Question

Kenya Motors Ltd. has listed the following actities as necessary in introducing a new vehicle moc the market. Activity Predecessor Expected Duration (Weeks) 12 А B С А 10 D А 8 E А 6 F С G 10 10 D H B.DE 10 H F.G.I 6 Required: a) A network diagram for the above project (10 Marks) b) The critical path (2 Marks) The project duration (2 Marks) d) if the start of activity B is delayed by 6 weeks activity E by 4 weeks and activity G by 5 weeks by how many weeks will the project be delayed? (5 Marks) e Activity completion times are beta distributed with the following standard deviations:

Answer 1

(a)

F Start Finish B H

(b)

Use the Critical Path Method (CPM) to find the critical path as follows:

Forward Pass:

ES of the starting activities = 0
ES of all other activities = Max. (EF of their immediate predecessors)
EF of an activity = Its ES + Its duration

Backward Pass:

LF of ending activities = Max. (All the EFs)
LF of all other activities = Min. (LS of their immediate successors)
LS of an activity = Its LF - Its duration

Total slack (or, float) = LF - EF for each activity.

Activity	Duration	ES	EF	LS	LF	Slack
A	12	0	12	0	12	0
B	6	0	6	14	20	14
C	10	12	22	14	24	2
D	8	12	20	12	20	0
E	6	12	18	14	20	2
F	10	22	32	24	34	2
G	10	20	30	24	34	4
H	10	20	30	20	30	0
I	4	30	34	30	34	0
J	6	34	40	34	40	0

The critical path of a project is composed of activities with zero total slack. So, the critical path is A-D-H-I-J.

(c)

Project duration = LF of the last activity 'J' = 40 weeks

(d)

Slack of 'B' = 14 weeks < the delay of 6 weeks
Slack of 'E' = 2 weeks > the delay of 4 weeks by 2 weeks
Slack of 'G' = 4 weeks < the delay of 5 weeks.

So, the project will be delayed only by 'E' by 2 weeks. So, it will finish in 42 weeks