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 arc tutorial question

A project consists of 14 activities (1,2,3,...,14). The duration of each activity and the activities which must immediately precede it are shown below. Draw an activity on arc network which represents these activities and their precedence relationships.

```Activity  Preceding  Duration
Activities (weeks)
1         -           1
2         1           3
3         2           2
4         2           2
5         2           4
6         4           1
7         3,6         4
8         6           2
9         6           1
10        3,5,8,9     8
11        7,10        2
12        11          2
13        7           4
14        12,13       2
```

For the activity on arc network shown below what are the critical activities?

What are the float times for the non-critical activities?

For the activity on arc network shown below calculate the earliest and latest start times and hence find the float for each activity, the critical activities and the overall project completion time.

How would the overall project completion time be affected by:

• an increase in the completion time for activity 1 of 2 weeks
• a decrease in the completion time for activity 10 of 1 week
• an increase in the completion time for activity 6 of 2 weeks.