Question

Problem 5-10 (Algo)

The following represents a project that should be scheduled using CPM:

	IMMEDIATE PREDECESSORS	TIMES (DAYS)
ACTIVITY		a	m	b
A	—	1	4	7
B	—	1	3	5
C	A	2	5	11
D	A	1	8	9
E	B	1	2	3
F	C,D	1	6	11
G	D,E	1	2	3
H	F,G	2	3	3

b. What is the critical path?

a. A-D-F-H

b. B-E-G-H

c.A-D-G-H

d.A-C-F-H

c. What is the expected project completion time? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

d. What is the probability of completing this project within 22 days? (Use Excel's NORM.S.DIST() function to find the correct probability for your computed Z-value. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Answer 1

Activity	Optimistic time-a	Expected completion time-m	Pessimistic time-b	Expected time= (a+4*m+ b)/6	Variance, (sigma)^2= (b-a/6)^2
A	1	4	7	4.00	1.00
B	1	3	5	3.00	0.44
C	2	5	11	5.50	2.25
D	1	8	9	7.00	1.78
E	1	2	3	2.00	0.11
F	1	6	11	6.00	2.78
G	1	2	3	2.00	0.11
H	2	3	3	2.83	0.03

PATHS

Path	Duration	Variance
ADFH	19.833	5.583
BEGH	9.833	0.667
ADGH	15.833	5.056
ACFH	18.333	1.889

Answer b: The critical path is the longest path i.e ADFH

Answer c: the expected project completion time through critical path is 19.833

Answer d: the probability of completing this project within 22 days is 0.8204

step 1	we will find the variance of the tasks which lie on critical path				5.58
step 2	mean project time (u) of critical path is=				19.83
step 3	Required completion time is				22
step 4	standard deviation= sqrt(variance)=				2.363
step 5	because Z= (given completion time- u)/standard deviation				0.917
step 6	P(z)= using NORM.S.DIST(z,true)				0.8204

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