PMP lesson · Schedule · Schedule · lesson 2 of 4 · about 8 minutes
Critical path and float
Predictive · also used for hardware in hybrid projectsFree full lesson
Goal: After this lesson you can find the critical path in a network, calculate total and free float, and say which delays will move the end date.
1The situation
Which delay matters?
Installing a robot cell involves five activities. Two problems are reported on the same morning: the guarding supplier will be 2 days late, and the electrician is sick, so wiring will be 2 days late.
The customer asks: “Will commissioning finish late?”
The surprising answer: one delay moves the end date, the other does not. To know which, you need the critical path.
2Paths and the critical path
A project is a network of activities connected by dependencies. A path is any chain of activities from start to finish.
Path
A chain of activities
Add the durations along the chain to get the path length.
A → C → D = 3 + 2 + 4 = 9 days
Critical path
The longest path
It decides the shortest possible project duration.
A → B → D = 12 days
Float
Slack
How long an activity can slip without delaying something.
C can slip 3 days
The critical path is the longest path, not the most important or most difficult work. Any delay on it delays the project.
Two kinds of float
Float always protects something. The question is what it protects.
Protects the project end date
Total float = LS − ES
How much an activity can slip without delaying the project.
Protects the next activity
Free float = ES (next) − EF
How much an activity can slip without delaying the early start of its successor.
ES/EF = early start and finish (forward pass, from the start). LS/LF = late start and finish (backward pass, from the end). Activities on the critical path have zero total float.
Watch out for
Near-critical paths: a path with little float (E → D has only 2 days) becomes critical after a small delay.
The critical path can change when activities are delayed, compressed or re-sequenced.
Negative float means the plan already cannot meet a fixed date.
3See it in one picture
Three paths lead to the end: A → B → D (12 days), E → D (10 days), A → C → D (9 days). The longest one is critical.
Forward and backward pass
Activity
Duration
ES
EF
LS
LF
Total float
Free float
A mount base
3
0
3
0
3
0
0
B wiring
5
3
8
3
8
0
0
C guarding
2
3
5
6
8
3
3
E offline program
6
0
6
2
8
2
2
D commissioning
4
8
12
8
12
0
0
D cannot start until B, C and E are all finished, so its early start is the latest of their finishes: day 8.
4Worked example: the two delays
Given: Guarding (C) will be 2 days late. Wiring (B) will be 2 days late.
C delayed 2 days
Total float of C = 3 days
2 < 3: the end date does not move. C still has 1 day of float.
B delayed 2 days
B is on the critical path (float 0)
The end date moves by 2 days: 12 → 14 days.
New critical path?
A → B → D = 14, E → D = 10, A → C → D = 11
A → B → D stays critical, now 14 days long.
Answer to the customer: “The wiring delay will move commissioning by 2 days. The guarding delay will not.” Recovery effort should go to the wiring, not the guarding.
5Wrong vs right: the common traps
✘ Wrong thinking
“The critical path is the most important or most difficult work.”
✔ Right thinking
It is simply the longest path through the network. Easy activities can be critical.
✘ Wrong thinking
“The shortest path decides when we finish.”
✔ Right thinking
The project cannot finish until every path is finished, so the longest path decides.
✘ Wrong thinking
“A delay within total float has no effect at all.”
✔ Right thinking
It does not move the end date, but if it is larger than free float, it delays the next activity.
✘ Wrong thinking
“Once we know the critical path, it never changes.”
✔ Right thinking
Delays, compression and re-sequencing can make another path critical. Recheck after every change.
✘ Wrong thinking
“Recover time by speeding up any late activity.”
✔ Right thinking
Only speeding up critical-path activities shortens the project. Speeding up activities with float wastes money.
6How it looks on the exam
Exam-style question 1. A network has three paths: Start–P–Q–Finish (14 days), Start–R–S–Finish (17 days) and Start–R–T–Finish (15 days). Activity Q is now expected to take 2 days longer than planned. What are the project duration and the effect of the delay?
A. 14 days; the project will be delayed by 2 days
B. 17 days; the delay to Q does not affect the end date
C. 17 days; the project will be delayed by 2 days
D. 16 days; Q becomes part of the critical path
Show the answer and the decode
Answer: B.
In simple English
Three paths, and one activity on the shortest path is late.
What is the question really asking?
How long the project takes, and whether this delay matters.
Key words / trigger
“2 days longer … Q”
PMP logic
Critical path = longest = R–S (17 days). Q is on a 14-day path with 3 days of float; a 2-day delay makes that path 16 days, still shorter than 17.
Why the wrong answer looks attractive
Any delay sounds bad, but a delay within the float does not move the end date.
Exam-style question 2. An activity on a non-critical path has a total float of 2 days. A supplier problem delays it by 4 days. What is the MOST likely effect, and what should the project manager do?
A. No effect, since the activity is not on the critical path
B. The project end date moves by 4 days; the PM should accept the delay
C. The project end date moves by 2 days and the path becomes critical; the PM should analyse recovery options on the new critical path
D. The project end date moves by 6 days
Show the answer and the decode
Answer: C.
In simple English
A task with 2 days of float is 4 days late.
What is the question really asking?
The effect on the end date and the right reaction.
Key words / trigger
“total float of 2 days … delays it by 4 days”
PMP logic
The first 2 days use up the float; the remaining 2 days delay the project. The path becomes critical, so recovery must focus there.
Why the wrong answer looks attractive
'It is not critical' was true before the delay, but the delay is larger than the float.
7Remember this
Your memory card
Critical path = the longest path = the shortest possible project duration
Total float = LS − ES (protects the end date) · Free float protects the next activity
Critical-path activities have zero total float; any delay on them delays the project
Watch near-critical paths: the critical path can change