Introducing the Example Business Problem
All models start off with a problem to be solved - in this case, we are going to be working with and extending a portfolio optimization problem introduced in Getting Started with Xpress, part of the Xpress documentation set.
Stating the problem:
An investor wishes to invest a certain amount of money. She is evaluating ten different share types and their countries of origin for her investment. She has made estimates of the percentage return on investment (ROI) for each share type over a period of one year. The following table contains the details of each share type, its country of origin, its risk category (R: high risk, N: low risk) and the expected ROI.
The investor specifies certain constraints. To spread the risk, she wishes to invest at most 30% of the capital into any individual share type. She further wishes to invest at least half of her capital in North American shares, and at most one third in high-risk shares.
| Number | Description | Country of Origin | Risk | ROI (percentage) |
|---|---|---|---|---|
| 1 | Treasury | Canada | N | 5 |
| 2 | Hardware | NA (North America) | R | 17 |
| 3 | Theater | NA | R | 26 |
| 4 | Telecom | NA | R | 12 |
| 5 | Brewery | UK | N | 8 |
| 6 | Highways | France | N | 9 |
| 7 | Cars | Germany | N | 7 |
| 8 | Bank | Luxemburg | N | 6 |
| 9 | Software | India | R | 31 |
| 10 | Electronics | Japan | R | 21 |
How should the capital be divided among the share types to obtain the highest expected ROI?