Every complex project is a web of interconnected tasks. Some can slip by days without consequence. Others, if delayed even slightly, cascade into missed deadlines, blown budgets, and frustrated stakeholders. Knowing which is which — and by how much — is the essence of the Critical Path Method.
Developed in the late 1950s by Morgan R. Walker and James E. Kelly, CPM is a project schedule modelling technique that maps every activity in a project, identifies the sequence that determines total duration, and reveals exactly where you have flexibility and where you don't. This guide covers everything from the basics through to schedule compression and precedence diagramming. Of course, even the best schedule only delivers results when you have a strong, coordinated project team executing it on the ground.
1. What Is the Critical Path?
A project network diagram contains many paths from start to finish. Each path has a total duration. The path with the longest duration is the critical path — and it defines how long your project will take.
Network diagram showing three parallel building construction paths
The critical path is simultaneously the longest path in the network and the shortest duration in which the project can be completed. These two definitions are two sides of the same coin.
Consider a project to construct three buildings: the first takes 31 months, the second 18 months, and the third 13 months. The first building's path is critical — the project cannot finish until the largest building is done. The other paths have float (slack): the second can start up to 13 months late; the third, up to 18 months late.
The path through the network diagram with the greatest total duration across all its activities.
The minimum time in which the project can be completed — identical to the critical path duration.
Activities on the critical path have no slack. Any delay immediately pushes the project end date.
A network should ideally have one critical path. Multiple critical paths multiply management complexity.
2. Finding the Critical Path: Step by Step
Network diagram with five paths — the basis for the worked example
A network diagram with five paths yields these durations:
Path 1 → Start › A › B › C › End = 31 days ← Critical Path
Path 2 → Start › D › E › F › End = 18 days (float: 13 days)
Path 3 → Start › D › B › C › End = 26 days (float: 5 days)
Path 4 → Start › G › H › I › End = 13 days (float: 18 days)
Path 5 → Start › G › E › F › End = 16 days (float: 15 days)
2.1 Early Start, Early Finish — the Forward Pass
Once the critical path is identified, we enrich the schedule with timing data through two passes:
ES of activity = EF of predecessor + 1
EF of activity = ES of activity + duration − 1
Note: when multiple predecessors exist, use the LARGEST EF.
The forward pass tells us the earliest each activity can start and finish given all its predecessors. Working through the critical path A → B → C: Activity A runs days 1–10; B runs days 11–22; C runs days 23–31, confirming the 31-day project length.
Early Start & Early Finish for path A → B → C → End
Early Start & Early Finish for path D → E → F → End
Early Start & Early Finish for path G → H → I → End
2.2 Late Start, Late Finish — the Backward Pass
The backward pass calculates the latest each activity can start without delaying the project. We begin at the last activity and work backwards.
LS of activity = LF of activity − duration + 1
LF of activity = LS of successor − 1
Note: when multiple successors exist, use the SMALLEST LS.
On the critical path, LS = ES and LF = EF for every activity. That's how you confirm you've found it.
Late Start & Late Finish for critical path A → B → C → End
Late Start & Late Finish for path D → E → F → End
Late Start & Late Finish for path G → H → I → End
3. Float — Total & Free
Float (or slack) measures scheduling flexibility. There are two important types, and understanding the difference is key to intelligent resource management.
How long an activity can be delayed without pushing back the project completion date. Zero on critical path activities.
How long an activity can be delayed without pushing back the Early Start of its immediate successor.
Example 1: Simple network diagram — path A→B→D (20 days) and A→C→D (12 days)
= Late Finish − Early Finish
Free Float = ES of next activity − EF of current activity − 1
When two activities converge into a single successor, only one of them can have free float — specifically the one whose Early Finish is earlier than the other. The one whose EF aligns directly with the successor's ES has zero free float.
Total float is always ≥ free float. On a critical path, both are zero.
4. Schedule Compression: Fast-Tracking & Crashing
Projects fall behind for many reasons — unrealistic baselines, resource shortfalls, unforeseen risks, or simply client pressure. Effective time management from the outset is your best defence against needing compression — but when recovery is needed without changing scope, two techniques apply exclusively to the critical path.
