This document describes Program Evaluation and Review Technique (PERT) and its use in planning and scheduling a project. It provides activity details like predecessor tasks, optimistic, most probable and pessimistic durations. It then shows the steps to 1) draw the activity on arrow (AOA) network, 2) calculate the total project time using PERT, 3) determine the probability the project finishes within 50 and 44 weeks, and 4) find the project completion time with 80% probability.

1. Program Evaluation and Review Technique
( P E R T )
Activity Predecessor
Pessimistic
( P )
Most probable
( M )
Optimistic
( O )
Constraint
V N,Q,D 8 6 4 D3B ,L2Q
D C 13 9 5 -
C B 13 6 5 F6
R - 10 7 4 -
X R 14 9 4 -
Q X,Z 4 3 2 D2X
N Z 9 7 5 -
Z - 10 7 4 F6
B R 14 9 4 D5
1. Draw (A.O.A) network for the given project.
2. Get total time for the project, according to the given durations using (PERT).
3. What’s the probability that the total time of the project dose not exceed ( 50 w)
and (44 w).
4. What’s the total time of the project with probability 80%.

2. Activity Predecessor ( P ) ( M ) ( O ) Constraint te
V N,Q,D 8 6 4 D3D ,L2Q 6
D C 13 9 5 - 9
C B 13 6 5 F6 7
R - 10 7 4 - 7
X R 14 9 4 - 9
Q X,Z 4 3 2 D2X 3
N Z 9 7 5 - 7
Z - 10 7 4 F6 7
B R 14 9 4 D5 9
R
N
Z
B
X
D
Q V
C
7
7
F6
7
7
F6
9
D5
3
D2X
6
D3D
L2Q
9
9
0
16
7
7
21 28
37 46
7
16
14
21
37
𝑃 + 4𝑀 + 𝑂
6

3. Activity ( P ) ( M ) ( O )
Variance
σ
Stander
Deviation
σ2
V 8 6 4 2 ̸ 3 4 ̸ 9
D 13 9 5 4 ̸ 3 16 ̸ 9
C 13 6 5 4 ̸ 3 16 ̸ 9
R 10 7 4 𝟏 1
X 14 9 4 - -
Q 4 3 2 - -
N 9 7 5 - -
Z 10 7 4 - -
B 14 9 4 5 ̸ 3 25 ̸ 𝟗
70 ̸ 𝟗Σ σ2
Stander Deviation (σ2 )= (
𝑝−𝑜
6
)2
Variance (σ) =
𝑃−𝑂
6

4. z =
𝑻 𝒑− 𝑻 𝒆𝒏𝒅
𝚺𝝈 𝟐
Tend :End time for the project
Tp :Probability time for the project
z =
𝑻 𝒑− 𝑻 𝒆𝒏𝒅
𝚺𝝈 𝟐
=
𝟓𝟎−𝟒𝟔
𝟕𝟎
𝟗
= 1.434 = 1.43 table Probability = 0.92364
= 92.364 %
3
z =
𝑻 𝒑− 𝑻 𝒆𝒏𝒅
𝚺𝝈 𝟐
=
𝟒𝟒−𝟒𝟔
𝟕𝟎
𝟗
= -0.717 = -0.72 table
Probability = 1 -0.76424 = 0.23576 = 23.576 %
What’s the probability that the total time of the project dose not exceed ( 50
w) and (44 w).

6. z =
𝑻 𝒑− 𝑻 𝒆𝒏𝒅
𝚺𝝈 𝟐
0.841612 =
𝑻 𝒑−𝟒𝟔
𝟕𝟎
𝟗
4
What’s the total time of the project with probability 80%.
0.85
0.84
X
0.802340.79955 0.8
0.00279
0.00045
𝟎. 𝟎𝟎𝟎𝟒𝟓
𝑿
=
𝟎. 𝟎𝟎𝟐𝟕𝟗
𝟎. 𝟎𝟏
X =
𝟎.𝟎𝟎𝟎𝟒𝟓 𝑿 𝟎.𝟎𝟏
𝟎.𝟎𝟎𝟐𝟕𝟗
= 𝟎. 𝟎𝟎𝟏𝟔𝟏𝟐
Z = 0.84 + 0.001612 = 0.841612
𝑻 𝒑 = 𝟒𝟖. 𝟑𝟒𝟕𝟏