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. Ten different share types and their countries of origin are being evaluated for the investment. The percentage return on investment (ROI) for each share type over a period of one year has been estimated. 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, no more than 30% of the capital will be invested into any individual share type, with at least half of the 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? The tutorial will demonstrate how to use a Python program model the business problem by interfacing with the Xpress Solver, but any solver can be used. Later sections in this chapter, and later chapters, will create a custom user interface.