# 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.

Integer programming project selection tutorial question

Suppose that we are considering four possible projects, over a 3 year time horizon, which have the following characteristics:

```                         Capital requirements (£m)
Project   Return (£m)    Year   1     2     3
1         0.2                   0.5   0.3   0.2
2         0.3                   -     0.8   0.2
3         0.5                   1.5   1.5   0.3
4         0.1                   0.1   0.4   -
Available capital (£m)          3.1   2.5   0.4```

Project 2, for example, requires no capital in year 1, 0.8 of capital in year 2 and 0.2 of capital in year 3. When it completes it gives a return of 0.3 (all figures in £m).

In addition we have the following restrictions:

• projects 1 and 2 are mutually exclusive
• if project 4 is chosen then all of its return (0.1 £m, as above) must be added to the capital available in year 3 (i.e. if project 4 is chosen then the only choice open to us is to use its return as capital in year 3)

Formulate this problem and solve it to decide which projects to choose.