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Critical path analysis

Edexcel IAL Business · WBS13 Business decisions and strategy

Projects such as building a store or launching a product involve many activities, some of which must happen in order and some at the same time. Critical path analysis (CPA) finds the shortest possible project time and the activities that cannot be delayed.

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Networks

A network shows activities in their logical order:

Activities are drawn as arrows (lines), labelled with a letter and duration.
Nodes (circles) mark the start and end of activities. Each node is split: the left half holds the node number, the top right the earliest start time (EST) of the activities that follow, and the bottom right the latest finish time (LFT) of the activities that end there.
A dependent activity cannot start until those before it are finished; activities with no dependence can run in parallel.

EST, LFT and float

EST: work forwards from 0. EST of an activity = the largest (EST + duration) of the activities that must finish first.
LFT: work backwards from the project end. LFT of an activity = the smallest (LFT - duration) of the activities that follow it.
Total float = LFT - duration - EST. It is how long an activity can be delayed without delaying the whole project.
The critical path is the chain of activities with zero float; its total duration is the minimum project time. Any delay to a critical activity delays the project.

Worked network

Activities (days): A 3 at the start; B 4 at the start; C 2 after A; D 6 after A; E 3 after B and C; F 2 after D and E.

Activity	Duration	Depends on	EST	LFT	Total float
A	3	none	0	3	0
B	4	none	0	6	2
C	2	A	3	6	1
D	6	A	3	9	0
E	3	B, C	5	9	1
F	2	D, E	9	11	0

Critical path A - D - F, minimum duration 11 days.

Benefits and limitations

Benefits: identifies the minimum project time and the critical activities to monitor; shows where resources can be moved from activities with float; helps with scheduling deliveries and staff just in time; helps cash flow planning; allows comparison of actual progress with the plan.

Limitations: durations are estimates; it does not show costs or guarantee quality; complex projects need software; it can encourage rushing that cuts quality; plans need constant updating when things change; it assumes resources are available when needed.

Worked example

Using the network above, find the EST of E and the total float of B, and say what happens if C is delayed by 2 days.

E needs B and C. B finishes at 0 + 4 = 4; C finishes at 3 + 2 = 5. EST of E = 5.
Float of B = LFT 6 - duration 4 - EST 0 = 2 days.
C has 1 day of float, so a 2-day delay uses the float and delays the project by 1 day: 12 days.

Answer: EST of E = 5; float of B = 2 days; the project would take 12 days.

Key idea: Activities on arrows, nodes hold EST (top right) and LFT (bottom right). EST forwards (largest), LFT backwards (smallest). Total float = LFT - duration - EST. Critical path: zero-float activities; its length is the minimum project time.

Check yourself

Activities: A 3 days at the start; B 4 days at the start; C 2 days after A; D 6 days after A; E 3 days after B and C; F 2 days after D and E. What is the minimum project duration?
Show answer
11 days. EST: C 3, D 3, E 5, F max(3 + 6, 5 + 3) = 9. Finish = 9 + 2 = 11 days.
In the same network, what is the earliest start time of activity F?
Show answer
9 days. F needs D (finishes 9) and E (finishes 8). EST = the larger = 9.
In the same network, what is the total float of activity B?
Show answer
2 days. LFT of B = latest start of E = 9 - 3 = 6. Float = 6 - 4 - 0 = 2.
Activities: P 5 days at the start; Q 3 days at the start; R 3 days after P; S 6 days after Q; T 2 days after R and S. Calculate the total float of activity R.
Show answer
1 days. EST of T = max(5 + 3, 3 + 6) = 9; duration 11. LFT of R = 9; float = 9 - 3 - 5 = 1.
In the first network (minimum duration 11 days), activity C has 1 day of total float. If C is delayed by 2 days, what is the new project duration?
Show answer
12 days. Only the delay beyond the float holds up the project: 2 - 1 = 1; 11 + 1 = 12 days.
Which activities form the critical path in a network?
- Those with the longest individual durations
- Those with zero total float
- Those that start at time 0
- Those with the most float
Show answer
Those with zero total float. Zero float means any delay delays the project.
For the network P 5 (start), Q 3 (start), R 3 after P, S 6 after Q, T 2 after R and S, which is the critical path?
- P - R - T
- Q - T
- P - Q - T
- Q - S - T
Show answer
Q - S - T. Q - S - T takes 3 + 6 + 2 = 11 days, longer than P - R - T (10 days), so it has zero float.
Explain one benefit to a business of using critical path analysis when opening a new store.
Show answer
It identifies the critical activities that cannot be delayed, so managers can monitor them closely and move resources from activities with float, helping the store open on time and avoiding extra costs.. Name what CPA identifies and how that helps.

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Sources

Pearson Edexcel International Advanced Subsidiary/Advanced Level in Business specification (XBS11/YBS11, 2018), Unit 3 Business decisions and strategy and Appendices 6, 7 and 9

Last updated 8 November 2026. Spotted a mistake? Tell us.