Project Management

In order to calculate the probability of the project to be completed in 21 days, the following calculation had to be completed.

Calculate the variance associated with each estimated time (ET) using the below formula:

σ^2= ((b-a)/6 )^2

Activity Estimated Time (ET) Pessimistic Time (b) Optimistic Time (a) Variance

σ^2= ((b-a)/6 )^2

Critical Path

A 3 9 1 1.777777776 X

B 7 13 5 1.777777776 X

C 4 10 2 1.777777776

D 5 7 3 0.444444443

E 8 15 5 2.777777775 X

F 6 12 4 1.777777776

G 4 6 2 0.444444443 X

H 6 6 6 0

I 5 12 2 2.777777775

J 2 3 1 1 X

Calculate the sum of the variance values associated with each activity of the Critical Path:

The Critical Path with the largest variance must be used. In this case, the Critical Path is Activity A, B, E, G, and J. The total sum of the Critical Path is 7.777777777.

Substitute the above calculation with the projected due date or desired completion date (D) and the project expected completion date (T_E):

In our case the projected due date (T_E) is 24 weeks and the expected completion date (D) is 21 weeks. The formula is:

Z = (D- T_E)/√(∑▒〖σ_cp^2.〗) = (21-24)/√7.777777777 = (-3)/2.788866754 = -1.075705748

Using the Z table, we must now calculated the probability of the project to be completed in 21 weeks:

We can see that the Z value of -1.075705747 (-1.08) equals to a probability of 14% (0.1401). Therefore, the probability of the project to be completed in 21 weeks is about 14%.

Question 4.

Activity Normal Time (weeks) (NT) Total Normal Cost (NC) Crash Time* (weeks) (CT) Total Crash Cost (CC)

A 6 $6,000 4 $12,000

B 10 $10,000 9 $11,000

C 8 $8,000 7 $10,000

D 12 $12,000 10 $14,000

E 10 $10,000 7 $12,000