4.1 Fast-Tracking
Fast-tracking rearranges activities that were planned sequentially so they run partially or fully in parallel. Per the PMBOK Guide 6th edition, it applies to activities or phases normally done in sequence, performed in parallel for at least a portion of their duration.
Sequential activities can typically be fast-tracked by up to 33% — start the next activity when the previous one is 66% complete. Beyond this threshold, risk increases beyond acceptable limits.
Fast-tracking does not add cost, but it does increase risk. Overlapping activities may produce rework, requiring coordination that wasn't originally planned. It's most effective when activities have a natural overlap potential — like starting carpentry and electrical work simultaneously once the building shell is complete.
On a compressed diagram, activities with lead and fast-tracked activities look identical. They're not. Lead is a scheduled dependency built into the network — it's already in the baseline. Fast-tracking is a forced overlap imposed later to recover schedule. Lead doesn't add risk; fast-tracking does.
Fast-tracking: overlapping sequential activities to compress the schedule
4.2 Crashing
Crashing shortens schedule duration by adding resources to critical activities — specifically, finding the greatest time reduction at the lowest incremental cost. Typical crashing measures include overtime, additional personnel, or financial incentives.
Crashing always has a cost but doesn't significantly increase risk. A cost-benefit analysis is essential: compare the crash cost against the value of the time saved (or the penalty of not saving it). Efficiency diminishes as crashing continues — early gains come cheaply; later gains become progressively expensive.
Important: crashing cannot be applied to all activities. Concrete must cure; approvals must clear. Physical and logical constraints set hard limits.
Crashing: adding resources to shorten critical path activity durations
4.3 Comparing the Two Techniques
| Dimension | Fast-Tracking | Crashing |
|---|---|---|
| Mechanism | Overlap sequential activities | Add resources to activities |
| Cost | Usually none | Increases cost |
| Risk | Increases risk & rework potential | Minimal additional risk |
| Best when | Activities can be overlapped | Client will pay; activities support it |
| Limits | ~33% overlap before risk spikes | Physical constraints; diminishing returns |
Why do these techniques target only the critical path? Because shortening any other path simply gives it more float — it does nothing to reduce the project end date.
In practice, start with fast-tracking (it's free), then layer in crashing if further compression is needed or if the client is willing to absorb the cost. Sometimes a combination is required when the penalty for delay outweighs the crash cost.
5. Precedence Diagramming Method (PDM)
The Precedence Diagramming Method — also called Activity on Node (AON) — is the graphical technique used to build the network diagrams on which CPM runs. Nodes (boxes) represent activities; arrows show the relationships between them.
Precedence Diagram Method (PDM / AON) — nodes represent activities, arrows show relationships
5.1 The Four Dependency Types
Cannot be avoided. The next activity literally cannot begin until its predecessor is done — e.g., you cannot construct the roof before the walls exist.
Preferred sequence for efficiency or resource optimisation, but it can be changed when beneficial.
Driven by factors outside the project, such as government approvals or third-party deliverables.
Driven by your own organisation's constraints — a shared resource on another project, procurement timelines, etc.
5.2 The Four Relationship Types
B cannot start until A finishes. Paint a wall only after it is built.
B cannot finish until A finishes. Both activities complete together.
B cannot start until A starts. A cleaning crew and coating crew begin simultaneously.
B cannot finish until A starts. Moving into a new home can't complete until construction begins.
Drawing a PDM
Activity on Node (AON) — nodes are activities; arrows show relationships. The standard in modern project management.
Activity on Arrow (AOA) — arrows are activities; nodes are milestones (events). Duration labels sit on the arrows. PERT is an example. AOA only supports Finish-to-Start relationships, making it less flexible than AON.
Modern teams often overlay PDM schedules onto BIM platforms for richer 4D scheduling — linking the network model directly to the 3D building model.
6. Benefits & Drawbacks of CPM
Ultimately, CPM is a planning tool — not a guarantee. Its power is fully realised when combined with skilled collaboration between clients, contractors, and PMCs, and when the team executing the schedule has the technical and soft skills to adapt when reality diverges from plan. See also: balancing technical and soft skills in project management.