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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.

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

List all activities on the vertical axis (usually in alphabetical or logical order).
Draw a horizontal time axis, start at 0, end at the minimum project duration.
For each activity, draw a solid bar starting at its EST and ending at EST + duration.
For non-critical activities, add a float window (dashed box) extending from the end of the bar to LST + duration (= LST(end node)).
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.

Project data (from Lesson 9 Worked Example 2):

Activity	Dur	EST	Float	Bar: start → end	Float window
A	2	0	0	0 → 2	None (critical)
B	4	2	0	2 → 6	None (critical)
C	3	2	4	2 → 5	5 → 9 (4 days)
D	5	6	0	6 → 11	None (critical)
E	2	5	4	5 → 7	7 → 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.

Dummy activities are zero-duration arrows used in activity-on-arc networks to show dependencies without implying a real activity. They maintain logical precedence when two activities share some but not all predecessors.

Pause, copy the dummy activity definition (zero-duration arrow showing a dependency only) and the two conditions that require one: (1) shared-but-not-identical predecessors between two activities; (2) ensuring unique identification of each activity by its start and end nodes into your book.

Reading a Gantt Chart

A dummy activity is a zero-duration arrow that shows a dependency without representing real work. It is needed whenever two activities share some, but not all, of their predecessors: without the dummy, drawing the network would incorrectly imply one activity depends on all of the other's predecessors rather than only the shared ones.

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

Start time of an activityleft edge of the solid bar
Finish time of an activityright edge of the solid bar
Durationlength of the solid bar (finish − start)
Floatlength of the dashed/open window after the bar
Latest finishright edge of the float window
Critical activityno float window (bar goes right to the deadline)
How many activities run simultaneouslycount bars overlapping at a given time

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.

To identify where a dummy is needed: if two activities have some predecessors in common but not all, a dummy from the common predecessor node to one of the activities preserves the dependency correctly.

Pause, copy the trigger rule: if activity C depends on both A and B, but activity D depends only on A (not B), draw a dummy from the end of A to the start of D to correctly show that D needs A but not B into your book.

Which item does NOT appear on a Gantt chart?

Crashing the Critical Path

Once you have identified the shared-predecessor trigger and drawn the dummy arrow, include it in the forward and backward scans exactly like a real activity, but with duration zero. Adding zero to EST means the dummy transfers the EST from its start node directly to its end node, and it can lie on the critical path if EST = LST at both its nodes.

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.

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?
A	5	3	2	Yes
B	4	4	0	Yes
C	3	2	1	No (float=4)
D	3	1	2	Yes

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.

When solving CPA problems with dummies, include them in forward/backward scans exactly as real activities but with duration zero. The critical path calculation is otherwise identical, dummies can lie on the critical path.

Pause, copy the dummy scanning rule: treat dummies as real activities with duration = 0 in both forward and backward scans, and note that a dummy can be on the critical path if EST = LST at both its start and end nodes into your book.

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

Activities

Multiple Choice

Short Answer

Answers

Activity	EST	Duration	Float
P	0	4	0
Q	4	3	2
R	4	5	0
S	9	2	0

Show MC Answers

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

Q2 → BCrashing 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.