2016年数学建模美赛题目原文及翻译-C [个人思路]

PROBLEM C: The Goodgrant Challenge

原题下载：MCM-2016-C

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.

The ProblemCDATA.zip data file contains:

 Problem C - IPEDS UID for Potential Candidate Schools.xlsx

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

 Problem C - CollegeScorecardDataDictionary-09-08-2015.xlsx

 IPEDS Variables for Data Selection.pdf

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

.

优质基金挑战

该Goodgrant基金会就是要帮助提高本科生参加在美国学院和大学教育表现的慈善组织。要做到这一点，该基金会拟共$ 100,000,000（US100万美元）捐给每年学校提供适当的小组，已经运行五年了，从2016年7月开始这样做，他们不希望重复投资和其他重点大型授予组织如盖茨基金会和Lumina的基础。

您的团队已要求由Goodgrant基金会建立一个模型，以确定最佳的投资策略，确定了学校，每所学校的投资金额，对投资回报率，以及持续时间，该组织的资金应提供有最高可能产生对学生的表现有很强的正效应。该战略应包括学校，你是根据每个候选学校的证明潜力有效地利用私人资金，建议投资适当的方式定义的1到N优化并优先候选名单，和投资回报（ROI）的预计收益慈善组织如Goodgrant基金会。

为了帮助你的努力，附加的数据文件（ProblemCDATA.zip）包含来自美国国家中心教育统计（www.nces.ed.gov/ipeds），它在几乎所有的后拥有大量的调查信息数据库中提取信息二级学院和大学在美国，与大学记分卡的数据集（https://collegescorecard.ed.gov），其中包括各种机构的性能数据。您的模型和随后的战略必须建立在这两个数据集的一些有意义的，可防御的子集。

除了必需的单页摘要您的MCM提交，你的报告必须包括信Goodgrant基金，阿尔法蒋介石先生，介绍了最优投资策略的首席财务官（CFO），您的建模方法和主要结果，和你提出了一个回报率的投资回报率（ROI）的概念进行了简要的讨论Goodgrant基金会应该采取评估的2016年捐款（S）和未来的慈善教育投资在美国境内的。这封信应不大于长两页多。

注意：当您提交最终的电子解决方案不包含任何数据库文件。应提交的唯一的事情就是你的电子（Word或PDF）的解决方案。

该ProblemCDATA.zip数据文件包含：

题C - IPEDS UID为潜在的候选Schools.xlsx

题C - 最近客群组数据（记分卡元素）的.xlsx

题C - CollegeScorecardDataDictionary-09-08-2015.xlsx

IPEDS数据Selection.pdf变量

您也可以下载基于以下网站的数据（ProblemCDATA.zip）：

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    

ProblemCDATA.zip

名词介绍：  

●ROI（Return On Investment）投资回报率，通过投资而应返回的价值，即企业从一项投资性商业活动的投资中得到的经济回报。计算公式：ROI=利润/投资×100%。公式：投入产出比（ROI）=总成交金额/花费 ‍

个人看法：

大数据问题， 确定 features  选择合适的 model 训练。 

这个大数据问题可以抽象成一个投资回报率模型的问题，影响一个学校的 group 被投资的资金数量的因素有很多，我们可以通过赛题提供的数据抽取相关的 features。 归一化，并组合我们的训练向量集合，使用适合的算法进行训练，得出当前较优的方案集合。

如何评价这个方案的回报呢，我觉得类似于 rank，将历史各个 group 各个成果作为之前投资选择的回报成果的打分，进一步优化投资方案，反而复之，将会把方案优化到一个不错的 rank 结果值

参考：

The Quest for Societal ROI in the Midst of the Perfect Storm: Can SCM Set the Standard for Twenty-First Century Business Education?

Return on Investment (ROI) training evaluation in Malaysian SMEs: factors influencing the adoption process

Estimating the financial return on a veterinary education