Problems on CPM

CPM Problem 1: 

Activity	Time(Days)	Predecessor
A	2	-
B	3	-
C	4	-
D	1	A
E	2	B
F	5	B
G	7	C
H	2	D,E
I	3	F,G
J	1	H,I

Network diagram :

Critical Path Network diagram :

Now apply Node rule to all the above activities as shown in fig  

Forward Pass:

Backward Pass:

Now upon calculating Total float or slack we found the Critical Path has :   C - G - I - J

Output: 

CRITICAL PATH : C-G-I-J

Try to solve the critical path for the below examples using the above said procedure 

Problem :

Activity	Time(Days)	Predecessor
A	3	-
B	4	A
C	2	A
D	5	B
E	1	C
F	2	C
G	4	D,E
H	3	F,G

Critical Path :  A-B-D-G-H

Problem :

Activity	Time(Days)	Predecessor
A	2	-
B	5	-
C	4	-
D	5	B
E	7	A
F	3	A
G	3	B
H	6	C,D
I	2	C,D
J	5	E
K	4	F,G,H
L	3	F,G,H
M	12	I
N	8	J,K

Critical Path : B-D-H-K-N