Question

Dave Fletcher was able to determine the activity times for constructing his laser scanning machine. Fletcher would like to determine ES, EF, LS, LF, and slack for e activity. The total project completion time and the critical path should also be determined. Here are the activity times: Activity Time (weeks) Immediate Predecessor(s) Activity Time (weeks) Immediate Predecessor(s) C, E D, F Dave's earliest start (ES) and earliest finish (EF) are: Activity ES EF

also needs daves latest start and latest finish:

Answer 1

Earliest Start (ES) = the earliest time when the activity can begin

Earliest Finish (EF) = ES + Activity Duration

Latest Finish (LF) = the latest time by when the activity can be finished without changing the project completion duration

Latest Start (LS) = LF - Activity Duration

Slack = LS-ES = LF-EF

To find LF, we start with LF for the activity which has the highest EF. LF for all independent activities is equal to highest EF.

Computing using the above gives us the below -

		Time	Earliest	Earliest	Latest	Latest
Activity	Predecessor	(Weeks)	Start Time	Finish Time	Start Time	Finish Time	Slack
A	-	6	0	6	4	10	4
B	-	7	0	7	0	7	0
C	A	2	6	8	10	12	4
D	A	2	6	8	15	17	9
E	B	5	7	12	7	12	0
F	B	5	7	12	12	17	5
G	C, E	11	12	23	12	23	0
H	D, F	6	12	18	17	23	5

Hence, Dave's ES and EF are -

	Earliest	Earliest
Activity	Start Time	Finish Time
A	0	6
B	0	7
C	6	8
D	6	8
E	7	12
F	7	12
G	12	23
H	12	18

Dave's LS and LF are -

	Latest	Latest
Activity	Start Time	Finish Time
A	4	10
B	0	7
C	10	12
D	15	17
E	7	12
F	12	17
G	12	23
H	17	23

Slack Times are -

Activity	Slack
A	4
B	0
C	4
D	9
E	0
F	5
G	0
H	5

To find the critical path, let us draw the network diagram -

Possible Network paths and their duration are -

ACG --> 6+2+11 = 19 weeks
ADH --> 6+2+6 = 14 weeks
BEG --> 7+5+11 = 23 weeks
BFH --> 7+5+6 = 18 weeks

Hence, critical path is B-E-G

Total project completion duration = duration of critical path = 23 weeks