Question

Consider the following network for a small maintenance project (all times are in days). [7 Marks]

Activity	Immediate Predecessor [s]	Optimistic Time	Most Likely Time	Pessimistic Time
A	-	2	3	4
B	-	5	6	7
C	-	5	6	7
D	A	3	4	5
E	A	2	3	4
F	C	3	4	5
G	C	8	10	16
H	B, E, F	5	6	7
I	B, E, F	7	11	15
J	B, E, F	2	3	4
K	G, J	3	4	5
L	D, H	7	11	15

1. Draw an activity on node network diagram for the project.
2. Calculate the minimum expected completion time of the project. Identify the critical path.
3. Estimate the total float, free float and independent float for activities F and G. Explain the meaning of these values.
4. Calculate the probability that the project would be completed within 25 days.
5. Calculate the probability that the project cannot be completed within 30 days.

Using an example, briefly explain how PERT can be used in project management.

Answer 1

a.

The diagram is shown below

b.

The expected completion time is 27 days. The critical path is C-F-H-L

c.

F is on the critical path and thus the float is 0. For the activity G the float will be 27-20.667 = 6.333

d.

The variance of critical path is 2.11. The standard deviation is sqrt(2.11) = 1.45

The z value for 25 days is z = (25-27)/1.45 = -1.37

The corresponding probability P(z=-1.37) = 0.0838

e.

The z value for 30 days is z = (30-27)/1.45 = 2.06

The corresponding probability P(z = 2.06) = 0.9807 for completing below 30 days.

The probability of completing in more than 30 days is 1-0.9807 = 0.0193