Module 6 · Networks and Critical Paths

Gantt Charts & Resource Allocation

Drawing Gantt charts from EST values · Reading schedules · Crashing the critical path

MST-12-S2-07 MST-12-S2-07 Lesson 10 of 12
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Orient and prepare

Connect the CPA results to the purpose and language of a Gantt chart.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

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Think First

A project manager has completed all the critical path calculations. She knows which activities are critical and which have float. Now she needs to present the schedule visually to her team.

Before reading on, how might you represent the start time and duration of each activity on a single diagram? What information would be most useful to show?

Learning Intentions

  • Draw a Gantt chart from EST values, showing each activity as a horizontal bar
  • Read a Gantt chart to determine start times, durations, and float windows
  • Distinguish critical activities (solid bars) from non-critical activities (bars with float windows)
  • Explain crashing: reducing a critical path activity's duration to shorten the project
  • Identify which activities can be crashed and the effect on project completion time

Key Terms

Gantt chart
A horizontal bar chart showing each activity as a bar spanning its start and finish times. Activities are listed on the vertical axis; time on the horizontal axis.
Bar length
Represents the duration of the activity. Start of bar = EST; end of bar = EST + duration.
Float window
Shown as a dashed or shaded extension after a non-critical activity's bar, indicating the latest possible finish time.
Crashing
Reducing the duration of a critical path activity (by adding extra resources) to shorten the overall project time.
Crash time
The minimum possible duration of an activity after crashing (adding maximum extra resources).
Resource allocation
Assigning workers or equipment to activities, using float windows to smooth out resource demand peaks.
2

Draw a Gantt chart

Turn EST values and durations into correctly positioned activity bars.

1

Drawing a Gantt Chart

A Gantt chart translates the numerical results of a CPA (EST values, durations, float) into a visual bar chart that is easy for teams to follow.

Steps to draw a Gantt chart

  1. List all activities on the vertical axis (usually in alphabetical or logical order).
  2. Draw a horizontal time axis, start at 0, end at the minimum project duration.
  3. For each activity, draw a solid bar starting at its EST and ending at EST + duration.
  4. For non-critical activities, add a float window (dashed box) extending from the end of the bar to LST + duration (= LST(end node)).
  5. Use a different colour (or pattern) for critical activities vs non-critical activities.
Exam convention: In HSC exams, critical activities are typically shown as solid shaded bars; non-critical activities show the float window as an open or dashed bar.
Worked Example 1, Gantt chart from CPA results

Project data (from Lesson 9 Worked Example 2):

Activity Dur EST Float Bar: start → end Float window
A2000 → 2None (critical)
B4202 → 6None (critical)
C3242 → 55 → 9 (4 days)
D5606 → 11None (critical)
E2545 → 77 → 11 (4 days)

On the Gantt chart, A, B, D are solid (critical); C and E have dashed float windows after their bars. The chart spans from 0 to 11 on the horizontal axis.

On a Gantt chart every activity is one horizontal bar: it starts at the activity's EST and its length is the duration, so it ends at EST + duration. A non-critical activity carries a dashed float window after its bar, running out to the LST of the node it ends at. Critical activities have no window.

Pause, copy the two Gantt rules: bar start = EST and bar length = duration, and float window = from the end of the bar out to LST(end node), with critical activities having no window at all into your book.

On a Gantt chart, activity F has EST = 4 and duration = 3. Its bar starts at day ___ and ends at day ___.
3

Read a Gantt chart

Interpret float windows, dependencies and scheduling choices.

2

Reading a Gantt Chart

Drawing the chart is only half of it. In the HSC you are just as likely to be handed a finished Gantt chart and asked to read values back out of it, so the same five features have to be recognised in reverse: where a bar starts, how long it is, how far its dashed window extends, and how many bars overlap on a given day.

