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1. Consider a project consisting of four activities A, B, C, and D. a) A and B,

ID: 450735 • Letter: 1

Question

1. Consider a project consisting of four activities A, B, C, and D. a) A and B, the first activities of the project, can be started simultaneously. b) C can be started only after A is completed. c) D can be started only after B is completed Suppose the activity times for the activities are A = 2 weeks, B = 2 weeks, C = 2 weeks, D = 2 weeks. a) How long does the project take to complete? b) We ask the engineer working on activity A to factor in uncertainty in activity times and to provide better estimates of the activity times. The engineers tell us that activity A takes 1 week 50% of the time, and 3 weeks 50% of the time. How long does the project now take to complete (on average)? c) We now also ask the engineer working on activity B to factor in uncertainty in activity times and to provide better estimates of the activity times. The engineer now tell us that activity B takes 1 week 50% of the time, and 3 weeks 50% of the time. How long does the project now take to complete (on average)? [ASSUME THAT BOTH ACTIVITY A AND ACTIVITY B ARE UNCERTAIN]

Explanation / Answer

a) A & B start simultaneously and take 2 weeks to complete, now: C starts after A & D starts after B and both take 2 weeks each (simulatneously) So it takes 4 weeks in total to complete the project.

b) A takes 1 week 50 % percent of the time and 3 weeks 50 percent of the time, so on average it will take: (0.5*1 + 0.5*3) = 2 weeks on an average, So it takes 4 weeks in total to complete the project.

c)Now with activity B also having similar probability, there are 4 scenarios:

A completes in 1 week, B completes in 1 week....25 % probability...max time to complete both activities= 1 week

A completes in 1 week, B completes in 3 weeks....25 % probability..max time to complete both activities=3 weeks

A completes in 3 weeks, B completes in 1 week....25 % probability..max time to complete both activities=3 weeks

A completes in 3 weeks, B completes in 3 weeks....25 % probability..max time to complete both activities=3 weeks

So, the average time to complete both the activities A & B is (0.25*1 +0.75*3) = 2.5 days

2 additional days are required to complete C & D

So, now the average time to complete the project is 4.5 days.