As we saw in the introduction to critical path analysis, an activity network is a graphical representation of activities and events that are needed for a process. There are several rules that have to be obeyed when creating accurate networks.

These rules are:

1. An edge is used to represent an activity.
2. A vertex represents an event, which is the start or end of one or more activities.
3. Events are numbered so that the activity ends at a higher numbered event than it started.
4. Events are numbered so that no activity starts and ends at the same event. An activity can therefore be uniquely identified by its start and end events.
5. In order to avoid ambiguity between activities you must use ‘dummy’ activities. These are activities that have zero length and are inserted to ensure that precedence requirements are met. They allow two activities that ought to have the same start and end events to be distinguished.
6. There should only be one start event and one finish event.
7. The activity detail (or code) and duration are written along the edges.
8. The edge length has no meaning.

Using these rules you should be able to create activity networks for any process that involves more than one activity.

Once you have drawn out an activity network the next step is to work out the earliest and latest possible times for each event. This will let you find the minimum time necessary for the tasks to be completed taking activity precedence into account.

In order to make the identification of earliest and latest times easier, they are often put into a pair of boxes. The left box will be the earliest time and the right box will be the latest time. When working out the earliest times for each event you must start at the first event and assign an earliest time of 0. Work through each event in turn. Add the duration of the activity to the earliest time of the start event to get the earliest time of the end event. If there is more than one way of arriving at the end event then take the largest value for the earliest time.

Once you have gone through the entire network assigning earliest times you can begin to work out the latest times. This is done by starting at the last event and working backwards though the network. To start the process let the latest time of the last event be equal to the earliest time of that event. By subtracting the duration of an activity from the event that it ends at you will be able to find the latest time for the start event for that activity. If there is more than one way to arrive at a start event then take the smallest value for the latest time.

By looking at the earliest / latest times for the last event you will know the minimum duration for the overall process.

Once you have decided on the critical path for an activity network you will need to allocate resources to each task.

Resources could take the form of equipment, people, money, or any number of other things. Most often we will use people. The question you need to ask yourself is “how many people do I need so that the project can be finished without any delay?” In answering this question you are halfway to allocating resources.

In the example we have been looking at, there are at most three things that can be happening at any one time. Do we need to use three people, or will two people be enough (have we got enough time to complete H and I before G is completed)? Looking at the activity network we can see that there will not be enough time to do this.

Another way of showing the resources needed is to draw a cascade chart and then a resource histogram.

The cascade chart in figure 2 shows the critical path on the lower row and has a row for each of the other activities, starting at their earliest time and showing float at the end. This allows the viewer to see where activities can be collapsed down to be allocated to a single worker. The collapsed form, as a resource histogram, is shown in figure 3.