Gantt Charts
Master Gantt charts for NSW Year 12 Mathematics Standard 2. A Gantt chart plots each activity of a project against time: every bar starts at the activity's earliest start time and its length is the duration, so the whole schedule — including the critical path and each activity's float — can be read straight off the chart.
You will learn to construct a Gantt chart from a precedence table and to interpret one: read an activity's start, duration and float, find the latest start time and the minimum completion time, identify the critical activities, and work out the effect on the finish of delaying a critical or a non-critical activity — a core Standard 2 critical-path skill for scheduling real projects.
Theory
A Gantt chart plots a project's activities against time so you can read the schedule at a glance. This Year 12 Standard 2 (NSW) guide shows how to construct and interpret one — reading each activity's earliest start, duration and float, finding the critical path and the minimum completion time, and judging the effect of delaying a critical or non-critical activity.
A Gantt chart is a horizontal bar chart that shows a project's activities against time. Each activity has one bar: it begins at the activity's earliest start time (EST) and its length is the activity's duration. Reading down the chart shows what runs when.
A light grey extension after a bar is that activity's float — the number of days it may be delayed without pushing back the finish. Its latest start time is \(\text{EST}+\text{float}\). Bars drawn in red have zero float: these are the critical activities, and together they make the critical path.
The minimum completion time of the whole project is where the last bar ends. This Year 12 Standard 2 (NSW) skill is to construct a Gantt chart from a precedence table and to interpret one — reading start, duration, float, the critical path and the completion time.
Everything is read straight off the bar for an activity:
How to construct and read a Gantt chart
- Scan forward. From the precedence table, each activity's earliest start is when its last predecessor finishes (activities with no predecessor start at day \(0\)).
- Draw the bars. Plot each activity from its earliest start, with length equal to its duration.
- Add the float. Show each activity's float as a grey extension; zero-float activities are critical — draw them red.
- Read the answers. Start day = bar start; duration = bar length; latest start = start \(+\) float; the critical path is the red chain; the minimum completion time is where the last bar ends.
Read the bar for \(C\), then the end of the last bar.
| \(\text{EST of } C\) | \(=\) | \(3\) |
| \(\text{duration of } C\) | \(=\) | \(7-3=4\) |
| \(\text{last bar } E \text{ ends}\) | \(=\) | \(7+2=9\) |
\(C\) starts on day \(3\), lasts 4 days, and the project finishes in 9 days.
Float is the grey length; latest start \(=\) EST \(+\) float; compare the delay with the float.
| \(\text{float of } C\) | \(=\) | \(8-6=2\) |
| \(\text{latest start}\) | \(=\) | \(2+2=4\) |
| \(\text{delay } 3\) | \(>\) | \(\text{float } 2\) |
| \(\text{new finish}\) | \(=\) | \(10+1=11\) |
Float \(= 2\) days, latest start \(=\) day \(4\); a \(3\)-day delay exceeds the float by \(1\), so the project now takes 11 days.
The red zero-float bars form the critical path; extra time on a critical activity adds on directly.
| \(\text{critical path}\) | \(:\) | \(A \to D \to E \to F\) |
| \(\text{current finish}\) | \(=\) | \(9\) |
| \(\text{extend } F \text{ by } 2\) | \(=\) | \(9+2=11\) |
The critical path is \(A \to D \to E \to F\); extending critical \(F\) by \(2\) days makes the project take 11 days.
Scan forward: each activity starts when its last predecessor finishes.
| Activity | Duration (days) | Preceded by |
|---|---|---|
| \(A\) | 3 | — |
| \(B\) | 2 | — |
| \(C\) | 2 | \(A\) |
| \(D\) | 4 | \(A, B\) |
| \(E\) | 3 | \(C, D\) |
| \(D \text{ waits for } A,B\) | \(=\) | \(\max(3,2)=3\) |
| \(D \text{ ends}\) | \(=\) | \(3+4=7\) |
| \(E \text{ ends}\) | \(=\) | \(7+3=10\) |
\(D\) starts on day \(3\), the project finishes in 10 days, and the critical path is \(A \to D \to E\).
Common pitfalls
Frequently asked questions
How do you read a Gantt chart?
Each activity has one horizontal bar. The bar starts at the activity's earliest start time, and its length is the duration, so the finish is where the bar ends. A grey extension after a bar is the float, and the whole project finishes where the last bar ends.
What does the float on a Gantt chart mean?
The float is the light grey extension drawn after an activity's solid bar. It is the number of days that activity can be delayed, or run over, without delaying the finish of the whole project. An activity with no grey extension has zero float.
Which activities are critical on a Gantt chart?
The critical activities are the ones with zero float, drawn in red. They have no grey extension, so any delay to them delays the entire project. Together, in order, they form the critical path.
How do you find the minimum completion time from a Gantt chart?
Look for the bar that finishes last and read where it ends on the time axis. That value is the minimum completion time of the project, assuming every activity starts as early as possible.
How do you build a Gantt chart from a precedence table?
Scan forward through the table: an activity with no predecessor starts at day 0, and every other activity starts when its last predecessor finishes. Draw each bar from its earliest start with length equal to its duration, add each activity's float as a grey extension, and colour the zero-float activities red.
What happens to the finish if an activity is delayed?
If you extend a critical activity, the extra time adds directly to the completion time. If you delay a non-critical activity, nothing changes until the delay is larger than its float; beyond that, only the amount over the float pushes the finish back.