Question

7. For the following schedule, draw the node network, perform the CPM calculations, mark the critical path, and complete the table.

Activity	IPA	Duration	ES	EF	LS	LF	TF	FF
A	-	3	0	3	3	6	3	5
B	-	5	0	5	5	10	5	2
C	A	6	3	9	9	14	5	4
D	A, B	9	5	14	14	23	9	9
E	A, B	4	5	9	9	12	7	4
F	B	6	5	11	11	17	6	3
G	C, D	5	14	19	19	24	5	5
H	D, E	12	14	26	26	30	12	12
I	D, E, F	7	14	21	21	20	7	12
J	E	9	9	10	10	27	9	8
K	G, H, I	10	26	36	36	46	10	15
L	I, J	6	21	27	27	33	6	6
M	G, I	4	21	25	25	29	4	11
N	K	2	36	38	38	40	2	30

Answer 1

Compute the Early Start (ES), Early Finish (EF), Late Start (LS), and Late Finish (LF) using the following rules.

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

Total Float (TF) = LF - EF

Free Float (FF) of an activity = Min. (ES of its successors) - EF

Calculations

The critical path is constituted by the activities with TF=0

So, the critical path is B-D-H-K-N and the duration is 38.