Question

A plant is acquiring new production machinery. Before the machinery can be fully functional, a number of activities must be performed, including roughing out for power, placing the machinery, installing the equipment that will feed product to the machinery, etc. The activities, their precedence relationships, and their durations are shown in the following table.

Days
Activity a m b immediate predecessors
A 8 10 12 -
B 6 7 8 -
C 3 3 6 -
D 10 20 30 A
E 6 7 8 C
F 9 10 11 B, D, E
G 6 7 11 B, D, E
H 14 15 16 F
I 10 11 12 F
J 6 7 8 G, H
K 4 7 10 I, J
L 1 2 6 G, H

Determine the expected times and variances for each activity.

Answer 1

The expected times and variances for each activity can be calculated using the three-point estimation method. The expected time is calculated as (a + 4m + b)/6, and the variance is calculated as ((b - a)/6)^2.

Step-by-step explanation:

To determine the expected times and variances for each activity, we need to use the three-point estimation method. The expected time for an activity is calculated as (a + 4m + b)/6, where a is the optimistic estimated duration, m is the most likely estimated duration, and b is the pessimistic estimated duration.

For example, for activity A, the expected time is (8 + 4(10) + 12)/6 = 10 days. The variance for an activity is calculated as ((b - a)/6)^2.

Using this method, we can calculate the expected times and variances for all the activities:

A: Expected time = 10 days, Variance = ((12 - 8)/6)^2 = 0.44

B: Expected time = 7 days, Variance = ((8 - 6)/6)^2 = 0.11

C: Expected time = 4.67 days, Variance = ((6 - 3)/6)^2 = 0.33

D: Expected time = 16.67 days, Variance = ((30 - 10)/6)^2 = 13.33

E: Expected time = 7.67 days, Variance = ((8 - 6)/6)^2 = 0.11

F: Expected time = 10.17 days, Variance = ((11 - 9)/6)^2 = 0.11

G: Expected time = 8.83 days, Variance = ((11 - 6)/6)^2 = 0.83

H: Expected time = 15 days, Variance = ((16 - 14)/6)^2 = 0.11

I: Expected time = 15.83 days, Variance = ((16 - 14)/6)^2 = 0.11

J: Expected time = 7.67 days, Variance = ((8 - 6)/6)^2 = 0.11

K: Expected time = 7.33 days, Variance = ((10 - 4)/6)^2 = 0.89

L: Expected time = 2.83 days, Variance = ((6 - 1)/6)^2 = 1.33