Project Management - Programme Evaluation and Review Technique (PERT)

 

Project Management

Programme Evaluation and Review Technique (PERT)

 

Part A: Discussion about –

1. Method of computation of expected project completion time, and

2. Method of determining the probability of completing a project in a certain fixed completion time.

Part B: YouTube link for the video on the above discussions including solution of one illustration involving -

1. Drawing the Network Diagram of a project,

2. Computation of expected completion time of the project, and

3. Determining the probability of completing the project in a certain fixed number of days.

Part A

Steps for computing the expected project completion time

Step: 1   –  Drawing the network diagram with optimistic time, most likely time and pessimistic time of each activity,

 

Step: 2   –  Calculation of expected completion time [T (ij)] and variance of completion time [V (ij)] of each activity,

 

Step: 3   –  Determining the Critical Path with the expected completion times of the activities,

 

Step: 4   –  Determining the expected completion time of the project Σ [T (ij)] and variance of completion time of the project Σ [V (ij)] with the expected completion times and variances of completion times respectively of the critical activities on the Critical Path, and

 

Step: 5   –  Determining the probability of completing the project in a certain fixed completion time.

 

Discussion of the steps 2 to 5 in details

Step: 2

Calculation of expected completion time and variance of completion time of each activity

 

Formulas:

Expected completion time of (i – j) activity,
T(ij) =	[(a + 4m + b) ÷ 6]
Variance of completion time of (i – j) activity,
V(ij) =	[(b – a) ÷ 6]^2
Where,
a =	Optimistic Time of completing the (i – j) activity
m =	Most Likely Time of completing the (i – j) activity
b =	Pessimistic Time of completing the (i – j) activity

 

Table for:

Calculation of Expected Completion Times [T (ij)] and Variances of Completion Times [V (ij)] of the Activities

 

Activity	Duration			T(ij) =	V(ij) =
	a	m	b	(a + 4m + b) ÷ 6	[(b − a) ÷ 6]^2
1 – 2
2 – 3
2 – 4

 

Step: 3

Critical Path of the project is the longest path from the initial node to the terminal node of the project with the expected completion times of the activities.

 

Step: 4

Computation of –

1	Expected project duration, μ =	Σ [T (ij)] for the critical path
2	Variance of the project duration, σ^2 =	[Σ [V (ij)]] for the critical path
3	Standard deviation of the project duration, σ =	[Σ [V (ij)]] ^ (1/2) for the critical path

 

Step: 5

Probability of completing the project in T days

= P(X ≤ T)

= P (Z ≤ (T − μ)/σ)

 

  Where,

Z      =	(X − μ)/σ and
X      =	Random Variable for Expected Completion Time of the Project following Normal Probability Distribution.

 

Part B

YouTube link for the video on the above discussions including solution of the following illustration –

Please click on the following YouTube Link:

Project Management - PERT

PERT –

Computation of Expected Project Completion Time

 

Illustration:

A project consists of nine activities which are indicated by A, B, C etc. Their time estimates and precedence relationship are given below:

		Time estimates (in days)
Activity	Preceding activity	Optimistic	Most likely	Pessimistic
A	–	4	6	8
B	A	5	7	15
C	A	4	8	12
D	B	15	20	25
E	B	10	18	26
F	C	8	9	16
G	E	4	8	12
H	D, F	1	2	3
I	G, H	6	7	8

 

You are required to –

1.    Draw the network diagram,

2.    Determine the critical path and compute the expected project        completion time, and

3.    Determine the probability of completing the project in 55 days.