Critical Path Method (CPM)

Critical Path Method (CPM)

Critical Path Method(CPM) is a project management technique that identifies the longest path of tasks in a project ,this longest path determines the project duration.Critical Path Method(CPM) was developed in about 1950 for large, complex industrial projects,construction & IT projects. It is deterministic , that means assumes known task times.Where PERT is Probabilistic CPM is deterministic.CPM mainly focuses on time, not cost (cost can be added).

What are Advantage of Critical Path Method(CPM) 

1) Produced clear project timeline.
2) Helps prioritize important tasks.
3) Improves resource allocation.
4) Supports cost-time trade-offs (crashing).
5) Enhances control on projects.
6) Enhance accountability of teams.

Limitations

1)Assumes fixed activity duration.
2)Less effective with uncertain estimates.
3)Network diagrams may become too complex.
4)Requires frequent updating.
5)Doesn’t directly handle resource constraints.

6)Can give misleading results if inputs are wrong.

7)Time-consuming for very large projects.

Terminology 

• Activities = tasks in a project.
• Events = milestones marking task completion.
• Duration = estimated time to finish a task.
• Dependencies = order in which tasks must be done.
• Network diagram = visual representation of activities.
• Nodes = represent tasks/events.
• Arrows = represent dependencies.
• Path = sequence of activities from start to end.
• Critical path = longest path (in time).
• Non-critical paths = shorter paths with slack.

Here is a simple math on CPM

For A missible projects , here is the breatdown 

Activity A : duration 4, start activity

Activity B : duration 3, depends on A

Activity C : duration 2, depends on A

Activity D : duration 5, depends on B

Activity E : duration 6, depends on C

Activity F : duration 2, depends on D and E (finish activity)

Forward pass — compute ES (Earliest Start) and EF (Earliest Finish)

ES of first activity = 0; 
EF = ES + duration; 
for an activity with multiple predecessors, ES = max(EF of predecessors).

Activity A: ES = 0 → EF = 0 + 4 = 4

Activity B: ES = EF(A) = 4 → EF = 4 + 3 = 7

Activity C: ES = EF(A) = 4 → EF = 4 + 2 = 6

Activity D: ES = EF(B) = 7 → EF = 7 + 5 = 12

Activity E: ES = EF(C) = 6 → EF = 6 + 6 = 12

Activity F: ES = max(EF(D), EF(E)) = max(12,12) = 12 → EF = 12 + 2 = 14

Project duration = EF(F) = 14 time units

Backward pass — compute LF (Latest Finish) and LS (Latest Start)

 LF of final activity = project duration; 

 LS = LF − duration; for predecessors, LF = min(LS of successors).

F: LF = 14 → LS = 14 − 2 = 12

Activity D: successor is F (LS_F = 12) → LF_D = 12 → LS_D = 12 − 5 = 7

Activity E: successor is F (LS_F = 12) → LF_E = 12 → LS_E = 12 − 6 = 6

Activity B: successor is D (LS_D = 7) → LF_B = 7 → LS_B = 7 − 3 = 4

Activity C: successor is E (LS_E = 6) → LF_C = 6 → LS_C = 6 − 2 = 4

Activity A: successors B and C have LS 4 and 4 → LF_A = min(4,4) = 4 → LS_A = 4 − 4 = 0

Slack

Activity	Dur	ES	EF	LS	LF	Float
A	4	0	4	0	4	0
B	3	4	7	4	7	0
C	2	4	6	4	6	0
D	5	7	12	7	12	0
E	6	6	12	6	12	0
F	2	12	14	12	14	0

Critical path(s)

Path 1: A → B → D → F (4 + 3 + 5 + 2 = 14)

Path 2: A → C → E → F (4 + 2 + 6 + 2 = 14)

                                                                    By:Ayan Banerjee