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Critical Path Method

The critical path method, or CPM, was developed by DuPont, to analyse the process of shutting down plants for maintenance, then restarting them at the end of the maintenance cycle. The process involved in this was so complicated, that the critical path method had to be developed to identify and prioritise the vital activities. Similar to a Gantt chart, the CPM provides a graphical representation of the project, and the times expected to complete each activity. However, the CPM does not fix the start and end times of each activity; rather it is used to determine the activities which fall on the critical path. The critical path is the path where all activities directly follow each other, and hence there is no idle time. As such, the length of the critical path determines the total time taken for the project.

The main difference between CPM and the Gantt chart is that CPM displays the activities as single nodes, with the dependencies as lines connecting the nodes. As such, the CPM shows all the paths and dependencies which will be followed throughout the project. This allows project managers to determine which paths will have some idle time, and which will be critical to the final project completion time, thus enabling project managers to prioritise resources to the critical path.

Steps in the CPM

1. Identify the individual tasks required
2. Identify any dependencies, and hence the sequences of tasks
3. Draw a network diagram to represent these tasks.
4. Obtain estimates of the time each task will take
5. Identify which path is the critical path: usually the path with the longest duration
6. Keep the network diagram and critical path up to date throughout the project

Identifying the individual tasks is generally done from the work breakdown structure. This enables a list of all tasks to be constructed. This list can also be used to determine which activities are dependent on others. The network diagram is constructed starting with the activities which have no dependencies. From these activities, lines can be drawn to indicate the activities which depend on them, and then the next stage of activities and so on, until the final activities are known. The time each task is likely to take can be estimated from previous projects, extrapolated from the technical requirements of the task, or simply estimated by an subject matter expert. The time estimates do not include any potential uncertainty or delays, and hence will generally consist of conservative estimates.

Once the network has been completed, the critical path can be determined. This path is the one with the longest total duration of all activities. As this path has the longest duration, it will correspond to the length of the project, and any delays to the critical path will hence delay the project. The critical path is determined by finding the earliest start time, earliest finish time, latest start time and latest finish time for all activities, based on the requirements of other activities. For example, the first activity in the project will have earliest and latest start times of 0, and the earliest and latest start times will be the duration of the project. The earliest start and finish times for other tasks will then depend on the speed at which all the preceding activities can be completed. This can be used to find the earliest start and finish time for all tasks in the project. The latest start and finish times can then be identified from the latest time that tasks would have to start and finish to avoid delaying the task in front of them. Most tasks will have some difference between their earliest and latest times, as tasks ahead of them will depend on other tasks that finish later. However, there will be one path through the network where the earliest and latest times are all the same. This is the critical path.

However, it is important to note that the CPM does not allow any uncertainty in duration of the tasks, or in the project completion time. Whilst this makes the analysis and path analysis simpler, it does not reflect real life, where tasks may be delayed, or may be completed ahead of schedule. This uncertainty limits the extent to which CPM is useful in the real world.

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