Introduction
The Problem C is newly introduced in 2016, described as Data Insights.From Overview of Problem C in COMAP, we know
Problme C is intended to focus on and amplify specific elements of mathematical modeling challenges associated with data. In this sense, techniques stemming from statistics and pattern classification will play a large role in creating a mathematical model on this problem than in previous contests.
Problem Formulation
__The Goodgrant Challenge__
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.
Your 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.
To assist your effort, the attached data file (ProblemCDATA.zip) contains information extracted from the U.S. National Center on Education Statistics (www.nces.ed.gov/ipeds), which maintains an extensive database of survey information on nearly all post-secondary colleges and universities in the United States, and the College Scorecard data set (https://collegescorecard.ed.gov) which contains various institutional performance data. Your model and subsequent strategy must be based on some meaningful and defendable subset of these two data sets.
In addition to the required one-page summary for your MCM submission, your report must include a letter to the Chief Financial Officer (CFO) of the Goodgrant Foundation, Mr. Alpha Chiang, that describes the optimal investment strategy, your modeling approach and major results, and a brief discussion of your proposed concept of a return-on-investment (ROI) that the Goodgrant Foundation should adopt for assessing the 2016 donation(s) and future philanthropic educational investments within the United States. This letter should be no more than two pages in length.
Note: When submitting your final electronic solution DO NOT include any database files. The only thing that should be submitted is your electronic (Word or PDF) solution.
You can download the data (ProblemCDATA.zip) on the following websites:
http://www.comap-math.com/mcm/ProblemCDATA.zip
http://www.mathismore.net/mcm/ProblemCDATA.zip
http://www.mathportals.com/mcm/ProblemCDATA.zip
http://www.immchallenge.org/mcm/ProblemCDATA.zip
Our Approach
It requires a multi-objective evaluation and optimize model. We offer a strategy that make a rank of investment priority, academic performance firstly, necessity, urgency of funds secondary and ROI thirdly and can avoid the duplicate investment, to some extent. The investment list is not sorted by ROI simly, since we believe ROI cannot be quantized authoritatively and the Goodgrant Foundation is a charitable organization.
Summary Sheet
Every penny of the investment can be the key to unlock the possibility inside every student. How to arrange their funds appropriately is a problem for charity foundations. Our main task is to develop a strategy to produce the best return by using the limited funds. Therefore, it requires a comprehensive evaluation of colleges. Based on the list, we develop a method to allocate the funds on the basis of realistic requirements of the foundation, and an evaluation criterion for the estimated return on investment.
For the comprehensive evaluation of colleges, we employ Analytic Hierarchy Process (AHP) as our approach to assess the colleges’ objective ability. We take a variety of metrics into consideration, and divide then into two categories: Academic level, Wages’ level. For academic level, it refers to colleges average ACT score, SAT score and the rate of graduating on time. While the wages’ level is defined by median earnings of students working and share of students earning over $25,000/year. Meanwhile, we believe academic level weighs more in the evaluation of a college’s comprehensive ability. As for data, there are some missing part in the data sheet. Therefore, we employ the method of Means of Nearly Points to generate the compensation value replacing the null value.
The determination of selected investment list and the money we invest are related to the number of colleges the foundation want to invest and whether it is urgent to help the college. We develop a strategy, which is flexible for the final number of colleges and can lessen the possibility of duplicated investment. Meanwhile, we can assess the Return on Investment (ROI) at the same time. As for time duration, we consider that it relays on colleges’ performance in last year and formulate elimination annually. Therefore, foundation is able to adjust their investment strategy per year to yield the best effect.
By varying the method in processing the missing part in the data sheet, we find it affect little on the selected investment list, which prove our model is flexible. While change the weight of metrics in the comprehensive evaluation model of colleges, the rank changes to a large extent, which means that the output can loyally reveal the change in the importance to fit the requirement in other circumstance.
Our model seems to bend the requirement of the Problem, due to the diversity of comprehension. We regard the complex optimization of all objects required is better.