# Network Analysis: Part 2- Worked Example (CPM)

### The Forward Pass

We can now calculate how long the project will take. Start by calculating the shortest time or ‘earliest finish’. Thus, if we start at time ‘0’ the earliest day that Designing can be finished is day 10. Therefore, the process of obtaining Approval cannot start until day 10: the earliest we can start obtaining approval is day 10, so the earliest finish for obtaining approval is 10 + 14 = day 24.

The earliest start time is written in the top left-hand corner of the task box, and the earliest finish time is written in the top right-hand corner of the task box.

For the Approval task, we thus say the Earliest Start Time (EST) is 10 and the Earliest Finish Time (EFT) is 24.

The earliest time both Approvals and Prepare site can start is day 10. So, the earliest finish time for Approvals will be 24 and for Prepare site day 17. However, Lay foundation cannot start on day 17 because Purchase materials has not been completed.

Note that the task Prepare site has some float or slack– it cannot start before day 10 and must finish before day 31 (start of Lay foundation), but as it only takes 7 days, there is a slack of 31 – 10 – 7 = 14 days.

When calculating the earliest times, one must consider all the paths or arrows coming into the task box and select the largest or longest time. Completing all the timings, or “Forward Pass” will result in a network picture as shown in Figure 3. The calculations show that the entire project will take 99 days- the ‘earliest finish time’ is 99 days.

Slack

You may recall that the task Prepare site had some slack available. The other tasks (i.e., those with no slack) are critical in that any delay in their completion will cause the entire project to be late. Thus, it is very important to discover the critical tasks and identify the critical path through the network.

Critical Path

Next, we need to find the Critical Path- the shortest time path through the network. In such a simple network it is easy to calculate the amount of slack available for each task. However, in complicated networks it is not easy to ‘see’ which tasks have slack and which zero slack.

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