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

## The Backward Pass

Till now we have calculated the Earliest Start Time (EST) and the Earliest Finish Time (EFT) for each task. Next, we need to re-time the network starting at the end and calculate the Latest Start Time (LST) and Latest Finish Time (LFT) for each task.

Therefore, starting with the earliest finish time for the whole project (99 days), we subtract the time of the last task (7 days) to obtain the latest time the finishing task can start without affecting the outcome.

Note that when making the backward pass to calculate latest times, one should consider all arrows coming out of a task box and choose the lowest or shortest time to that task. Completing this procedure for all activities yields a network picture as shown in Figure 4.

Slack

Now that we have completed the timings by a forward and backward pass, we can look for slack. In this simple network it is easy to see that the task Prepare site has slack. As mentioned earlier, Prepare site can start on day 10 but must finish by day 31. Since it takes only 7 days to complete, the slack is 14 days. We will write the slack in the empty slot in the bottom centre of the box. The remaining tasks have no slack at all (Figure 5).

The Critical Path

To find the critical path, we look at the tasks whose earliest and latest start times are identical. Next, we determine which path between such tasks has no slack. By definition, that path is the critical path. The critical path is indicated by bold lines in Figure 6.

## Conclusion:

In its modern form, network analysis incorporates elements of both PERT and CPM. The presence of slack indicates that a task may be completed later than the Earliest Finish Time (EFT) without affecting the overall project duration. The critical path is the shortest path through the network and has no slack. Any delay in the critical path will delay the project.

## Useful Links:

Link to the first article in this series:

https://communitymedicine4all.com/2020/12/30/network-analysis-part-1-overview/

Link to notes on Operations Research by JE Beasly:

http://people.brunel.ac.uk/~mastjjb/jeb/or/netanal.html

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