The following represents a project that should be scheduled using CPM: 10 IMMEDI

Question

The following represents a project that should be scheduled using CPM: 10 IMMEDIATE TIMES (DAYS) ACTIVITY PREDECESSORS a m 14 3 5 2 5 4 6 1 2 C,D 3 5 D,E 1 2 F,G 2 5 b. What is the critical path? O B-E-G-H O A-C-F-H O A-D-F-H O A-D-G-H c. What is the expected project completion time? (Round your answer to 3 decimal places.) Project completion time days d. What is the probability of completing this project within 22 days? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Probability

Explanation / Answer

b. We need to compute the expected time of each activity. Expected time = (a+4m+b)/6

Expected duration of each path:

The highest duration is 20.167 and hence A-D-F-H is the critical path.

c. Expected project completion time = duration of the critical path (as calculated above) = 20.167 days

d. Variance = ((pessimistic activity time estimate - optimistic activity time estimate)/6)^2

Variance of critical path = 1+1.361+0.444+0.444 = 3.25

z = (22 - 20.167)/(3.25^2)

= 1.02

Thus probability associated with z value of 1.02 = 0.8461 (from Z table)

Activity a m b Expected time = (a+4m+b)/6 A   1.00 4 7.00 4.00 B 3.00 5.00 10.00 5.50 C 2.00 5.00 8.00 5.00 D 4.00 6.00 11.00 6.50 E 1.00 2.00 3.00 2.00 F 3.00 5.00 7.00 5.00 G 1.00 2.00 6.00 2.50 H 2.00 5.00 6.00 4.67

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