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POSTER 24
Extension · Schedule Management

Schedule & the Critical Path

The critical path is the longest path through the network — it sets the shortest possible duration, and its activities have zero float. Find it with a forward & backward pass; protect it; and if you must go faster, crash (spend) or fast-track (risk).

Visual Map — A Worked Network

each box: name · dur / ES EF / LS LF · float A · 3 ES 1 EF 3 LS 1 LF 3 · fl 0 B · 4 ES 4 EF 7 LS 6 LF 9 · fl 2 C · 6 ES 4 EF 9 LS 4 LF 9 · fl 0 D · 2 ES 10 EF 11 LS 10 LF 11 · fl 0 Critical path A → C → D = 11 days (zero float) · B carries 2 days of float

Forward pass sets ES/EF left→right (take the later predecessor at a merge). Backward pass sets LS/LF right→left (take the earlier successor). Float = LS − ES; zero float = critical.

Passes & Float

Forward: EF = ES + Dur − 1

Backward: LS = LF − Dur + 1

Total Float = LS − ES = LF − EF

Free Float = ESₙₑₓₜ − EF − 1

Critical path = longest path = zero total float. (Drop −1/+1 if counting from day 0.)

Schedule Compression

Crashing
add resources to critical-path tasks → adds cost. Crash the cheapest $/day first; watch diminishing returns.
Fast-tracking
overlap normally-sequential activities → adds risk & rework, no extra cost.

Both target the critical path — compressing anything else won't shorten the project.

Dependencies & Logic

  • FS finish-to-start (most common) · SS · FF · SF (rare).
  • Type: mandatory (hard) · discretionary (soft) · external · internal.
  • Lead = overlap (negative lag); lag = imposed delay.

Exam Concepts

  • Critical path = longest duration / least (zero) float.
  • Float = LS − ES.
  • Crashing adds cost; fast-tracking adds risk.
  • Resource levelling can change the critical path & extend duration.
  • Near-critical / multiple paths raise schedule risk.

Executive View

  • Focus & protect the critical path — that's where time is won or lost.
  • Compression always costs money or risk — never free.
  • Float is manoeuvre room; watch near-critical paths.

Relationships

  • The schedule baseline feeds EVM's PV (Poster 14).
  • Schedule reserve covers schedule risk (Poster 12).
  • Critical Chain adds buffers — a tailoring choice (Poster 5).

Industry Example

Manufacturing
  • Line install: the critical path runs through long-lead equipment + commissioning. Fast-track civil works alongside procurement; crash commissioning with extra techs to recover a slip.

Memory Hooks

  • "Critical path = longest path = zero float."
  • "Crash = cash; Fast-track = risk."
  • Float = LS − ES; relationships F-S, S-S, F-F, S-F.
60-sec Review Find the critical path in the network Forward & backward pass Float = LS − ES Crash vs fast-track Name the 4 dependencies
PMI Visual Wall · Poster 24 · Schedule & the Critical Path · original instructional design · A3 landscape