Question

The following table represents the set of activities required to complete a project, along with their time estimates for PERT calculations. a. Using the data in the table, calculate the expected time (ET) and variance for each activity. Job Predecessor mi expected variance number Job(s) time (ET) --- 468 B A 3 4 5 CIA 234|| D C 34 11 E B, C 13 5 D, E 2 46 F b. [Sketch the network diagram for the project on a sheet of paper. YOU DO NOT HAVE TO SUBMIT THE SKETCH AS PART OF YOUR ANSWER]. c. List each unique path through the network. For example, "A, B, C" would indicate a path consisting of activity A, followed by activity B, which is followed by activity C. d. Indicate the critical path. (You can do this by inspecting the paths -- you do not have to calculate ES, EF, LS, LF.) What is the expected completion tim for the project? e. What is the probability that the project will be completed in 24 days or less? f. What is the probability that the project will take more than 24 days to complete?

Answer 1

Answer a:

Activity	Optimistic time-a	Expected completion time-m	Pessimistic time-b	Expected time= (a+4*m+ b)/6	Variance, (sigma)^2= (b-a/6)^2
A	4	6	8	6.00	0.44
B	3	4	5	4.00	0.11
C	2	3	4	3.00	0.11
D	3	4	11	5.00	1.78
E	1	3	5	3.00	0.44
F	2	4	6	4.00	0.44

Answer b:

Answer c:

Paths	Duration
ABEF	17.00	Longest path
ACEF	16.00
ACDF	16.00

Answer d: Critical path is ABEF. The expected completion time of the project is 17 days.