2. Consider the following project, which consists of ten tasks: None None B. E F

Question

2. Consider the following project, which consists of ten tasks: None None B. E F, G, I a. What is the critical path through this network? What is the completion time of this project? b. What is the slack in Task F? c. Suppose the project has just been started. What is the longest you could delay beginning work on Activity A, without delaying the completion of the project? d. Suppose someone tells you they could get activity C done in 1 day, instead of the 3 days you were planning on. Of course, they expect a bonus for this. What is your reaction?

Explanation / Answer

The Precedence diagram of the activities as follows :

                                                                                      A

                 B

             D

C

                            E

       F

               G

                                          H

                                        I

                                                                                J

The possible parallel paths and their corresponding durations as follows :

A-D = 6 + 5 = 11

A-C-F-J = 6 + 3 + 2 + 2 = 13

A-E-G-J = 6 + 3 + 3 + 2 = 14

A-E-H-I-J = 6 + 3 + 4 + 2 + 2 = 17

B-H-I-J = 2 + 4 + 2 + 2 = 10

Since , A-E-H-I-J has the longest duration , it forms the Critical Path . Completion time of the project is same as duration of critical path,. Therefore , project completion time is 17

CRITICAL PATH THROUGH THIS NETWORK     : A-E-H-I-J

COMPLETION TIME OF THE PROJECT : 17

Slack of activity A, C

= Duration of A-E-H-I-J - Duration of A-C-F-J

= 17 - 13

= 4

SLACK IN TASK F = 4

Since A is on the Critical Path , any delay in activity A will delay completion time of the project.

LONGEST ONE COULD DELAY BEGINNING WORK ON ACTIVITY A IS ZERO

If duration of activity C changes from 3 days to 1 day , the revised duration of A-C-F-J becomes 11. However the critical path remain unchanged at A-E-H-I-J with duration of 17 . Therefore , project completion time remains unchanged at 17

In other words reduction in duration of C does not change the duration of the project and therefore it is not worth paying bonus for reduction in duration of C by 2 days

                                                                                      A

                 B

             D

C

                            E

       F

               G

                                          H

                                        I

                                                                                J

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