Question

1. Using the following information, create a network diagram. Calculate the total duration (days) of the project, its early start, early finish, late start, and late finish times, and the slack for each activity. Finally, identify the project’s critical path. (4 pts.)

Activity		Duration		Predecessors	ES	EF	LS	LF	Free Slack	Total Slack
A		15		--
B		6		A
C		12		--
D		15		B, C
E		12		A
F		9		E
G		17		C, D, E
H		10		E, F
I		13		C, G
J		3		G, H
K		12		J, I

Now, assume that activity E has taken 10 days past its anticipated duration to complete. What happens to the project’s schedule? Has the duration changed? Is there a new critical path?

Answer 1

step 1	find early start, and early finish from the start of the project for each activity
step 2	Find Maximum EF and keep it as the LF of last activities. Max of EF's is 78
step 3	calculate LS for each activity after calculating its EF

Activity	Duration, D	Early start, ES=Max of early finish of preceding activities	Early finish, EF = ES + D	Late finish, LF= Min of LS of successor activities	Late start, LS= LF - D	Total slack= LF-EF	Critical activity, activities with 0 slack time	Free slack= Min(ES of Successor)- ES -Duration
A	15	0	15	15	0	0	Yes	0
B	6	15	21	21	15	0	Yes	0
C	12	0	12	21	9	9	No	9
D	15	21	36	36	21	0	Yes	0
E	12	15	27	36	24	9	No	0
F	9	27	36	53	44	17	No	0
G	17	36	53	53	36	0	Yes	0
H	10	36	46	63	53	17	No	7
I	13	53	66	66	53	0	Yes	0
J	3	53	56	66	63	10	No	10
K	12	66	78	78	66	0	Yes	0

Project duration is 78,

Critical path with 0 slack is A-B-D-G-I-K

If E takes 10 days more

Activity	Duration, D	Early start, ES=Max of early finish of preceding activities	Early finish, EF = ES + D	Late finish, LF= Min of LS of successor activities	Late start, LS= LF - D	Total slack= LF-EF	Critical activity, activities with 0 slack time
A	15	0	15	15	0	0	Yes
B	6	15	21	22	16	1	No
C	12	0	12	22	10	10	No
D	15	21	36	37	22	1	No
E	12+10= 22	15	37	37	15	0	Yes
F	9	27	36	54	45	18	No
G	17	37	54	54	37	0	Yes
H	10	36	46	64	54	18	No
I	13	54	67	67	54	0	Yes
J	3	54	57	67	64	10	No
K	12	67	79	79	67	0	Yes

Project duration is 79,

NEW Critical path with 0 slack is A-E-G-I-K