Question

In managing a project of the scale and type indicated below, the Critical path method(CPM) is utilized, composed of the following activities and their durations.

Activity	Time in days	preceding activities
A	10	--
B	6	--
C	8	A
D	3	B
E	7	C
G	12	B
H	5	C
F	3	D, G
I	5	E, H
J K	8 8	C F, I, J

a) Draw a critical path network(CPM) network diagram for this project on a separate sheet.

b) Calculate the Early and Late statistics for each activity with their associate slacks.

c) Identify the critical path.

d) Specify the project duration.

e) How long can activities namely:

i) D be delayed without delaying the project completion time?

ii) H be delayed without delaying the project completion time?

iii) J be delayed without delaying the project completion time?

Answer 1

The Critical Path Method (CPM) Network Diagram is as below :

Now, we tabulate the activities and the Earliest Start (ES), Earliest Finish (EF), Latest Start (LS) and Latest Finish (LF) and calculate the slack as below :

Questions A & B are answered above. Now, using the above table, we answer the rest of the questions :

C) Critical Path is the longest path in the network and contains activities with zero slack. So we can infer that the Critical Path is A-C-E-I-K and the duration of the critical path is 10+8+7+5+8 = 38

D) The Project Duration is 38 days

E) The Slack determines how long the activities can be delayed without delaying the project completion time..

Ei) D can be delayed by 18 days

Eii) H can be delayed by 2 days

Eiii) J can be delayed by 4 days