Pert-ho-19_rlnav30rmx.docx

Title: PERT

MBA HR: 2019

1. Find Critical path for PERT network. Activit 1-2 2-3 2-4 3-5 4-5 y 4 1 8 3 1 to 8 4 12 5 1 tm 12 7 16 7 1 tp

4-6

5-7

5-8

7-9

8-9

9-10

6-10

3 6 9

3 6 9

4 6 8

4 8 12

2 5 8

4 10 16

4 6 8

2. Refer Table Below: Path Activity to tm tp a-b-c a 1 3 4 b 2 4 6 c 2 3 5 d-e-f d 3 4 5 e 3 5 7 f 5 7 9 g-h-i g 2 3 6 h 4 6 8 i 3 4 6 (a) Make a network. (b) Compute the expected time for each activity and the expected duration for each path. (c)Identify the critical path. (d) Compute the variance of each activity and the variance and standard deviation of each path. (e)What is the probability that the project will be completed within 17 weeks of its start? (f) What is the probability that the project will be completed within 15 weeks of its start? 3. A construction company is preparing a PERT network for laying the foundation of a new art gallery. Given below are the following set of activities, their predecessor requirements and three estimates of completion times in weeks, (i) Draw the PERT network. (ii) Compute the float for each activity and determine the critical path. (iii) The contract specified an Rs 5,000/- per week penalty for each week if the completion of the project extends beyond 37 weeks. What is the probability that this company will have to pay a maximum penalty of Rs 15,000/-? Activity A B C D E F G H I

Predecessor --A B C C C, D F, G E

To 2 8 7 6 9 10 11 6 4

Tm 3 8 9 6 10 14 11 10 5

Tp 4 8 11 6 11 18 11 14 6

J K

I H

3 1

4 1

5 1

4.The Biltimore Company wants to build a deluxe hotel ready for holiday season. The project manager, together with project team has identified the principal activities for construction together with time estimates in weeks, based on pessimistic, optimistic & most likely times. This is given in table below:Activity

Predecessor

Optimistic Time Pessimistic Most Likely Time Time A None 15 20 25 B None 8 10 12 C A 25 30 40 D B 15 15 15 E B 22 25 27 F E 15 20 22 G D 20 20 22 Analyse the Project to find out the critical path & expected duration of the project. 5. The data for the PERT network is given in the following table. Activity Nodes 1-2 1-3 1-4 2-3 2-5 3-4 3-6 4-6 5-6 i. ii. iii. iv. v.

Optimistic Time (days) 2 6 6 2 12 15 3 9 4

Most Likely Time (days) 4 6 12 5 14 24 6 15 10

Pessimistic Time (days) 6 6 24 8 28 45 9 27 16

Draw a network and estimate the earliest and latest event times for all nodes and hence derive critical path. Estimate the expected duration of the project and corresponding variance. What is the probability that the project duration will be completed in 60 days? What is the chance of completing the project between 45 and 54 days? What is the probability of completing the project within 40 days?