Question

Please provide detailed solutions to the following problem.

The estimated times and immediate predecessors for the activities in a project at Paccar Winch are given in the following table. Assume that the activity times are independent.

Activity	Immediate Predecessor	Time (Weeks)
		a	m	b
A	-	9	10	11
B	-	4	10	16
C	A	9	10	11
D	B	5	8	11

a) Calculate the expected time and variance for each activity.

b) What is the expected completion time of the critical path? What is the expected completion time of the other path in the network?

c) What is the variance of the critical path? What is the variance of the other path in the network?

d) If the time to complete path A–C is normally distributed, what is the probability that this path will be finished in 22 weeks or less?

e) If the time to complete path B–D is normally distributed, what is the probability that this path will be finished in 22 weeks or less?

f) Explain why the probability that the critical path will be finished in 22 weeks or less is not necessarily the probability that the project will be finished in 22 weeks or less.

Answer 1

a) We find expected time and variance for each activity as shown below:

Based on above table, we prepare project network diagram as shown below;

b) Hence, as seen from above, A-C is the critical path. The expected completion of critical path A-C is 20 weeks The expected completion time of other path B-D is 18 weeks

c) Variance of critical path = variance for A + Variance for C = 0.11 + 0.11 = 0.22.

Variance for path B-D = variance for B + Variance for D = 4+1 = 5

d) Probability for completion within 22 weeks

Probability is found out by finding z value as follows:

z = = = 4.26

From normal distribution table, we get the probability for value of z = 4.26 as 100%

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