PERT Chart : Program Evaluation and Review Technique

PERT Chart : Program Evaluation and Review Technique

Full form of PERT Chart is "Program Evaluation and Review Technique" ,It is a project management tool.PERT chart is used to plan, schedule, and control complex projects.it was developed in the late 1950s byU.S. Navy during Polaris missile project.

PERT Chart is an event-oriented chart ,it focus on Focuses on events,it represents project activities visually.

    1) Each activity is shown as an arrow.
    2) Each event is shown as a node.
    3) Nodes represent the start or completion of activities.

    4) Identifies dependencies between tasks.

    5) Estimates minimum project completion time.

    6) PERT Chart is useful for projects with uncertainty and helps in decision-making.

    7) PERT Chart emphasizes on time , while CPM emphasizes cost.

    8) PERT Chart is read from left to right.

    9) PERT Chart arrows indicate task order.

    10) PERT Chart events are represented by circles/ellipses.

    11) Suitable for R&D projects.Identifies dependencies between tasks.

Time Estimation in PERT Chart

PERT Chart uses three time estimates Optimistic time (O),Pessimistic time (P) ,Most likely time (M).

Expected time (TE) = (O + 4M + P) ÷ 6.

This formula reduces bias and gives weighted average when accounts for uncertainty (For R&D Projects).This makes estimation more realistic and can work wide ranges projects have higher risk.This identify probable completion time and Standard deviation is used for analysis.

Variance (σ²) = [(P – O) ÷ 6]².

Standard deviation (σ) = (P – O) ÷ 6.

Project variance = sum of variances on critical path.

Probability of completion can be calculated.
Formula: 

Z = (Due Date – TE Project) ÷ σ

Higher Z = higher probability
Lower Z = lower probability

By PERT Chart 

• Risk analysis becomes possible.

• Helps avoid unrealistic scheduling.

• Improves confidence in planning.

• Saves time and cost indirectly.

• Brings accuracy in complex projects.

How To Create  PERT Chart 

• Identify all activities of the project.
• Define dependencies between activities.
• List immediate predecessors.
• Draw network diagram.
• Place events (nodes) in correct order.
• Represent activities with arrows.
• Ensure logical sequence.
• Assign time estimates (O, M, P).
• Calculate expected time (TE).
• Identify critical path.
• Critical path = longest path in the network.
• Calculate earliest start (ES) for each activity.
• ES = earliest time an activity can begin.
• Calculate earliest finish (EF).
• EF = ES + activity time.
• Calculate latest finish (LF).
• LF = latest time an activity can finish without delay.
• Calculate latest start (LS).
• LS = LF – activity time.
• Find total float (slack).
• Float = LS – ES (or LF – EF).
• Zero float = critical activity.
• Positive float = non-critical activity.
• Negative float = project delay risk.
• Mark the critical path.
• Check project duration.
• Analyze variances and risk.
• Recheck logical sequence. 

An Example of PERT Chart 

Here is an example of Work - brakdown and how task is dependent on one another .

Activity	Duration	Predecessor(s)
A	3 days	–
B	6 days	A
C	2 days	A
D	5 days	B, C
E	4 days	C
F	3 days	E
G	6 days	D, F
H	5 days	G

Predecessor  menaing one task is dependent on another task , that means (B, C) , C will starts after B finished

Forward Pass (Earliest Times)

A: ES=0 → EF=3

B: ES=3 (after A) → EF=9

C: ES=3 (after A) → EF=5

D: ES=max(EF(B), EF(C))=max(9,5)=9 → EF=14

E: ES=5 (after C) → EF=9

F: ES=9 (after E) → EF=12

G: ES=max(EF(D), EF(F))=max(14,12)=14 → EF=20

H: ES=20 (after G) → EF=25

Project Duration = 25 days (Project will finish in 25 days minimum)

Backward Pass (Latest Times)

Start from project completion at 25:

H: LF=25 → LS=20

G: LF=20 → LS=14

D: LF=14 → LS=9

F: LF=14 → LS=11

E: LF=11 → LS=7

C: LF=min(9 (D), 7 (E))=7 → LS=5

B: LF=9 → LS=3

A: LF=min(3 (B), 5 (C))=3 → LS=0

Slack Calculation : Slack = LS – ES (or LF – EF)

Activity	ES	EF	LS	LF	Slack
A	0	3	0	3	0
B	3	9	3	9	0
C	3	5	5	7	2
D	9	14	9	14	0
E	5	9	7	11	2
F	9	12	11	14	2
G	14	20	14	20	0
H	20	25	20	25	0

Critical Path :A → B → D → G → H

Project Duration = 25 days

By :Ayan Banerjee 

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