What is the critical path method?
The critical path method (CPM) was developed in the late 1950s at DuPont to schedule plant maintenance and construction. It models a project as a network of activities linked by dependencies and finds the longest path through it. That path, the critical path, determines the shortest possible project duration. Every other activity has some float: room to move without delaying the finish. Knowing which is which tells a project manager where to focus.
How the calculation works
| Value | Formula | Meaning |
|---|---|---|
| ES (early start) | Largest EF of all predecessors (0 if none) | Earliest the activity can start |
| EF (early finish) | ES + duration | Earliest it can finish |
| LF (late finish) | Smallest LS of all successors (project end if none) | Latest it can finish without delaying the project |
| LS (late start) | LF − duration | Latest it can start |
| Total float | LS − ES | Delay allowed without delaying the project |
| Free float | Smallest ES of successors − EF | Delay allowed without delaying any successor |
Critical path example
Installing a new packaging line takes ten activities. The equipment's 30-day supplier lead time dominates: layout (5 days), ordering (3), delivery (30), installation (8), IQ/OQ (6), PQ runs (5) and release (1) form the critical path of 58 days. Floor preparation (12 days) has 21 days of float, writing SOPs has 33, and operator training 2. The best way to shorten the project is to negotiate a shorter delivery or to pre-qualify parts of the line at the supplier, not to hurry the SOPs.
Using the critical path
- Focus attention on critical activities: review them daily and remove their blockers first.
- Use float to level resources: move non-critical work to when people are free.
- Watch near-critical paths with little float; they become critical with small delays.
- Show the plan on a timeline with the Gantt chart, and model uncertainty with PERT.
- Plan for what could go wrong on the critical path with a PDPC.
How to use this Critical Path Method tool
- List the activities. Add each activity with a short code, a name and its duration in hours, days or weeks.
- Set the dependencies. For each activity, enter the codes of the activities that must finish first, e.g. "C, D".
- Read the network. The network diagram shows each activity with its earliest and latest start and finish, and the float.
- Find the critical path. Red boxes and arrows mark the critical path; the project duration is shown in the key.
- Use the float. Activities with float can move without delaying the project; use it to level resources.
- Export. Export the network and the schedule table to PDF, PNG or Excel.
Frequently asked questions
What is the critical path method?
The critical path method (CPM) is a project scheduling technique. You list the activities, their durations and which activities must finish before others can start. A forward and backward pass through the network gives each activity its earliest and latest start and finish. The longest chain of dependent activities is the critical path: it sets the project duration.
How do you find the critical path?
Forward pass: each activity starts as early as all its predecessors allow (ES = largest EF of the predecessors; EF = ES + duration). The project duration is the largest EF. Backward pass: each activity finishes as late as its successors allow (LF = smallest LS of the successors; LS = LF − duration). Activities with zero float (LS = ES) are on the critical path.
What is float (slack)?
Total float is how long an activity can be delayed without delaying the project: LS − ES. Free float is how long it can be delayed without delaying the next activity. Critical activities have zero total float.
Can a project have more than one critical path?
Yes. If two chains of activities have the same, longest duration, both are critical. Projects with several critical or near-critical paths are riskier, because a delay on any of them delays the project.
What is the difference between CPM and PERT?
CPM uses one duration per activity and focuses on the schedule and float. PERT uses three estimates (optimistic, most likely, pessimistic) to model uncertainty and estimate the probability of finishing by a given date. Use the PERT chart tool when durations are uncertain.
How do you shorten the critical path?
Only shortening critical activities shortens the project. Options are crashing (adding resources to a critical activity), fast-tracking (overlapping activities that were in sequence) or changing the plan. Each time, recalculate: another path may become critical.