Expected time of activity = (Optimistic+Pessimistic+4*Most likely) / 6 Variance

Question

Expected time of activity = (Optimistic+Pessimistic+4*Most likely) / 6

Variance of an activity = ((Pessimistic - Optimistic)/6)2

Earliest times uses forward pass and Latest times uses backward pass methods with Earliest=Latest for Start and End events.

Critical path is made up of critical activities, longest path from Start to End, Expected duration is the duration of critical path.

Calculations are as follows:

Expected project duration is 23 days

Answer a, b, c, and d are given above

Answer e

Project duration X follows normal distribution with mean 23 days and variance (2/3) or s.d. of 0.816

Hence probability that project is completed within 23 days is 50%=0.50

Answer f

Probability that project will take more than 26 days = 1 - Prob.(X<=26) = 1-0.999882 say almost negligible as value of Z standard normal is more than 3, in fact Z = (X-mean)/s.d.= (26-23)/.816=3.6764

Activity Preceed. Optimistic Pessimistic Most likely Expected ES EF LS LF Slack S.D. Variance A - 4 6 5 5 0 5 0 5 0 0.333333 0.111111 B - 2 8 5 5 0 5 3 8 3 1 1 C A 5 9 7 7 5 12 5 12 0 0.666667 0.444444 D A 4 6 5 5 5 10 10 15 5 0.333333 0.111111 E B 2 6 4 4 5 9 8 12 3 0.666667 0.444444 F B 3 9 6 6 5 11 9 15 4 1 1 G C,E 10 12 11 11 12 23 12 23 0 0.333333 0.111111 H D,F 7 9 8 8 11 19 15 23 4 0.333333 0.111111

Explanation / Answer

Tom Schriber, a director of personnel at Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resumes, writing letters, making appointments to see prospective employers, researching companies, and industries, and so on. Necessary information on the activities is shown in the following table:

ACTIVITY OPTIMISTIC PESSIMISTIC MOST LIKELY IMMEDIATE PREDECESSORS

A 4 6 5 -

B 2 8 5 -

C 5 9 7 A

D 4 6 5 A

E 2 6 4 B

F 3 9 6 B

G 10 12 11 C,E

H 7 9 8 D,F

Required:

a.Construct a network for this problem.

b.Compute the expected time for each activity, also the variance.

c.Determine ES, EF, LS, LF, and slack for each activity.

d.Determine the critical path and project completion time.

e.Determine the probability that the project will be finished in 23 days or less.

f.Determine the probability the the project will NOT be finished in 26 days or less.

g.Determine the probability that the project will be finished in 25 days or less.

h.If a manager considers crashing any of the tasks to reduce the duration of the project completion time, which tasks should he/she focus on? Why?

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.