodology which was developed by the Du Pont Company in the mid-1950s to assist in the construction of major chemical plants. A similar system known as Program Evaluation and Review Technique, PERT, was developed in the US Navy at about the same time and was successfully used in the development of the Polaris missile.

CPM and PERT differ in the way they use estimates of time, but are similar in the way they display the sequence of activities. Both techniques build on the concept of the precedent diagram or Dependency Chart introduced in the previous section. From this point on we shall concentrate on CPM but shall use the more familiar term CPA or Critical Path Analysis. 

Critical Path Analysis

Critical path analysis helps us determine:

  • How long it will take us to complete the project (assuming we have the necessary resources)
  • Those tasks that cannot be delayed if we want to meet the end date of the project (these lie on the critical path)
  • Those tasks that have some flexibility in their start and finish times
  • Where we most need to apply risk management
  • The impact of changes to the schedule on the overall duration of the project.

Critical path analysis is illustrated through use of the worked example we used earlier. Refer to Product Based Planning.

The Critical Path Convention

Critical path analysis requires us to make a number of calculations about when each activity must start and finish in order to ensure that the overall timescale for the project is not exceeded. To aid this process we redraw the dependency chart with each activity box segmented into smaller boxes. The convention is shown below.

Step 1 - Duration

We have estimated the following elapsed times:

  • Initiation Document - 3 days
  • Venue Specification - 3 days
  • Venue Selection - 6 days
  • Venue Contract - 3 days
  • Call for Papers - 15 days
  • Select Papers - 4 days
  • Speaker agreements - 4 days
  • Draft Advertisement - 3 days
  • Approved Advertisement - 3 days
  • Target Audience Identified - 3 days
  • Mailshot - 3 days
  • Registrations Received - 15 days
  • Conference - 1 day

The first step is to fill in the duration of each activity. This is written in the top centre box

 


Step 2 – Forward Pass

The next step requires us to calculate the earliest time we can start and finish each activity in the network. This will provide us with the shortest possible time to finish this stage of the project.

By convention, we start at 0. This is entered into the top left hand box of the first activity box providing us with the earliest start time (EST). The earliest finish time (EFT) is calculated by adding the duration of the activity to the earliest start time. This is entered in the top right hand box. So, for any activity:

EFT = EST + Duration

On any single path: 

EST of the following activity = EFT of the preceding activity

However, whenever we have two or more paths merging to form a single path, the EST of the following activity must be the same as the highest EFT of the preceding activities. This is because all merging paths must complete before the next activity can start:

EST of the following activity = Highest EFT of the preceding activities

Finally, the earliest finish time of the project overall is the highest earliest finish of any of the activities in the network.

EFT of the project = Highest EFT of all activities.


 


Part 3 – Backward Pass

If we want to complete our project in the earliest possible time, the earliest finish time of the project overall is also the latest finish time of the project. The EFT for the project is, therefore, copied as the LFT for the project in the bottom right hand box of final activity (or activities if there is more than one).

The backward pass is used to calculate the latest time we can start and finish any activity and still complete the project by the latest finish time of the project overall.

To calculate the latest start time of any activity, simply subtract the duration from the latest finish time. This figure is entered into the bottom left hand box.

LST = LFT – Duration

For activities having only one following activity, the latest start time of the following activity becomes the latest finish time of the current activity. So working right to left in the diagram (backward pass):

LFT of the preceding activity = LST of the following activity

However, where we have two or more paths following a single activity the LFT of that activity must be the same as the LST of all the following activities. This is because no following activity can start until the preceding activity has finished.

LFT of the preceding activity = Lowest LST of the following activities

Finally, the latest start time of the project overall is indicated by the latest start time of any activity in the network, which is clearly 0, as defined at the beginning.

LST of the project = Lowest LST of all activities


 


Step 4 – Calculating the Float

The float tells us how much flexibility we have to delay the start or finish of any activity in the network and still manage to complete the project by the latest finish time.

This is useful for project managers as it helps both in resource allocation and in risk determination.

Looking at ‘Specification’, we can see that there is a difference of 11 days between the earliest start time and latest start time (and between the earliest finish time and latest finish time). That means we could delay the start or finish of this activity by up to 11 days without jeopardising the project end date. We might choose to do this if we have resourcing problems at this point in the project. It is worth noting, however, that if we use up the float on one activity, we also use up the float on subsequent activities on that path.

Float = LFT – EFT (or LST - EST)

 


Step 5 – Identifying the Critical Path

We can see from the diagram that some activities have zero float. This is where:

EST = LST and EFT = LFT

There is no opportunity to delay the start or finish of these activities without jeopardising the overall duration of the project. These activities form a path through the network known as the Critical Path.

The Project Manager should pay particular attention to the risk of any of these activities being delayed as the room for re-scheduling may be restricted.