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Lesson 2 — Gantt Charts, the Critical Path, and Float

At a glance

  • Module: 06 — Schedule Management
  • Level: Intermediate
  • Estimated time: 45 minutes
  • Example project: the LMS and the admission portal

Learning objectives

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

  1. Identify the critical path through a network and explain why it determines the finish date.
  2. Calculate total float for each activity and interpret what it means.
  3. Read a Gantt chart and state what it shows and what it hides.
  4. Evaluate schedule compression techniques and their trade-offs.

Prerequisites

Introduction

A network diagram has no dates. This lesson turns it into a schedule by finding the sequence that determines when the project can finish — the critical path — and by calculating how much time everything else can absorb.

This is the most arithmetic-heavy lesson in the course, and it is worth doing by hand at least once. The critical path is not an administrative detail: it is the answer to "what actually has to go well?", and it changes every time a dependency or a duration changes.

1. The critical path

The critical path is the longest chain of dependent activities from start to finish. It determines the shortest possible project duration, and it does so because every other chain is shorter and therefore has time to spare.

Find it in two passes:

  1. Forward pass — start at day 0 and push each activity as early as its dependencies allow. This gives each activity's earliest start and finish.
  2. Backward pass — start from the project finish and pull each activity as late as its successors allow. This gives each activity's latest start and finish.

Activities whose earliest and latest times are equal have no float, and they form the critical path. If any of them slips by a day, the project finishes a day later.

2. Float

Total float is how long an activity can be delayed without delaying the project:

total float = latest finish − earliest finish

Float is not a spare day to spend. It is information:

  • Zero float — this activity is on the critical path; manage it closely.
  • Some float — the activity can absorb delay, but only up to the limit, and only for now. Float is consumed by reality and cannot be banked.
  • Large float — the estimate may be padded, or the activity may be less critical than assumed.

A project where every activity has float has an arithmetic error in it.

3. Gantt charts

A Gantt chart shows activities as bars along a time axis. It is the most widely used scheduling view because it answers "when?" at a glance, and it is a poor tool for answering "why?".

Gantt charts show well Gantt charts hide
Duration and timing of each activity The reason one activity follows another
Overlap between activities Which chain is actually critical
Overall shape of the schedule Resource contention, unless levelled
Milestones and deadlines The assumption that made the estimate

Read a Gantt chart with the network beside it. The chart tells you when; the network tells you why, and therefore what happens if it changes.

4. Compression

When a date must be met, two techniques are available — and both have a bill.

Technique How it works Cost
Crashing Add resources to critical activities Money, coordination overhead, and often less than proportional gain
Fast-tracking Run sequential activities in parallel Rework risk, since later work starts before earlier plans are settled
Reduce scope Deliver less The benefit is reduced; often the only honest option
Reuse or buy Replace building with adopting Fit to requirements; vendor dependency
Remove a discretionary dependency Overlap work that was serial by choice Rework risk, as with fast-tracking

Compression only helps if applied to the critical path. Adding people to an activity with float spends money and changes nothing.

Key terms

Term Meaning
Critical path The longest chain of dependent activities; it sets the shortest duration
Forward pass Calculating earliest start and finish for each activity
Backward pass Calculating latest start and finish for each activity
Total float Time an activity can slip without delaying the project
Gantt chart A time-axis bar chart of activities
Crashing Adding resources to a critical activity to shorten it
Fast-tracking Performing sequential activities in parallel
Schedule baseline The approved version of the schedule

Worked example

Task: find the critical path, calculate float, and evaluate a compression request for the LMS submission release. All durations are invented for illustration.

Step 1 — Restate the network with durations. A: 2 d. B: 2 d (after A). C: 4 d (after B). D: 3 d (after B). E: 3 d (after C). F: 3 d (after D and E).

Step 2 — Forward pass.

Activity Earliest start Earliest finish
A 0 2
B 2 4
C 4 8
D 4 7
E 8 11
F max(7, 11) = 11 14

Project duration: 14 days.

Step 3 — Backward pass from day 14.

