2023年12月7日发(作者：广东一模数学试卷理科)

Team Control Number

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44952

Problem Chosen

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C

One in a hundred --The Goodgrant Challenge

Summary

The Goodgrant Foundation wants to donate money to an appropriate group of

schools per year, we were asked to develop a model to determine an optimal investment

strategy.

Firstly, filtering data. Because the problem has a large number of additional data,

we must preliminarily classify the data. We use SPSS to achieve above purpose, after

that we get the valid data of 2936 potential candidate schools.

Secondly, using Grey Relational Analysis (GRA) to optimize the data roughly. By

using MATLAB we calculate the grey relational coefficient and grey weight relation.

And then we compare the size of every grey weight relation, taking the first 300

potential candidate schools as the evaluation objects.

Thirdly, using Principal Component Analysis (PCA) to build up the ROI (return on

investment) Model. During the process of GRA, there are so many indexes influence the

result, we can’t get the accurate solution. So we use “ PCA” method to simplify the

problem and evaluate the ROI of every school. By using SPSS, we determine the main

components and calculate the comprehensive score. We rank the evaluation objects on

the basis of score and choose the first 40 objects as the optimization result.

And then, testing the reliability. We standardize the indexes of PCA, by comparing

the optimization result with well-known universities which we don’t choose (such as

Harvard University), we can examine the rationality of our model and get the candidates

list.

Finally, using TOPSIS method to build up the Investment Prediction Model. We

use the previous data (2009~2013) to make the Linear Regression Forecasting(LRF),

after that we get the predicted data from 2016 to 2020. We use TOPSIS method to

evaluate the candidate school list. According to the comprehensive score from 2016 to

2020, we find the first 20 schools which get the higher score are always higher than

other school from 2016 to we choose that 20 school which both have higher

ROI and development potential as the final candidate school list. According to the final

candidate school list, we use the TOPSIS method again to calculate the final

comprehensive score, According to the score, we decide how much money The

Goodgrant Foundation should invest for each school which is showed in Table 6.2 .

Key Words: GRA, PCA, TOPSIS, ROI, LRF Contents

uction ............................................................................................................................ 1

1.1 Background ....................................................................................................................... 1

1.2 Foundation & ROI ............................................................................................................. 1

2 Task ........................................................................................................................................ 1

3 Fundamental assumptions ..................................................................................................... 2

4 Definitions and Notations ...................................................................................................... 2

5 Models ..................................................................................................................................... 3

5.1 3

5.2 Object Selection Model (Grey Relational Analysis) .......................................................... 4

5.2.1 Model analysis ........................................................................................................... 4

5.2.2 Model solution .......................................................................................................... 4

5.3 ROI Model (Principal Component Analysis) ...................................................................... 5

5.3.1 Model analysis ........................................................................................................... 5

5.3.2 Model solution .......................................................................................................... 6

5.4 Verify the possibility ......................................................................................................... 9

5.4.1 Comparison ............................................................................................................... 9

5.4.2 External factor ......................................................................................................... 10

5.5 Investment Forecast Model ............................................................................................ 11

5.5.1 Linear Regression Forecasting Model ..................................................................... 11

5.5.2 School potential Prediction (TOPSIS) ...................................................................... 12

5.5.3 Final investment (TOPSIS) ....................................................................................... 13

6 Conclusions ........................................................................................................................... 16

7 Strengths and Weaknesses ................................................................................................... 18

7.1 Strengths ......................................................................................................................... 19

7.2 Weaknesses .................................................................................................................... 20

8 Letter to Mr. Alpha Chiang ................................................................................................... 21

9 References ............................................................................................................................. 22

Team # 44952 Page 1 of 22

1 Introduction

1.1 Background

The Goodgrant Foundation is a charitable organization that wants to help improve

educational performance of undergraduates attending colleges and universities in the United

States. To do this, the foundation intends to donate a total of $100,000,000 (US100 million) to

an appropriate group of schools per year, for five years, starting July 2016. In doing so, they

do not want to duplicate the investments and focus of other large grant organizations such as

the Gates Foundation and Lumina Foundation.

Our team has been asked by the Goodgrant Foundation to develop a model to determine

an optimal investment strategy that identifies the schools, the investment amount per school,

the return on that investment, and the time duration that the organization’s money should be

provided to have the highest likelihood of producing a strong positive effect on student

performance. This strategy should contain a 1 to N optimized and prioritized candidate list of

schools you are recommending for investment based on each candidate school’s demonstrated

potential for effective use of private funding, and an estimated return on investment (ROI)

defined in a manner appropriate for a charitable organization such as the Goodgrant

Foundation.

1.2 Foundation & ROI

Foundation (charitable foundation) refers to the nonprofit legal person who uses the

property of the natural persons, legal persons or other organizations to engage in public

welfare undertakings. In terms of its nature, foundation is a kind of folk non-profit

organizations.

ROI is a performance measure used to evaluate the efficiency of an investment or to

compare the efficiency of a number of different investments. ROI measures the amount of

return on an investment relative to the investment’s cost. To calculate ROI, the benefit (or

return) of an investment is divided by the cost of the investment, and the result is expressed as

a percentage or a ratio.

2 Task

 One-page summary for our MCM submission

 Using our models to achieve the candidate list of schools

 Calculate the time duration that the organization’s money should be provided to have the

highest likelihood of producing a strong positive effect on student performance

 Calculate the investment amount Goodgrant Foundation would pay for each school

 Calculate the ROI of the Goodgrant Foundation

 Forecast the development of this kind of investment mode

 Write a letter to the CFO of the Goodgrant Foundation, Mr. Alpha Chiang, that describes

the optimal investment strategy


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