Question

A project involves the following activities, their predecessors, and the times (in weeks) associated with each activity.

Activity	Immediate Predecessor	Optimistic (a)	Most Likely (m)	Pessimistic (b)
A	--	1	2	3
B	--	2	3	4
C	--	3	4	5
D	A	4	5	12
E	B	1	3	5
F	B	3	4	11
G	C	5	6	13
H	D, E	8	9	10
I	F, G	4	5	6
J	H, I	1	1	1

What is the probability that the project will be finished in 21 weeks or less?

What is the probability that the project will take between 19 to 21 weeks to be completed?

If we want a 95% chance of completing the project on time, how far ahead of the schedule meeting time should the project be started?

If activity F is delayed and takes 10 weeks to complete, would the project completion time be any different? If yes, what would be the critical path and the expected completion time?

Answer 1

EXPECTED TIME

FORMULA:

(a + (4m) + b) / 6

A = (1 + (4 * 2) + 3) / 6 = 2

B = (2 + (4 * 3) + 4) / 6 = 3

C = (3 + (4 * 4) + 5) / 6 = 4

D = (4 + (4 * 5) + 12) / 6 = 6

E = (1 + (4 * 3) + 5) / 6 = 3

F = (3 + (4 * 4) + 11) / 6 = 5

G = (5 + (4 * 6) + 13) / 6 = 7

H = (8 + (4 * 9) + 10) / 6 = 9

I = (4 + (4 * 5) + 6) / 6 = 5

J = (1 + (4 * 1) + 1) / 6 = 1

VARIANCE

FORMULA:

((b - a) / 6) ^ 2

A = (3 - 1) / 6) ^ 2 = 0.11

B = (4 - 2) / 6) ^ 2 = 0.11

C = (5 - 3) / 6) ^ 2 = 0.11

D = (12 - 4) / 6) ^ 2 = 1.78

E = (5 - 1) / 6) ^ 2 = 0.44

F = (11 - 3) / 6) ^ 2 = 1.78

G = (13 - 5) / 6) ^ 2 = 1.78

H = (10 - 8) / 6) ^ 2 = 0.11

I = (6 - 4) / 6) ^ 2 = 0.11

J = (1 - 1) / 6) ^ 2 = 0

CPM ANALYSIS

ACTIVITY	DURATION	ES	EF	LS	LF	SLACK
A	2	0	2	0	2	0
B	3	0	3	2	5	2
C	4	0	4	1	5	1
D	6	2	8	2	8	0
E	3	3	6	5	8	2
F	5	3	8	7	12	4
G	7	4	11	5	12	1
H	9	8	17	8	17	0
I	5	11	16	12	17	1
J	1	17	18	17	18	0

FORWARD PASS

1. Go from left to right in a network.

2. ES = maximum of the EF value from all the direct predecessors.

3. EF = ES + Duration.

BACKWARD PASS

1. Go from right to left in a network.

2. LF = minimum of the LS value from all the direct predecessors.

3. LS = LF - Duration.

CRITICAL PATH

1. Total slack of all activities should be 0.

2. The total duration of all the activities should be the highest.

3. Slack = LF - EF or LS - ES

CRITICAL PATH & DURATION

A + D + H + J = 18

ESTIMATES

VARIANCE OF CRITICAL PATH = 0.11 + 1.78 + 0.11 + 0 = 2

Due time = 21

Expected time = 18

Variance = 2

Stdev = sqrt(variance) = sqrt(2) = 1.41(ROUNDED)

Z = DUE - EXPECTED / STDEV

Z = 21 - 18 / 1.41 = 2.13

Z value of 2.13 gives a distribution of 0.9834 OR 98.34 % probability of completion of the project by the due time of 21