Activity Latest finish Latest start Total float
F 14 11 0
E 11 8 0
D 11 8 4
C 8 4 0
B 4 2 0
A 2 0 0

Step 4 — State the critical path. A → B → C → E → F, duration 14 days. Every activity on it has zero float. D has 4 days of float: storage can slip four days without delaying testing.

Step 5 — Test a compression request. The sponsor asks to finish in 12 days. Two days must come off the critical path, and only from A, B, C, E, or F. Adding a person to D would achieve nothing, because D is not critical.

Step 6 — Evaluate real options. Crash E: add a developer to grading, 3 d → 2 d, saving one day, with a coordination cost. Fast-track C and E: start grading work before the form design is final, saving perhaps two days at the cost of rework if the design changes. Reduce scope or reuse an existing component may be cheaper than either.

Step 7 — Answer with the option and its price. "Twelve days is possible by fast-tracking grading and the form, with a risk of rework we would absorb in testing. Alternatively, one day by adding a developer to grading, at additional cost. Which do you prefer?"

Common misconceptions

“The critical path is the most difficult work”

It is the longest chain, which is a property of durations and dependencies, not difficulty. A trivial but long activity can be critical while the hardest work has float.

“Float can be spent freely”

Float is shared. Two activities on the same non-critical chain draw on the same reserve; if both use it, the project is late.

“Crashing always shortens the schedule”

Only on the critical path, and only until the activity stops responding. Adding people to a three-day task may produce a three-day task with more people in it.

Practical activity

Find the critical path. Using the network you built in Lesson 1:

  1. Complete a forward pass, tabulating earliest start and finish for each activity.
  2. Complete a backward pass, giving latest start, latest finish, and total float.
  3. State the critical path and the total project duration.
  4. Draw a Gantt-style view as a Mermaid gantt diagram.
  5. Assume the deadline is two days shorter than your duration, and evaluate two compression options with their costs.

What "good" looks like: correct arithmetic, at least one activity with non-zero float, and a compression answer that names what it costs rather than only what it saves.

Self-assessment

  1. Why does the longest chain, rather than the busiest-looking work, determine the finish date?
  2. An activity has four days of total float. What can and cannot be concluded from that?

  3. A manager proposes adding a developer to every activity to finish faster. What is wrong with that instruction?

  4. Apply it — admission portal resource request. A Gantt chart shows three activities ending in week 12: one on the critical path, one with one week of total float, one with six weeks of total float. Another project is short of a person for a week and the sponsor asks you to release someone.

    Hint: A strong answer names which activity can give up the person, what must be checked before releasing them, and why float is not a personal allowance.

Show answers
  1. Because every other chain is shorter, so it has slack; the longest chain has none. Delaying any activity on it delays the project one-for-one, while a delay elsewhere is absorbed by that chain's float.
  2. You can conclude that it may slip up to four days without delaying the project as currently planned. You cannot conclude that the four days are a personal allowance: the float may be shared with other activities on the same chain, and it disappears if an earlier activity consumes it.
  3. It spends money where it may change nothing, because only critical activities affect the finish date. Worse, it adds coordination overhead and can slow activities that were fine. Effort should be directed at the critical path, and reassurance sought from the arithmetic rather than from intuition.
  4. Release from the activity with six weeks of float, never the critical-path activity, and only after checking two things: that no other activity on the same chain is depending on that float, because total float is shared along a path and is consumed by whoever uses it first; and that the person is actually interchangeable — if the float exists on a specialised activity, lending a generalist does not buy the other project anything. The activity with one week of float is not a candidate: consuming it leaves no room for the slippage that has not happened yet. Float belongs to the plan, not to a person; treating it as spare capacity is how teams spend a buffer twice and discover it at the milestone. Note also what the Gantt chart is not telling you: it shows when work happens, and the network is what shows why the critical path is critical.

Summary

  • The critical path is the longest dependent chain; it sets the finish date and has zero float.
  • Forward and backward passes give earliest and latest times; the difference is total float.
  • Float is information about a plan, not an allowance for a person, and it is shared along a chain.
  • Gantt charts show when; the network shows why. Use them together.
  • Compression works only on the critical path, and always costs something — money, rework risk, or scope.

Further learning

Next

You have completed Module 06. Continue to Module 07 — Cost & Estimation.