New Zealand
Level 8 - NCEA Level 3

# Critical path analysis

Lesson

Let’s take a closer look at the network after completing the forward and backward scan in the last lesson:

Notice that there is a single path from start to finish through vertices where the earliest start time and the latest start time are the same - if we highlight this path, we have what is called the critical path.

The difference between the top and bottom numbers is called the float time (sometimes called slack time), and it tells you how much leeway there is on the task. Tasks that have a float time of $0$0 lie on the critical path - these tasks need your best people! Delays in these tasks will either result in an overall delay for the whole project, or additional expenditure to get things back on track (called crashing).

For the other tasks, you can see how much “extra time” the person doing it can take. I have put the float times for tasks not on the critical path within the vertex to illustrate:

It’s important for us to return back to the original motivation for the problem to interpret our results. We now have the earliest and latest start times for each task, but also the amount of time we have to waste for each task. Some observations:

• The tasks $B$B, $F$F, $J$J, and $L$L cannot have any delay.
• Task $M$M can take up to $13$13 days even though it only needs $5$5.
• Task $G$G can take $16$16 days even though it only needs $10$10.
• The tasks lying above the critical path ($A$A, $C$C, $D$D, $E$E, $G$G) have only $6$6 days of leeway between all of them. If task $A$A takes $7$7 days instead of $1$1, all subsequent tasks must be started on their latest start date in order to avoid delays.

What else can you observe?

### Outcomes

#### M8-5

Develop network diagrams to find optimal solutions, including critical paths.

#### 91576

Use critical path analysis in solving problems