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Lab 10 — Creating a Gantt Chart with the Critical Path

At a glance

Learning objectives

By the end of this lab you should be able to:

  1. Complete a forward pass to establish earliest start and finish for every activity.
  2. Complete a backward pass to establish latest start and finish, and calculate total float.
  3. Identify the critical path and explain why it — and not the busiest work — determines the finish date.
  4. Read the difference between what a Gantt chart shows and what it hides.

Scenario

This lab continues from Labs 08 and 09 on the Admission Management System. Lab 08 produced the activity list and durations; Lab 09 produced the dependency logic and the network. Both are reproduced here so you can work from this page alone.

# Activity Duration (days) Predecessors
A Requirements workshops 5 —
B Data model design 4 A
C Applicant form build 6 B
D Document upload build 5 B
E Eligibility rules engine 8 B
F Admin review console 6 C
G Student-record integration 7 D
H Security review of the integration 10 G
I System testing 5 E, F, H
J UAT and training 4 I

Project start: Monday 2 March 2026. Five-day working week. Two public holidays fall inside the window: 20 March and 6 April.

flowchart LR
    accTitle: The activity network for the admission system
    accDescr {
    Activity A of 5 days leads to B of 4 days. B leads to C of 6 days, D of 5 days and E of 8 days.
    C leads to F of 6 days; D leads to G of 7 days; G leads to H of 10 days. E leads to I of 5 days,
    and F and H also lead to I, which leads to J of 4 days.
    }
    A[A 5d] --> B[B 4d]
    B --> C[C 6d]
    B --> D[D 5d]
    B --> E[E 8d]
    C --> F[F 6d]
    D --> G[G 7d]
    G --> H[H 10d]
    E --> I[I 5d]
    F --> I
    H --> I
    I --> J[J 4d]

Your role

You are the project manager, and the steering committee has asked one question: "when will it be done?" You must answer with arithmetic that survives challenge, not with a date that sounds reasonable.

Project information and assumptions

The scenario is part of the example-project library — read the full description there if you want the wider context.

  • Durations are in working days and are given. Do not revise them.
  • Ignore the data-migration activity you added in Lab 09 — this lab establishes the baseline network only. Note the consequence of that omission in your reflection.
  • Day 0 is the start of activity A. Express earliest and latest times as day numbers from 0, then convert to dates for the milestone at the end.
  • Assume resources are available; resource levelling is Lab 21's problem.

Tasks

Task 1 — Forward pass

Complete the table, showing your working for each row:

Activity Duration Earliest start Earliest finish
A 5 0 5
B 4
C 6
D 5
E 8
F 6
G 7
H 10
I 5
J 4

State the total project duration in working days.

Task 2 — Backward pass and float

Starting from the project finish, complete:

Activity Earliest finish Latest finish Latest start Total float
A 5
B 9
C 15
D 14
E 17
F 21
G 21
H 31
I 36
J 40

Task 3 — State the critical path

Write the critical path as a sequence of activity letters. Then answer, in two or three sentences:

  1. Why does the longest chain — not the chain with the most work in it — determine the finish date?
  2. Two activities may look like candidates for the critical path. Which ones, and why do they not qualify?

Task 4 — Interpret the float

Take the three activities with non-zero float and answer for each:

  1. How many days of float does it have?
  2. What would you have to do to spend that float?
  3. What would be the consequence of spending it?
  4. Is the float available to any single person to use at will? Explain.

Task 5 — Draw the Gantt chart

Produce a Mermaid gantt chart showing all ten activities against a working-day axis, with the critical path visually distinguished (use the crit tag on critical tasks and active or a separate section for the others).

Then produce a two-column commentary:

What the Gantt chart shows well What it hides
(four items) (four items)

Name at least one thing on the "hides" side that could cause the committee to make a wrong decision if they saw only the chart.

Task 6 — Convert to a date

The project starts Monday 2 March 2026, with 20 March and 6 April as public holidays.

  1. State the calendar date of the project finish for a 40-working-day duration.
  2. The 16-week window ends on Friday 19 June 2026. State the margin between your finish date and the window, in working days.
  3. Write three sentences explaining why that margin is not spare time, naming at least two things that will consume it.
  4. State the date by which activity G (integration) must finish if the security review (H) is to complete before testing must begin.

Deliverable

  1. The completed forward pass table with working.
  2. The completed backward pass and float table.
  3. The critical path and your answers to the two questions in Task 3.
  4. The float interpretation for the three non-critical activities.
  5. A Mermaid Gantt chart with the critical path marked.
  6. The two-column Gantt commentary.
  7. The calendar dates and the margin explanation.

Hints and guidance

  • Forward pass: earliest start = the latest earliest finish among all predecessors. For activity I that is the maximum of three numbers — take the largest, not the sum.
  • Backward pass: latest finish = the earliest latest start among all successors. For activity B that is the minimum of three numbers.
  • Float = latest finish − earliest finish. An activity with zero float is on the critical path.
  • Two activities can both be critical on one path. The critical path is a chain, not a single activity.
  • Dates are working days. Excluding a weekend when counting is where most errors appear; count weekdays and then subtract the holidays.

Self-check criteria

Check How to verify it
Forward pass arithmetic Each earliest start equals the maximum earliest finish of its predecessors
Duration is consistent The largest earliest finish in the table equals the project duration
Backward pass starts correctly Activity J's latest finish equals the project duration
Float is correct by two methods latest finish − earliest finish matches latest start − earliest start for every row
Critical path is a valid chain Each activity on it is a predecessor of the next, and the durations sum to the project duration
Non-critical activities have positive float only No activity outside the path shows zero float
Gantt chart marks the critical path The crit tag is present on exactly the critical activities
Date arithmetic excludes holidays Both 20 March and 6 April are omitted from the count

Reflection

  1. You omitted the data-migration activity from this network to keep the lab manageable. What does that omission do to the deliverable you are handing the steering committee?
  2. If the security review (H) were reduced from ten days to five, would the project finish five days earlier? Answer with reference to the network, not by intuition.
  3. Which non-critical activity would you most want to keep its float, and why?
  4. The committee sees only the Gantt chart. Write the one sentence you would add underneath it to prevent the most likely misreading.
Check your numbers

Expected results — verify yours against these before reading the full working in the answer key.

  • Project duration: 40 working days.
  • Critical path: A → B → D → G → H → I → J (5 + 4 + 5 + 7 + 10 + 5 + 4 = 40). Every activity on it has zero float.
  • Total float: C = 10 days, E = 14 days, F = 10 days. All other activities have zero float.
  • Calendar finish: Tuesday 28 April 2026 (40 working days from Monday 2 March, excluding 20 March and 6 April).
  • Margin to the 16-week window end (Friday 19 June 2026): approximately 34 working days.

Extension challenge

Compress the schedule by five working days using two different techniques, and cost each one:

  1. Fast-tracking — overlap activities D and G, accepting that integration work begins before the upload component is finished.
  2. Crashing — add a second developer to the security review's preparatory work, reducing the queue's effect by two days.

For each, state how many days it actually saves, what it costs in money and risk, and whether it touches the critical path. Then state which you would choose, and identify the single change to the network that would make the other one worth reconsidering.