In the HSC, you may be given a Gantt chart and asked to extract information. Key things to read:

  • Start time of an activity left edge of the solid bar
  • Finish time of an activity right edge of the solid bar
  • Duration length of the solid bar (finish − start)
  • Float length of the dashed/open window after the bar
  • Latest finish right edge of the float window
  • Critical activity no float window (bar goes right to the deadline)
  • How many activities run simultaneously count bars overlapping at a given time
Worked Example 2, Reading from a Gantt chart description

A Gantt chart shows: Activity G has a bar from day 3 to day 8 followed by a dashed window from day 8 to day 11.

  • EST of G = 3
  • Duration of G = 8 − 3 = 5
  • Float of G = 11 − 8 = 3
  • Latest start of G = 3 + 3 = 6 (= EST + float)
  • Latest finish of G = 11 (LST of end node for G's path)
  • G is non-critical (it has float)

How many workers needed simultaneously? If at day 5, activities A (0→7), G (3→8), and H (2→6) are all running, you need at least 3 workers at that time.

Reading a Gantt chart: the left edge of a bar is the EST, the bar length is the duration, the right edge of the bar is the earliest finish, and the right edge of the dashed window is the latest finish. Float is the length of the dashed window, so an activity with no window is critical.

Pause, copy how to read each value off a Gantt chart: left edge of bar = EST, bar length = duration, right edge of dashed window = latest finish, length of dashed window = float, and no window = critical into your book.

Which item does NOT appear on a Gantt chart?
4

Crash the critical path

Decide which activities can reduce the overall project time.

3

Crashing the Critical Path

Reading a chart tells you where the slack sits. The next question a manager asks is what it would take to finish sooner, and the Gantt chart answers that too: the bars with no dashed window are the only ones whose length controls the deadline, so they are the only ones worth paying to shorten.

Crashing means reducing the duration of one or more activities by adding extra resources (more workers, overtime, better equipment), at extra cost. The goal is to shorten the project's minimum completion time.

Key crashing rules

  • You can only reduce total project time by crashing critical path activities. Crashing non-critical activities does not shorten the project (it just increases their float).
  • Each crashed activity reduces the critical path length by the amount crashed.
  • After crashing, re-check the critical path, a different path may become critical.
  • Crashing is limited by the crash time (minimum possible duration) of each activity.
HSC exam tip: Questions often ask "by how many days can the project be shortened?", the answer is found by identifying the total crash time available across critical activities, subject to the constraint that no other path becomes longer than the reduced critical path.
Worked Example 3, Crashing analysis

Project: Critical path A(5) → B(4) → D(3) = 12 days. Non-critical: C(3) with float 4.

Crash data:

Activity Normal dur Crash time Max crash On critical path?
A532Yes
B440Yes
C321No (float=4)
D312Yes

Maximum project reduction:

  • Crash A by 2 days: critical path → 10 days
  • Crash D by 2 days: critical path → 8 days
  • Crash B: cannot (crash time = normal duration)

Check non-critical path: C has float 4. After crashing A by 2 and D by 2 (total 4 days saved), the critical path is now 8 days. Non-critical path through C = 3 + 3 = 6 ≤ 8. ✓ Still not critical.

Maximum reduction = 4 days. New minimum project duration = 8 days.

Note that C never becomes critical here: even at maximum crash the A → C path is 3 + 3 = 6 days against a critical path of 8. A cannot be crashed further either, since its crash time of 3 is already reached. In other projects a parallel path can catch up mid-crash and become critical, which is why you re-scan after every crash rather than assuming the same path stays longest.

Crashing shortens an activity by spending more on it, and only crashing a critical activity shortens the project. Each activity can be crashed no further than its crash time, and after every crash you must re-scan, because a path that was shorter can catch up and become critical.

Pause, copy the three crashing rules: only critical activities shorten the project, no activity can go below its crash time, and re-scan after each crash because the critical path can move into your book.

