# OR-Notes

## J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

#### Network analysis - activity on node tutorial question

The following table defines the various activities in a small project:

```Activity   Completion time (weeks)
1                1
2                4
3                2
4                6
5                2
6                5
7                3
8                6
9                1```

The immediate precedence relationships are:

```Activity                       Activity
number                         number
1      must be finished before 3     can start
2                              4,5,6
3                              5,6
4                              7
5                              8
6,7                            9```
• Draw the network diagram.
• Calculate the critical activities, the overall project completion time and the total float times for each activity.
• How would the overall project completion time be affected if the following were to happen (where you should take each of the situations below separately, do not try and estimate the effect if they both happen):
• the completion time for activity 6 increased from 5 weeks to 7 weeks?
• the completion time for activity 8 could be cut from 6 weeks to 4 weeks?
• A colleague is arguing that if the completion time for activity 4 (a critical activity) could be cut by 3 weeks then the time taken to complete the entire project could also be cut by 3 weeks. Would you agree or not? If not what effect would cutting the completion time for activity 4 by 3 weeks have?
• Comment on the progress of the project if (ignoring the changes in completion times given above), at the end of 8 weeks, the status of the activities is as follows:
• Finished - 1,2,3
• In progress - 4 (1 week to completion)
• In progress - 5 (1 week to completion)
• In progress - 6 (4 weeks to completion)