Question

activity	follows	optimistic duration	most likely direction	pessimistic duration
A	-	4	6	14
B	A,C	3	4	5
C	-	3	5	13
D	A,E	12	18	24
E	-	8	10	18
F	A,E	4	6	8
G	B,F	7	8	9
H	G	10	12	14
I	G	5	6	7
J	D,I	5	7	9

a) Calculate mean duration and standard deviation for all the activities using the beta distribution. [4pts]
  
b) Construct a network diagram for this problem using the mean durations calculated in part (a), calculate the LS(Foll.), ES(Prec.) and total float for all the activities, and hence identify the critical path . What is the mean completion time for the project? What is the standard deviation of the critical path? [30 pts ]
  
c) What is the 92% confidence interval for the length of the critical path? [4 pts]
  
d) Assuming the probability distribution of the length of the critical path can be approximated by a normal distribution with the mean and standard deviation calculated in part (b), calculate the probability of completing the project within 42 weeks. [4 pts]

e) Calculate the probability of completing the project between 35 and 40 weeks? [4 pts]
  
f) Answer the project manager’s question: “I want to tell the client that there is a 10.03% chance the project will take longer than X weeks _{- what figure should I give them (i.e. find X)?” [4]}

(please show work step by step and excel file)

Answer 1

Activity	To	Tm	Tp	Te	(Var)^0.5	Var
A	4	6	14	7	1.666667	2.777778
B	3	4	5	4	0.333333	0.111111
C	3	5	13	6	1.666667	2.777778
D	12	18	24	18	2	4
E	8	10	18	11	1.666667	2.777778
F	4	6	8	6	0.666667	0.444444
G	7	8	9	8	0.333333	0.111111
H	10	12	14	12	0.666667	0.444444
I	5	6	7	6	0.333333	0.111111
J	5	7	9	7	0.666667	0.444444

Activity	ES	EF	LS	LF	Slack
A	0	7	6	13	6
B	7	11	13	17	6
C	0	6	7	13	7
D	11	29	13	31	2
E	0	11	0	11	0
F	11	17	11	17	0
G	17	25	17	25	0
H	25	37	26	38	1
I	25	31	25	31	0
J	31	38	31	38	0

Critical path is EFGIJ with duration 38.

Variance of the CP=3.8887

SD of critical path = (3.8887)^0.5 =1.9719

Time for 92% probability is given by

z = T-38/1.9719

z =1.41

1.41 = T-38/1.9719

T =40.78

(d) Prob. that the project will be completed within 42 weeks

z = 42-38/1.9719 =2.02

which gives a probability of 0.9783

Note : As per policies, I can answer first 4 parts of a problem. Inconvenience is regretted