美赛论文(最终版)

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2016 MCM/ICM Summary Sheet

An Optimal Investment Strategy Model

Summary

We develop an optimal investment strategy model that appears to hold promise for providing insight into not only how to sort the schools according to investment priority, but also identify optimal investment amount of a specific school. This model considers a large number of parameters thought to be important to investment in the given College Scorecard Data Set.

In order to develop the required model, two sub-models are constructed as follows: 1.For Analytic Hierarchy Process (AHP) Model, we identify the prioritized

candidate list of schools by synthesizing the elements which have an influence on investment. First we define the specific value of any two elements’ effect on investment. And then the weight of each element’s influence on investment can be identified. Ultimately, we take the relevant parameters into the calculated weight, and then we get any school’s recommended value of investment.

2.For Return On Investment M odel, it’s constructed on the basis of AHP Model.

Let us suppose that all the investment is used to help the students to pay tuition fee.Then we can see optimal investment as that we help more students to the universities of higher return rate. However, because of dropout rate, there will be an optimization investment amount in each university. Therefore, we can change the problem into a nonlinear programming problem. We identify the optimal investment amount by maximizing return-on-investment.

Specific attention is given to the stability and error analysis of our model. The influence of the model is discussed when several fundamental parameters vary. We attempt to use our model to prioritize the schools and identify investment amount of the candidate schools, and then an optimal investment strategy is generated. Ultimately, to demonstrate how our model works, we apply it to the given College Scorecard Data Set. For various situations, we propose an optimal solution. And we also analyze the strengths and weaknesses of our model. We believe that we can make our model more precise if more information are provided.

Contents

1.Introduction 2

1.1Restatement of the Problem (2)

1.2Our Approach (2)

2.Assumptions 2

3.Notations 3

4.The Optimal Investment Model 4

4.1Analytic Hierarchy Process Model (4)

4.1.1Constructing the Hierarchy (4)

4.1.2Constructing the Judgement Matrix (5)

4.1.3Hierarchical Ranking (7)

4.2Return On Investment Model (8)

4.2.1Overview of the investment strategy (8)

4.2.2Analysis of net income and investment cost (9)

4.2.3Calculate Return On Investment (11)

4.2.4Maximize the Total Net Income (11)

5.Test the Model12

5.1Error Analysis (12)

5.2Stability Analysis (13)

6.Results13

6.1Results of Analytic Hierarchy Process (13)

6.2Results of Return On Investment Model (14)

7.Strengths and Weaknesses15

7.1Strengths (15)

7.2Weaknesses (16)

References16 Appendix A Letter to the Chief Financial Officer, Mr. Alpha Chiang.17