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## The Open University

Skip to 0 minutes and 1 secondSPEAKER: This video will introduce you to some of the basic elements of the critical path method. The critical path is the longest set of activities in a project that have to be completed on time if the project is going to finish on time. First, we need to calculate the duration of the whole project. We can do this by adding together the durations of each activity on the critical path. This Gantt chart shows a project that has just four activities. Shopping, cooking, laying the table, and eating. This means that while the cooking and clearing can start once the shopping has been done, Tom and Sarah will have to wait until both of these activities are complete before they can eat.

Skip to 0 minutes and 45 secondsIn this case, the critical path activities are A, B, and D. Activity A, shopping, starts at 0 and ends at 40 minutes. Activity B, cooking, starts immediately after the shopping, at 40 minutes and lasts for half an hour, until 70 minutes. Finally, activity D, eating, has to wait until the cooking is finished, so it can start at 70 minutes. Eating takes 50 minutes, so we can work out that the whole project lasts for 120 minutes. As you can see, activity C, laying the table, is not on the critical path. Taking the project completion time and the activity durations, we can calculate the early start and early finish dates.

Skip to 1 minute and 35 secondsThe early start date is the earliest time when work can start on an activity, while the early finish date is the earliest time an activity can be completed if it is started as soon as possible. The late start and late finish dates are similar. To work out these times, we need to go to the end of the project and work back from there. Here, we will start with the last activity, eating the meal. The project is due to last 120 minutes. So the late finish date is 120. To calculate the late start date, we subtract the duration of the activity from its late finish date.

Skip to 2 minutes and 15 secondsIn this case, the late finish date is 120 while the duration is 50, leaving a late start date of 70 minutes. Now, we can turn to the previous activities, cooking and laying the table. The late finish date of these activities is the same as the late start date of the activity that follows them. This is because they have to be completed before the next activity can commence. Finally, we come to activity A. The late finish date of activity A depends on the activities that follow it, activities B and C. The earliest late start date between activities B and C is Activity B, with a start time of 40 minutes.

Skip to 3 minutes and 0 secondsSo the late finish date of activity A is 40, while, because the duration of activity A is 40, the late start time is 0. Now we've filled in the table, we can see that there are some activities which have the same early and late start dates as well as the same early and late finish dates. These are activities A, B, and D. These activities are called the critical path. We define them as critical because they cannot be delayed without effecting the project generation. These activities contrast with activity C. How long activities can be delayed without affecting the end date of the project is called the project float.

Skip to 3 minutes and 45 secondsThis can be worked out by subtracting the early start dates from the late start dates. In this case, it is 60 minutes minus 40 minutes, meaning there are 20 minutes of float available on this project.

# Introducing the critical path method (CPM)

The critical path method (CPM) is a technique based on calculating the start and end dates of project activities given their duration and dependencies on one another (in other words whether one has to take place before another can happen).

Understanding how CPM works will help you decide which activities can be run in parallel.

The necessary information for constructing a CPM is as follows:

• list of activities
• the duration of each activity
• the priorities or in other words, the predecessor(s) of each activity.

The CPM returns:

• The final project end date: how long will the project take if it starts at day 0?
• Earliest start and end dates for each activity: taking into consideration which activities need to take place before others can happen, how soon can each activity start and end?
• Latest start and end dates for each activity: taking into consideration which activities can only happen after others have taken place, how late can each activity start and end without delaying the whole project?
• Critical path(s): a sequence of activities starting from the first activity of the project and ending with the last. Activities on a critical path cannot be delayed without extending the project duration
• Possible floats of activities: the possible delays that activities not on the critical path can tolerate without affecting the project duration.