Question

uction needs to complete construction of Shopping Mall project, which is start in August. They are concerned with the completion time. Some of the ighly unreliable. List of activities and their optimistic, pessimistic, and most ion times in weeks) are given in following table: Optimistic Most Likely Pessimistic E(t) 3 5 9 13 11 0.1111 2.7778 7 Immediate Predecessor(s) None A None None AC D, E D, E F G F DF 2 6 9 5 10 6 5 2 9 7 4 18 15 6 1.0000 4.0000 2.7778 0.4444 1.0000 0.1111 4 6 IN 7 8 8 11 9 12 21 8 8 7 5.4444 aw the project network. Calculate early, late times and slack times for each ctivity and find the critical path(s). What is the expected completion time of the oject? What is the probability that MIKO will complete the project within 50 weeks? What is the probability that MIKO will complete the project in more than 45 reeks? s - 4+ F2 0 F4 FS F7 FB # > $ 7. & 3 * 4 5 6 7 U ۳ 8 w 7 V E. و R في T Y

Answer 1

Network diagram:

Start E F к Finish H

Forward Pass:

ES of the starting activities = 0
ES of all other activities = Max. (EF of their immediate predecessors)
EF of an activity = Its ES + Its duration

Backward Pass:

LF of ending activities = Max. (All the EFs)
LF of all other activities = Min. (LS of their immediate successors)
LS of an activity = Its LF - Its duration

Total slack (or, float) = LF - EF for each activity.

Activity	Duration	ES	EF	LS	LF	Slack
A	2	0	2	7	9	7
B	6	2	8	41	47	39
C	9	0	9	0	9	0
D	5	0	5	14	19	14
E	10	9	19	9	19	0
F	(5+4*7+15)/6 = 8	19	27	19	27	0
G	4	19	23	37	41	18
H	6	27	33	41	47	14
I	8	27	35	27	35	0
J	8	27	35	27	35	0
K	(7+4*11+21)/6 = 12	35	47	35	47	0

So, there are two critical paths - C-E-F-I-K and C-E-F-J-K both having expected duration = 47 weeks

So, the expected completion time for the project is 47 weeks.

For probability calculation, take the critical path having a higher variance. This is the path C-E-F-J-K.

Activity	E(t)	σ2
C	9	(11 - 7)2/36 = 0.4444
E	10	4
F	8	2.7778
J	8	(12 - 4)2/36 = 1.7778
K	12	5.444
Totals	47	14.444

So,

Mean duration = 47 weeks
Stdev = SQRT(14.444) = 3.8 weeks

Traget=50 weeks, so, z = (50 - 47)/3.8 = 0.789. F(z) = 0.785. So, there is a 78.5% chance that the project will be completed by 50 weeks

Target=45 weeks, so, z = (45 - 47)/3.8 = -0.5263. F(z) = 0.30. So, there is a 30% chance that the project will be completed by 45 weeks and a 70% chance that it takes more than 45 weeks.