Question

The construction department is planning to bid on a large project for the development of a new airport in Chicago area. The following table shows major activities, times, and sequence required:

Activity	Immediate Predecessor	Activity Duration, Months
		Optimistic	Most Likely	Pessimistic
A	-	2	3	4
B	A	1	2	3
C	A	4	5	12
D	A	3	4	11
E	B	1	3	5
F	C	1	2	3
G	D	1	8	9
H	E, F	2	4	6
I	H	2	4	12
J	G	3	4	5
K	I, J	5	7	9

1. *Draw the network diagram, using appropriate technology and the nomenclature that is used in the solved Exercise for this Chapter.
2. Determine the expected time (T_e) and the variance for each activity.
3. *Determine and show the early start, early finish, late start and late finish for each activity (use the nomenclature used in the solved Exercise).
4. Determine the critical path and the expected project completion time.
5. What is the probability that the project can be completed in:
   1. 25 months
   2. 30 months
6. There is a 85% chance that the project can be completed in X months or less. What is X?

*For problems A and C, the textbook focused on the Critical Path Method (AON Network/PERT Chart).

Answer 1

a.

b.c.

Formula

d. Critical path is A-C-F-H-I-K as all the activities have 0 slack.

Expected project duration = Duration of critical path = 27 months
e.

project variation = sum of variations of critical activities

We know, Z = (Required project completion time-expected project completion time)/project standard deviation

When Required project completion time = 25 months,

Z = (25-27)/sqrt(5.666666667) = -0.84016805

Corresponding probability = norm.s.dist(-0.84016805,TRUE) = 0.200407085 = probability of completing the project within 25 months

When Required project completion time = 30 months,

Z = (30-27)/sqrt(5.666666667) = 1.260252076

Corresponding probability = norm.s.dist(1.260252076,TRUE) = 0.896210779 = probability of completing the project within 30 months

f.

Z score for 85% probability = normsinv(0.85) = 1.036433389

We know, Z = (Required project completion time-expected project completion time)/project standard deviation

or, 1.036433389 =(Required project completion time-27)/sqrt(5.666666667)

or, Required project completion time = sqrt(5.666666667)*1.036433389+27 = 29.46720496 months (Answer)