Question

Consider the following precedence chart:

ACTIVITY	PRECEDING ACTIVITIES	OPTIMISTIC TIME (days)	MOST LIKELY TIME (days)	PESSIMISTIC TIME (days)
A	-	5	10	15
B	-	10	12	14
C	-	10	10	10
D	B,C	2	4	6
E	A	4	8	12
F	A	4	8	12
G	D,E	10	12	14
I	F	4	8	12
J	G	2	4	6

The total slack for activity F is __________

	a.	8
	b.	4
	c.	2
	d.	0

Answer 1

Solution:

From the given information, network diagram can be drawn as below:

The estimated expected time of each activity is calculated as;

Expected time, T = (a + 4m + b) / 6

where,

a = Optimistic time

m = Most likely time

b = Pessimistic time

Expected time of Activity A = [5 + (4 x 10) + 15) / 6 = 10

Expected time of Activity B = [10 + (4 x 12) + 14) / 6 = 12

Expected time of Activity C = [10 + (4 x 10) + 10) / 6 = 10

Expected time of Activity D = [2 + (4 x 4) + 6) / 6 = 4

Expected time of Activity E = [4 + (4 x 8) + 12) / 6 = 8

Expected time of Activity F = [4 + (4 x 8) + 12) / 6 = 8

Expected time of Activity G = [10 + (4 x 12) + 14) / 6 = 12

Expected time of Activity I = [4 + (4 x 8) + 12) / 6 = 8

Expected time of Activity J = [2 + (4 x 4) + 6) / 6 = 4

From the network diagram, the values of ES, EF, LS, LF can be computed as below:

ES = Early Start

EF = Early Finish

LS = Late Start

LF = Late Finish

From the above diagram,

ES for activity F = 10

EF for activity F = 18

LS for activity F = 18

LF for activity F = 26

Slack is calculated as;

Slack = (LS - ES) or (LF -EF)

Slack = 18 - 10

Slack = 8

The total slack for activity F = 8

Answer: Option (a) - 8