Question

1) Consider the network corresponding to the following information.

Activity	Immediate Predecessor(s)	Time (Weeks)
A	---	3
B	---	4
C	A	6
D	B	9
E	B	6
F	C, D	6
G	D, E	8
H	G, F	9

1. Draw the network corresponding to the above information.
2. Using a table format, identify the critical path.
3. What is the project completion time?

Answer 1

2. Critical path: It is the longest distance between the start and finish of the project.

The available paths are:

ACFH = 24

BDFH = 28

BDGH = 30

BEGH = 27

Here, the critical path is BDGH as it has longest time duration.

Hence, ES and EF are calculated in the forward pass fashion from this path.

Next, BDFH path is calculated. Then, BEGH and ACHF are calculated respectively.

Same sequence is followed for calculating Backward pass.

EF denotes the Early Finish.

LS denotes the Latest Start.

LF denotes the Latest finish.

ES is the time of initiation of the activity.

EF = ES + Activity time

LF is the latest finish of the activity.

LS = LF – Activity time

Slack = LS – ES or LF – EF (Both the formulas lead to same result)

ES for the starting activity will be Zero and for other activities the EF value of the previous activity will be the ES for current activity.

Activity	Duration	ES	EF	LS	LF	Slack
A	3	0	3	6	9	6
B	4	0	4	0	4	0
C	6	3	9	9	15	6
D	9	4	13	4	13	0
E	6	4	10	7	13	3
F	6	13	19	15	21	2
G	8	13	21	13	21	0
H	9	21	30	21	30	0

The slack of the activity path BDGH is 0. Hence it can be considered as critical path.

3. Hence, the project completion time is 30 weeks as BDGH is the critical path.

1. The below is the network diagram.