6.4 Critical Path and Schedule Calculations

Network Diagram Basics

A project schedule network diagram shows the logical dependencies between activities. The most common method, Precedence Diagramming Method (PDM), draws each activity as a node and uses four relationship types: Finish-to-Start (FS) is by far the most common, plus Start-to-Start (SS), Finish-to-Finish (FF), and the rare Start-to-Finish (SF). Each node carries the scheduling values:

+------+----------+------+
|  ES  | Duration |  EF  |
+------+----------+------+
|        Activity        |
+------+----------+------+
|  LS  |  Float   |  LF  |
+------+----------+------+

The critical path is the longest duration path through the network; it sets the shortest possible project duration. Its activities have zero total float, so any delay to them delays the whole project.

Forward Pass — Compute ES and EF

Move left to right. EF = ES + Duration. The first activity starts at ES = 0 (this guide uses the zero convention; some texts start at 1). When an activity has multiple predecessors, its ES = MAX of all predecessor EFs — it cannot start until every predecessor finishes.

Network: A(3) -> B(5) and C(4); B and C -> D(2).

• A: ES = 0, EF = 0 + 3 = 3
• B (after A): ES = 3, EF = 3 + 5 = 8
• C (after A): ES = 3, EF = 3 + 4 = 7
• D (after B and C): ES = MAX(8, 7) = 8, EF = 8 + 2 = 10

Project duration = 10 (the EF of the last activity).

Backward Pass — Compute LF and LS

Move right to left. LS = LF - Duration. The last activity's LF equals the project duration. When an activity has multiple successors, its LF = MIN of all successor LSs.

• D: LF = 10, LS = 10 - 2 = 8
• B: LF = 8 (LS of D), LS = 8 - 5 = 3
• C: LF = 8 (LS of D), LS = 8 - 4 = 4
• A: LF = MIN(3, 4) = 3, LS = 3 - 3 = 0

Calculating Float

Total float = LS - ES = LF - EF. It is how long an activity can slip without delaying the project finish. Free float is different: how long an activity can slip without delaying the early start of any successor. On the exam, unqualified "float" means total float.

Critical path: A -> B -> D (the zero-float chain; length 3 + 5 + 2 = 10). Activity C has 1 day of float, so it can slip one day without harming the finish date.

Leads and Lags

Lag example: after pouring concrete you must wait 3 days for curing before building walls — FS + 3. Lead example: you begin editing a document 2 days before drafting fully finishes — FS - 2.

Schedule Compression

Two techniques shorten the schedule; both apply only to the critical path, because shortening a non-critical activity does nothing for the finish date.

Crashing

Add resources/cost to shorten duration. Always crash the critical-path activity with the lowest cost per time unit first, then recompute — the critical path can shift.

If A and B are on the critical path, crash A first ($1,000/day beats $1,500/day). Crashing increases cost and may not preserve quality, but it does not add scope risk.

Fast-tracking

Perform activities (or phases) in parallel that were planned sequentially — e.g., start design of module 2 before module 1 design is fully done. Fast-tracking adds no direct cost but increases risk and rework.

Exam tips: (1) Never crash a non-critical activity — it cannot shorten the project. (2) After any compression, recalculate the network; a previously near-critical path may become the critical path. (3) If two paths tie for longest, the project has two critical paths, and any delay on either delays the project.