BUS 660 Grand Canyon University Integer Linear Programming Discussion

Hello, Sir and Class

An example of a real-life problem that can be modeled using a 0, 1 integer model is determining how much one should invest in a mix of assets, including stocks and bonds. In this case, the total value of investments that can be made in both assets is $1,000, which has to be distributed between the two asset classes in ways that will maximize the total returns that can be made. To solve this problem using a linear model, Let Xa represent shares, and Xb represent bonds. Each share that can be included in the portfolio costs 5, while bond prices are 10 for each unit. The prices can be used as weights for each category of assets that will be included in the model. The main decision variables will be Xa = 1 if shares are to be included in the portfolio and Xa = 0 if they are not to be included. The objective function will be:

Max Z = 5Xa + 10Xb

s.t.

5Xa + 10Xb <= 1000

Xa, Xb >= 0

The model aims to maximize the total returns generated if one invests only in shares and bonds priced at 5 and 10. Optimization can then be done to identify the most ideal value of each asset that should be included in the portfolio. The model captures all critical constraints related to the problem, meaning an optimal output is highly likely to be attained. The model also makes it easier to conduct a sensitivity analysis, if necessary, to understand how variations in key variables will impact the total returns that can be made. The solution to the model shows that investing only in bonds will maximize the total returns that can be made if there are no other constraints. The ideal portfolio will, therefore, include 100 units of bonds priced at $10 each and no units of shares.

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. L., Fry, M. J., & Ohlmann, J. W. (2016). Quantitative methods for business with CengageNOW (13th ed.). Boston, MA: Cengage Learning. ISBN-13: 9781305799257

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