Question

Consider a project with activities as follows:

Activity Depends on Duration (weeks)
A - 3
B A 5
C A 4
D B,C 3
Suppose that the duration of B can either be 2 or 8, each with equal likelihood. How long, on average, does the project take to complete?

Answer 1

The average time to complete the project, considering the varying duration of Activity B, is the mean of the timelines calculated for each possible duration of B. With an equal likelihood for B taking 2 weeks and 8 weeks, the average project duration is 12 weeks.

Step-by-step explanation:

To calculate the average time it takes to complete the project given the varying duration of Activity B, we need to consider the sequence of activities and their dependencies. Activity A takes 3 weeks, and Activities B and C depend on A. Activity D depends on the completion of both B and C and takes 3 weeks. We will calculate the project duration for both possible durations of Activity B (2 weeks and 8 weeks) and then find the average.

If Activity B takes 2 weeks, the total project duration is the longer path through either B or C, which in this case is through C (3 weeks for A, 4 weeks for C, and 3 weeks for D), totaling 10 weeks. If Activity B takes 8 weeks, then the duration through B would be longer (3 weeks for A, 8 weeks for B, 3 weeks for D), totaling 14 weeks. Since each duration has an equal likelihood, the average project duration is the mean of these two durations.

Therefore, the average duration is (10 weeks + 14 weeks) / 2 = 12 weeks. This is the final answer, considering the equal likelihood of both durations of Activity B.