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.