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For ofﬁce use only

Team Control Number

50193

Problem Chosen

For ofﬁce use only

2016

MCM/ICM

Summary Sheet

An Educational Donation Mechanism Based On Data Insight

Summary

Recent years, Big Data has become increasingly popular and the guidance of big data is

required in many ﬁelds, including charitable ﬁeld. In our paper, we construct a new ROI

evaluation system for charitable organization using data mining methods to process data,

and succeed in determining an optimal investment strategy for Goodgrant Foundation.

First, we operate on the data. We do data screening according to the integrity and re-

dundancy of the information, deleting data with information less than the threshold, and

merging different attributes using linear ﬁtting and PCA. For the reserved attributes and

schools, we do data imputation to ﬁll the missing data based on K-means Clustering.

Then we normalize all the data to make them comparable in the following analysis.

Second, we construct a ROI evaluation criteria, which is a ratio of output and input mul-

tiplying an adjustment coefﬁcient, named “urgency”. The ratio reﬂects the beneﬁts in

related to the cost, while urgency reﬂects the demand for money which is an important

factor should be considered by charitable organization. We use PCA to select attributes,

letting salary, education quality and some others to represent output, tuition to represent

input and Federal loan, debt and some others to represent urgency. Then, AHP is used to

measure the importance between different factors and allocate weights.

Third, we put forward two kinds of model, basic model for one year and time series model

for ﬁve year. Seeing the ROI as beneﬁts from investment, we introduce the ﬂuctuation

of output as “risk”, imitating the concept of Modern Portfolio Theory in the ﬁnancial

sector to solve the problems. In the basic model, we develop a Mixed Integer Linear Pro-

gramming Algorithm and succeed in ﬁnding 14 schools for the investment. Further, we

consider the time factor and improve the model into a time series model, using MILP and

Grey Prediction to determine the long-term investment strategy. 16 schools are chosen

with different time duration and different amounts of money.

Finally, we make sensitivity analysis for our model, changing the amount of schools, the

restriction for money, whether allocating the money equally or not and so on to analyze

the different results of the output and to ﬁnd the better parameters for ideal results.

To sum up, our model is a feasible and reasonable model with technical and data support.

Because of the subjectivity, this model can be used ﬂexibly after data training.

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Team # 50193 Page 3 of 22

1 Introduction

1.1 Background

If it were a decade ago, you would not image that the pageview of ”Facebook” can be

more than millions in one minute; you would not image that when you open ”google

maps”, all the travel information is already in the palm of your hand; you would not

image that through data mining you can gain an insight into the development trend of an

enterprise to guide your investment. Nowadays big data has penetrated into our work and

lives, and has brought such huge changes. In turn, it has become particularly important

for us to ﬁnd useful information from the mass of data to guide our work and life.

As a special column from ”New York Times” in Feb., 2012 says, Big Data Era has come.

In the commercial, economic and other areas, information will increasingly be made

based on data and analysis, rather than based on experience and intuition. Also the ﬁeld of

charity is in the same case. In the past, it is more difﬁcult to give money away intelligently

than to earn it in the ﬁrst place.[1] We do not know how to do the charitable giving

rationally, thus, the calculation of ROI is also out of the question. But now new and

faster information could make charitable giving more effective and efﬁcient. Moreover,

it provides a possibility to link charitable giving issues with the investment issues in the

ﬁnancial sector.

This article is about a charitable donation issue of universities in the U.S. We aim to

design a measure system of the return on investment based on large quantities of data

through data mining methods. To solve the problem, we will use the Portfolio Theory,

Linear Programming, Grey Theory and some other methods to determine the optimal

strategy in terms of dimension of time.

1.2 Overview of Our Work

First, we ﬁnd a few key points in this question :

• The volume of data is large and of different types. How to do the normalization of

the data.

• Among the massive data, there are many missing data in the ﬁles, which contains

less information and not easy to do batch processing.

• How to classify the large amount of attributes of universities.

