Question

QUESTION 3

The Kingdom International Medical Research Center has an important project, i.e. to combat the recently spreading virus. The head of the research division has identified ten groups in his division which will need to carry out different phases of this research and development project. The manager of each group has provided a most likely estimate, an optimistic estimate, and a pessimistic estimate of the duration of that group’s activity. The following Table shows the work to be done by the respective groups, the precedence relationships for when these groups need to do their work, and the estimated times from the manager of each group. (6.5 Marks)

Activity	Immediate	Estimate time (Weeks)
	predecessors	Optimistic	Pessimistic	Most likely
A	-	1.5	15	2
B	-	2	21	3.5
C	A	1	18	1.5
D	B	0.5	15	1
E	A	3	24	5
F	C	1	16	2
G	D	0.5	14	1
H	B	2.5	25	3.5
I	E, F	1	18	3
J	G, H	2	18	3

1.   Draw the complete project network.
2. Determine the expected total time to complete the project.
3. Determine the slack for each activity.
4. Determine the critical path and critical activities.
5. Determine the probability that the project can be completed within 22 weeks.
6. How many weeks can the project be completed with a probability of 30%?

Answer 1

Expected time,Duration of the activity is equal to (Optimistic time+(4*Most likely time)+Pessimisstic time)/6

Variance =Square of ((Pessimistic time-Optimistic time)/6)

a.Network diagram is as follows

Paths are

A-C-F-I ,Duration 17.58 weeks

A-E-I ,Duration 17.08 weeks

B-H-J,Duration 18.42 weeks

B-D-G-J, Duration 17.83 weeks

b.Expected time to complete the project is 18.42 weeks

c.Slack of each activity is

d.Critical Path is B-H-J with duration of 18.42 weeks.

Critical activities are B,H,J (For critical activities slack is 0)

e.73.89%

Calculation

f.15.49 weeks rounded to 16 weeks

Calculation