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 C is __________

Answer 1

Solution:

Expected time for each activity is calculated as;

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

Expected time for activity A = [5 + (4 x 10) + 15] / 6 = 10

Expected time for activity B = [10 + (4 x 12) + 14] / 6 = 12

Expected time for activity C = [10 + (4 x 10) + 10] / 6 = 10

Expected time for activity D = [2 + (4 x 4) + 6] / 6 = 4

Expected time for activity E = [4 + (4 x 8) + 12] / 6 = 8

Expected time for activity F = [4 + (4 x 8) + 12] / 6 = 8

Expected time for activity G = [10 + (4 x 12) + 14] / 6 = 12

Expected time for activity I = [4 + (4 x 8) + 12] / 6 = 8

Expected time for activity J = [2 + (4 x 4) + 6] / 6 = 4

From the given information, the network diagram of the project is drawn below:

From the network diagram, the values of ES, EF, LS, LF are calculated as below:

ES - Early Start

EF - Early Finish

LS - Late Start

LF - Late Finish

Total Slack is calcluated as;

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

Total Slack for activity C = 4 - 0 = 4

Total Slack for activity C = 4 days