# ASSIGNMENT QUESTIONS 1 Question 1 Dummy Consider the

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ASSIGNMENT QUESTIONS 1

Question 1 (Dummy) Consider the PERT/CPM network shown below. 2 A 1 D 3 E B F G 4 6 J 7 H C I 5 a. Add the dummy activities that will eliminate the problem of activities having the same starting and ending nodes. 2

Network exercise b. Add dummy activities that will satisfy the following immediate predecessor requirements: Activity H I G Immediate Predecessor B, C D, E 3

Q 2. Solve the network Activity A B C D E F Immediate Predecessor A A, B C 4

Q 3. Solve the network Activity A B C D E F G H I J K L M Immediate Predecessor A A, B C A D, E, F C D, E, F G, H D, E, F I, J 5

Q 4. Solve the network Activity A B C D E F G H I Followed by Preceded by B, C D E, B F G, F H H, I I - C, A A B C E, D E G, F G, H 6

Critical path Method (CPM) • Critical Path - The path through the project where, if any activity is delayed, the project is delayed – There is always a critical path – There can be more than one critical path • The sequence of critical activities in a network is called the critical path. • It is the longest path in the network from the starting event to the ending event and defines the minimum time required to complete the project. • In the network it is denoted by double line. This path identifies all the critical activities of the project.

The critical path method consists of the following steps: 1. Calculate the time schedule for each activity 2. Calculate the time schedule for the completion of the entire project 3. Identify the critical activities and find the critical path : Critical activities are the once which must be started and completed on schedule or else the project may get delayed. The path containing these activities is the critical path and is the longest path in terms of duration.

Example Question Network exercise with time Construct a AOA network for a project with the following activities and times: Activity A B C D E F G Immediate Predecessor A A C, B D, E Time (months) 4 6 2 6 3 3 5 a) Find the critical path for this project network. b) This project must be complete in 1 1/2 years; do you anticipate difficulty in meeting the deadline? Explain. 9

Network exercise with time Solution – first construct the network and label activities D 2 4 G A E C 1 B F 5 3 10

Network exercise with time Solution –label activities with time duration 2 4 G 5 C 2 3 B 6 3 Paths: 1. ADG-15 3. ACF-9 5. BF-9 5 E 1 A 4 D 6 F 3 2. ACEG-14 4. BEG-14 11

Network exercise with time Solution –Determine critical path 2 4 G 5 C 2 5 E B 6 3 1 A 4 D 6 3 F 3 a. Critical path: A-D-G; Time: 15 months. b. Activities on the critical path require 15 months to complete. Thus the project should easily be completed in 1 12 1/2 years even if some activities take longer than expected.

ASSIGNMENT QUESTION 13

Question 1 Network exercise with time A project involving the installation of a computer system consists of eight activities. The immediate predecessor and activity time in weeks are shown below: Activity Immediate Time Predecessor (weeks) A 3 B 6 C A 2 D B, C 5 E D 4 F E 3 G B, C 9 H F, G 3 a. Draw the AOA network for this project. b. What are the critical path activities? c. What is the expected project completion time? 14