Subject : Optimization in Operation Research.

Book : Bernard W . Taylor Introduction to Management Science 11th Edition Book

Chapter 5 Integer Programming

Case Study on Page no. 231

Developing Kathleen Taylors 401(k) Plan Kathleen Taylor has been working for a government contractor, Summit Solutions, in Washington, DC, for over a year. She is now eligible to participate in the companys 401(k) retirement plan. The company has provided Kathleen with the information in the table on the following page about the various funds that are available for her to invest in.

	Evening Star Rating	5 Year Return	Fund Size ($ 1,000,000s)	Expense Ratio
International
Parham International Value	3	12.58	2,066	1.67
Jarus Overseas	4	6.94	7,404	1.97
U.S. Fund EuroPacific	2	7.86	19,859	1.19
Admiral Foreign Investor	5	7.54	42,035	1.32
SPS Emerging Market	3	5.57	11,139	1.15
Small Cap
Maxam Small Cap Return	4	5.87	1,302	1.43
U.S. Small Cap Select	2	3.99	770	1.21
Veritas Small Cap Value	4	2.97	3,049	1.74
Oak Small Cap Growth	3	3.8	4,320	1.49
Mid Cap
Federal Mid Cap Growth	3	4.13	729	1.05
T. Row Price Growth 2	2	6.3	4,145	1.33
Draper Structured Mid Cap	2	7.73	1,467	1.31
Jarus Mid Cap Value	3	4.05	4,632	1.52
Maxam Mid Cap Opportunity	4	5.76	2,537	1.17
Large Cap
T. Row Price Bluechip Growth	3	6.01	6,374	1.23
Jarus Diversified Equity Income	2	3.22	962	1.05
Draper Strategic Growth	4	7.81	9,991	1.16
Centennial Common Stock Growth	3	2.16	20,194	0.99
Marius Stock Growth	2	9.88	19,648	1.12
Bond
Maxam Global Bond	3	8.37	12,942	1.03
Parham High Yield	5	6.25	3,106	1
Madison Federated Bond Portfolio	3	5.66	8,402	1.14
Draper U.S. Government Bond	4	7.41	1,045	0.9
Federated High Income	3	5.85	11,211	0.82

International funds invest in global/overseas companies; small-cap funds invest in companies that have a market capitalization (i.e., the number of outstanding shares multiplied by the stock price per share), in general, between $300 million and $2 billion; mid-cap funds invest in companies with a market capitalization between $2 and$10 billion; and large-cap funds invest in companies over $10 billion. The Evening Star rating is developed by an independent investment analysis firm, and it rates funds based on their risk-adjusted performance over various time periods. 5 is best, 1 is worst; stocks trading close to their analysts fair value estimates receive a 3, while stocks trading at large discounts compared to their analysts fair value estimate receive a 4 or 5 rating. The expense ratio is the total percentage of fund assets used for operating expenses (i.e., administrative, management ,advertising, etc.). Since Kathleen is young and expects to build her401(k) plan over a long period of time, she wants to employ a relatively aggressive investment strategy. She has read investment literature that suggests a relatively aggressive plan would invest 5% to 35% in international funds, 5% to 25% in small-cap funds, 5% to 35% in mid-cap funds, 20% to 50% in large-cap funds, and 5% to 10% in bond funds. Kathleen plans to contribute $900 of her salary each month to her plan, which the company will match. She has also developed a few of her own investment guidelines: to diversify, she wants to invest in five funds, one in each investment category; she wants to achieve an average Evening Star rating of at least 3.7; she wants to invest in funds that average at least $10,000 million in size; she wants to achieve an average expense ratio for her five funds of no more than 1.10; and she wants to maximize the average 5-year return of the five funds she selects, weighted by the amount she invests in each.

Develop an investment plan for Kathleen using linear programming. How would her investment plan change if she wanted to maximize the Evening Star rating?

Please explain how the income of Kathleen can be used in the constraints.