• Different attributes focus on different aspects and how to judge their importance.

• How to choose schools from the candidate list and how the allocate investment

amount among them.

• The charitable investment process lasts for 5 years, so time is an important factor

which will inﬂuence our ROI criteria.

Team # 50193 Page 4 of 22

On the basis of above discussion, to determine the optimal investment strategy, we may

boil down the tasks to the following four steps :

• First, we do data screening according to the integrity and usefulness of the informa-

tion. For the retention attributes and schools, we use K-means clustering method

to ﬁll the missing data. And normalize all the data.

• Second, we use PCA method to choose and classify different attributes. Then we

use AHP method and knowledge of ﬁnance to construct ROI concept. And we use

the ROI concept to process data, ranking the candidate schools.

• Third, we introduce the concept of Modern Portfolio Theory and construct two

models. In the basic model, we develop a Mixed Integer Linear Programming Al-

gorithm to determine an optimal investment strategy. Further, we consider the time

factor and improve the model into a timing model, using Dynamic Programming

Algorithm and Grey Prediction to determine the long-term investment strategy.

• Further analysis and discussion of the model.

1.3 Assumptions

• Ignore inﬂation and deﬂation of money and other time value of money. The value

of money remains unchanged.

• As a charitable organization, our aim is to improve educational performance and

expect for more social beneﬁts rather than gaining proﬁt.

• Our charitable donation is a comprehensive scholarship, not rewarding for the out-

standing contributions in speciﬁc ﬁelds.

• If we have different goals and strategies from other charitable organization, we

believe it can reduce the possibility of duplication of investment to a great extend.

• The object for evaluating and scholarship granting is school, not individual, though

some individual information is included in our criteria. And it is business of school

to allocate the money.

• We focus on the fairness of our strategy so as to invest more schools regardless of

the reputation of them.

• Because of Marginal utility, we try not to invest large amount of money to one

school.

• In the timing model, we assume that the inﬂuence of other factors which are ex-

cluded outside the model can be ignored. That’s to say, future is predictable.

Team # 50193 Page 5 of 22

2 Data Processing

2.1 Data Screening

The amount of raw data is large, so we should ﬁrst do data screening according to the

integrity and usefulness of the information.

First, we do data screening on 7805 schools :

• We only consider the 2978 candidate schools in the ﬁle Problem C - IPEDS UID

for Potential Candidate Schools, and match the schools with their 95 attributes in

the ﬁle Problem C - Most Recent Cohorts Data (Scorecard Elements).xlsx.

• Delete the schools which are not currently operating institution and which are on

Heightened Cash Monitoring 2 by Department of Education, meaning that they

encounter economic depression and lack students and which has no or very limited

information about percentage of degrees awarded. It’s meaningless to invest on

these schools.

• Delete the schools of whom 50% of the attributes are ”NULL”. If the percentage

of missing data exceeds 50%, the imputation will result in great error, which we

treat as a threshold for missing data.[2]

Second, we do data screening on 95 attributes :

• We combine some binary variables together. For example, we delete the net price

for different income classes and combine the total net price for public school and

private school together, named as ”Net Price”. And we use the total retention

rate for weighting to combine retention rate for full-time and part-time students

together, named as ”Retention Rate”.

• Though there are large quantities of missing data in ”SAT scores” and ”ACT scores”,

we reserve the midpoint of them as categorical variables. High entrance require-

ments with SAT or ACT scores would indicate higher education quality, which we

will treat differently from the low entrance requirements school in the following

ROI evaluation system.

• Besides, we reserve all the ﬂag attributes like ”ﬂag for Historically Black College

and University”, ”ﬂag for women-only college” and all the subject attributes like

”percentage of degrees awarded in Architecture And Related Services”, using them

for the clustering and data imputation in the next step.

• We delete location, age of students and some other information contributes less to

our ROI evaluation system.

After data screening, there are about 2700 schools each with about 60 attributes in the

candidate list.

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