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Module 6 · Networks and Critical Paths

Gantt Charts & Resource Allocation

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

MS12-7 MS-N3 Lesson 10 of 12

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.
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.

Book Notes

On a Gantt chart, activity F has EST = 4 and duration = 3. Its bar starts at day ___ and ends at day ___.
2

Reading a Gantt Chart

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.

Book Notes

Which item does NOT appear on a Gantt chart?
3

Crashing the Critical Path

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.

If you crashed further (say A by 3 days), the critical path would be 9 days but the C path might become critical. Always verify after each crash.

Book Notes

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

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?

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 3→8 + float window 8→10), 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: A (0→6) and D (8→10) are critical. Float for B = 10 − 8 = 2 days. Float for C = 6 − 4 = 2 days. Critical path: A → D (noting B starts at 3, during A; D starts when A ends at 6... then 8→10). Actually: A ends 6, D starts 8 — there's a gap. Check: if A is critical (bar 0→6, no float) and D is critical (8→10, no float), the critical path must include an activity 6→8. In the given description, B starts at 3 (not 6) and has float. So the critical path is A (0→6) + (implied activity 6→8 not shown or D actually starts at 6). Minimum project duration = 10 days (D finishes at 10, no float).

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.

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.