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Calculate the Network
Critical Path
Example Schedule

After you have established the network logic, activity durations and drawn your network, the next step is to calculate the network. This operation tells you:

• Each activity's earliest and latest start and finish dates.
• The shortest possible project duration.

· Which activities must be completed on time if this shortest project duration is to be achieved. These are the critical activities, which together form the critical path.

· The amount of spare time available for non-critical activities. This spare time is called float.

You can calculate this information manually or using Hornet.

Hornet calculates the network using a time schedule to work out the project’s dates.

A time schedule works out the project’s dates by performing a forward pass and backward pass to identify float. It also helps to identify a project’s critical path.

Example schedule

Click here to jump to an example project illustrating the forward pass, backward pass and calculation of float.

Forward pass

The forward pass consists of working forwards through the network adding up all the activity durations to find the shortest possible project duration. It calculates how long the project would take if every activity started as early as possible: that is, if no preceding activities were delayed.

In other words, the forward pass shows the earliest date each activity can start (its early start date), and the earliest date it can finish (its early finish date).

Backward pass

The backward pass works out the latest time when the activities must start in order not to delay the project beyond the minimum project duration. It consists of working backwards through the network from the project end date, subtracting each activity duration.

In other words, the backward pass shows the latest date when the activity must start (its late start date), and the latest date it can finish (its late finish date).

In practice, the backward pass always reveals that extra time is available for some activities than the time needed. The extra time revealed by the backward pass is known as float.

Float

Float is the difference between the time necessary to complete an activity and the time available. Some, but not all, activities have float.

Total float

The period by which a non-critical activity can be delayed is the float. While there are other types of float, Hornet always shows total float, for which the precise formula is:

Total float = Late finish - early start - duration + 1

One time unit is added because the start and finish dates are inclusive.

Free float

The period by which a non-critical activity can be delayed without ani impact on succeeding activities is the free float. This can be thought of as the amount of slack available for this activity in isolation. Great care must be taken when considering free float, especially if project resources are limitied.

A series of critical activities forms a continuous path through every network. If any activity on a critical path is delayed beyond its early start date, the entire project will be delayed.

The critical path determines the shortest possible time the network will take to complete. If you know which activities are critical, it becomes much easier to control a project, because you know where to concentrate your attention.

There may be more than one critical path through a network if there is more than one series of critical activities forming a continuous path through the network and having the same maximum duration.

Float and criticality

Viewing the critical path

If you were working out a time schedule manually, you would perform the forward pass, the backward pass, and you would therefore know which activities were critical and which were not. By physically drawing a line linking the critical activities, you could identify the critical path(s) on your network diagram.

Hornet performs these operations for you. How do you look at the critical path? One of the easiest ways to view the critical path is in a bar chart. This is a typical Hornet bar chart.

The critical activities are represented by a red border, ordinary scheduled activities by a black border, while horizontal lines (=) indicate float. The critical path runs from one critical activity to the next.

Float and criticality

An activity that is not on the critical path can still be worthy of close attention. We have defined a critical activity as one that has the same start and finish dates on the forward pass as on the backward pass. However, there is another criterion for criticality, which is that critical activities do not have float.

Float is the period by which an activity can be delayed without delaying the project finish. Activities can have different amounts of float - 2 days, 10 days, 10 weeks, etc.

As a result, it can be important to keep an eye on activities that are not on the critical path but which have very little float or no float, as they too can have a significant effect on the project duration.

Network diagram

This network diagram shows a simplified project with four activities joined by start-to-finish links.

Logic

A and D are not dependent on any activity.

B cannot start until A is complete.

C cannot start until B and D are complete.

Forward pass

In the forward pass we find the early starts and finishes by adding up the activity durations.

A Can start on day l. As its duration is four days, it can finish on day 4.

D Can also start on day 1. As its duration is 5 days, it can finish on day 5.

B Is dependent on A, and therefore it cannot start before day 5. It will finish on day 7.

C Cannot start before B and D have finished. It will start on day 8 and finish on day 14.

The shortest possible completion time is therefore 14 days. The results are shown below:

D may finish on day 5, C cannot start until day 8 so D does not have to be finished until the end of day 7. We could delay D for up to 2 days without delaying the overall project. For example, if D required important resources, we could transfer those resources to more urgent tasks for two days. This is a powerful factor in managing projects.

Backward pass

We perform the backward pass working backwards from the project's minimum completion date, subtracting the durations from the project end date.

We start from the last day of the network, day 14, assuming that this is C's late finish. We subtract C's duration to find its late start (day 8). As B and D can finish the day before C starts, their late finishes are day 7.

We now subtract B's duration from its late finish (7-3). Its late start is therefore day 5. By the same logic, A must finish on day 4 and start on day 1.

At this point, because we know the earliest and latest dates in the network, we know the network early start date, the network early finish date, the network late start date and the network late finish date.

Critical activities

Activities A, B and C will all start and finish on the same days as indicated by the forward pass. They must start and finish on these dates to maintain project completion and are therefore critical.

When we subtract D's duration from its late finish, we find that it could start on day 3 without delaying completion. There is a difference of two days between the time necessary to complete D (5 days) and the time available for it (7 days). It is not critical.