Question

Given the following activity list and times in days: (15 points)

Activity           Optimistic       Most Likely     Pessimistic

                        Time                Time                Time

A                     7                      10                    12

B                     6                      8                      14

C                     5                      9                      12

D                     12                    14                    21

E                      10                    12                    15

F                      4                      5                      8

G                     1                      3                      8

H                     12                    15                    17

NOTE 1: ASSUME THE CRITTCAL PATH IS “B-E-H”.

1. Calculate the schedule duration of the critical path in days.

2. What is the probability of the project being completed in 39 days?

3. If you want a probability that the project will finish with no less that 85% certainty what is the project duration for that certainty? (5 points)

Note no interpolation is necessary from the table of Z values attached.

Answer 1

Answer to question a :

Refer below table for activities on critical path :

Activity	Optimistic	Most likely	Pessimistic	Mean	Variance
B	6	8	14	8.67	1.78
E	10	12	15	12.17	0.69
H	12	15	17	14.83	0.69

Mean = ( Optimistic + 4 x Most likely + Pessimistic) / 6

Variance = ( Pessimistic – Optimistic)^2/36

Schedule duration of the critical path

= Sum of means

= 8.67 + 12.17 + 14.83

= 35.67 days

Answer to question b :

Variance of the critical path

= Sum of variances of activities on critical path

= 1.78 + 0.69 + 0.69

= 3.16 days

Standard deviation of the critical path

= Square root ( Variance of critical path )

= 1.78

Let Z value for the probability of the project being completed in 39 days

= Z1

Therefore ,

Schedule duration of critical path + Z1 x Standard deviation of critical path = 39

Or, 35.67 + Z1x 1.78 = 39

Or, 1.78.Z1 = 3.33

Or, Z1 = 1.87

Corresponding probability for Z = 1.87 as derived from Z table =0 .9693

Answer to question C :

Required probability = 0.85

Corresponding Z value = NORMSINV ( 0.85) = 1.036

Project duration for this certainty

= Schedule duration + Z value x Standard deviation of duration of critical path

= 35.67 + 1.036 x 1.78

= 35.67 + 1.844

= 37.514 days