Crashing a path activity shortens the project. Crashing a non-critical activity only increases its .
5

Apply Gantt analysis

Build and analyse schedules in independent project contexts.

Activities

Activity 1, Drawing a Gantt Chart

A project has the following CPA results:

Activity EST Duration Float
P040
Q432
R450
S920
  1. Draw a Gantt chart for this project (minimum project time = 11 days).
  2. For activity Q, draw the float window.
  3. What is the latest day Q can start? What is the latest day Q can finish?
  4. How many activities run simultaneously on day 5?

Activity 2, Crashing Analysis

A construction project has critical path: Foundation (6 days) → Frame (5 days) → Roof (4 days) = 15 days. A parallel non-critical path has 3 days of float.

Crash data: Foundation can be crashed by 2 days; Frame cannot be crashed; Roof can be crashed by 1 day.

  1. What is the maximum number of days the project can be shortened?
  2. After crashing Foundation by 2 and Roof by 1, what is the new project duration?
  3. After crashing, does the non-critical path (with original float of 3) become critical? Show your reasoning.
  4. Why is crashing Frame pointless in this scenario?
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Show what you can do

Complete the fixed drills and short-answer questions, then check each worked answer.

Multiple Choice

Q1. On a Gantt chart, the length of a solid bar represents the activity's:

Q2. Crashing a non-critical activity will:

Q3. Activity H has EST = 5, duration = 4, and float = 3. On the Gantt chart, the float window extends from day:

Q4. A project has critical path duration 14 days. Activity X (critical, normal duration 6 days) can be crashed to 4 days. Activity Y (non-critical, float = 3) cannot be crashed. After crashing X, the project duration is:

Q5. A Gantt chart shows activity J starting at day 2 with a bar ending at day 7 and a dashed window ending at day 10. The float for J is:

Short Answer

SAQ 1. A Gantt chart for a project shows: Activity A (bar 0→6), Activity B (bar 6→8), Activity C (bar 0→4 + float window 4→6), Activity D (bar 8→10). Identify the critical path activities and state the minimum project duration. Calculate the float for activities B and C.

SAQ 2. Explain why a project manager should only crash critical path activities if the goal is to reduce project completion time. Use the concept of float in your answer.

Answers

Show MC Answers

Q1 → D (Duration) Bar length = duration of the activity.

Q2 → B Crashing a non-critical activity does not affect project time; it only increases the activity's float.

Q3 → B (9 to 12) Bar runs from EST=5 to EST+dur=9. Float window runs from 9 to 9+3=12.

Q4 → C (12) Crash X by 2 days: 14 − 2 = 12. Check: non-critical path had float 3, so it doesn't become critical (its length ≤ 12).

Q5 → D (3) Bar ends day 7, float window ends day 10. Float = 10 − 7 = 3.

Show SAQ Model Answers

SAQ 1: Activities without float windows are A (0→6), B (6→8) and D (8→10), so the critical path is A → B → D. The minimum project duration is 10 days. Float for B is 0 days because it is critical. Float for C = 6 − 4 = 2 days.

SAQ 2: Non-critical activities have float, they can be delayed by up to their float value without affecting project completion. So shortening a non-critical activity just increases its float; the project's minimum time (set by the critical path) is unchanged. Only by shortening a critical path activity, one with zero float, does the critical path length decrease and thus the project completion time decrease.

7

Retrieve, reflect and finish

Return to the opening problem, mark the lesson complete and choose the next destination.

Revisit, Think First Answer

A Gantt chart is the answer. Each activity gets a horizontal bar: start at its EST, length equal to its duration. Non-critical activities get a dashed extension showing their float window. This lets the team immediately see which activities can be rescheduled (those with float) and which cannot (critical activities). For resource planning, the chart also shows which days have the most activities running in parallel, helping to spread worker demand evenly.

Lesson Complete!

You can now draw and read Gantt charts, show float windows, and analyse crashing decisions on the critical path.