2016年美赛C题清华大学获奖论文

摘 要：本文以深圳河流域特区为例，模拟了“分流清源”与“混流截排”收集机制的雨水管道与污水管道网络，对两种系统对各种参数的灵敏性和稳定性进行了分析，并对经济效果进行了估算和判断。

本文设计了一种建设方案，得到在五年内建造污水管道网络的最佳策略，使得建设完成前排入环境的污水量最少，同时满足政府治污的“一、三、五年目标”，且最节约经济成本。

求解第一问“分流清源”建设方案: 我们根据资料中污水处理厂、污水产生源的位置通过“最小生成树”算法规划出“分流清源”模型中建设的管道主干，通过计算深圳水管网络的分形维数，得到整个系统长度共142公里，并根据资料估算工程费用约7.7亿元。

题目指出“后续管理困难而很难保证不会再出现污水管错接问题”，所以需要对该系统进行了稳定性评估。

在已知各污水厂容纳量和污水源产生量和管道连接状况的情况下，通过规划得到了在部分管道错接或损坏的情况下，分别会导致多少污水溢出。

结论是在一条管道损毁或错接的情况下，平均溢出增量百分比为6.6%，因此对于该最小生成树管道系统，除了一些关键路径需要额外措施保护之外，其他边稳定性良好。

对于“混流截排”方案: 题目提到“政府已有较大的投入到截排”，我们模拟设定雨水管道（连接污水源和初期雨水池）为三角形网格且已经建好，初期雨水池以及雨污管道已经建好，雨污管道仍然采用“最小生成树”。

我们分析了无雨、中小雨、暴雨三种情况下初期雨水池接收雨水和污水的比例。

通过“最小溢出固定流”的规划算法，得出各雨水池溢出混水量的最低值。

我们通过改变降雨强度、个别雨池容量、排污比例、排污点的参数，来研究这些参数对溢出混水量最低值的影响。

因为环境污染和经济投入量纲不一致，我们用隶属函数和稀释理论两种不同的角度去评估清源和截排的优劣。

根据文献中溢出混水的化学需氧量（COD ）就可以估算溢出污水的环境代价，它与污水处理费在五年内共14.1亿元,而清源方案的总代价是18.6亿元。

另一方面，我们采取ω(x )=1-e −(x λ)2的隶属函数来评价污染和花费，把两个拐点分别设置为政府预算20亿和现有污染排放量467万吨这两个位置。

Contents1.Introduction (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 Filter data (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 221 Introduction1.1 BackgroundThe 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 organi zation’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 bas ed 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 & ROIFoundation (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 durati on that the organization’s money should be provided to have thehighest 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 describesthe optimal investment strategy。

小区开放对道路通行的影响评价模型摘要本文针对小区开放对道路的影响进行了研究，建立了层次分析模型、通行能力评价模型，使用了MATLAB、EXCEL等软件，得出小区开放在不同条件下会对道路交通产生不同的影响。

首先运用层次分析法，分析得出整体一般情况下小区开放有利于周边道路交通的结论。

之后构建了不同类型的小区，并分析得出小区开放的效果与小区结构及周边道路结构、车流量有关，因此小区开放不能盲目采取，要因地制宜。

最后根据分析结果，从交通通行的角度，向城市规划和交通管理部门提出了关于小区开放的合理化建议。

本文的突出特点是使用了层次分析法定量的比较了小区开放前后道路合理性，构建了对于研究该问题具有代表性的三种类型的小区，并建立了影响评估模型，客观的对不同小区结构及周边道路结构、车辆通行的影响进行评价。

针对问题一，首先查阅相关资料选取影响道路通行的指标，并对选取的指标进行筛选，然后运用各项指标进行层次分析，通过小区开放和小区封闭对道路交通和理性的判断来分析小区开放对道路通行的影响最后得出从整体看来，小区开放有利于道路通行。

针对问题二，通过查阅有关道路通行能力的相关资料建立了通行能力评价模型，首先根据模型求出道路基本通行能力的表达式，基本通行能力是理想状态下的通行能力，与实际情况分析对比存在差异。

因此基于差异，通过各实际因素对道路通行能力的影响进行修正，得到实际道路通行能力的数据。

最终计算出小区开放前后实际通行能力的相对系数。

针对问题三，构建了三种类型的小区，不同类型的小区具有不同的结构及不同的周边道路结构、车流量，应用问题二建立的模型分别对三种小区开放和封闭条件下周边道路的实际通行能力进行了计算，通过相对系数评价不同类型的小区开放对道路通行的影响，分析得出小区开放与地理位置、内部结构等因素有关，不能一概而论。

针对问题四，结合前述模型结果分析结果，从交通出行角度对城市规划部门和交通管理部门提出了合理化意见。

小区开放要合理的实施以体现小区开放的意义。

For office use onlyT1________________ T2________________ T3________________ T4________________Team Control Number 46639Problem ChosenCFor office use onlyF1________________F2________________F3________________F4________________2016 MCM/ICM Summary SheetAn Optimal Investment Strategy ModelSummaryWe 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 prioritizedcandidate 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.Contents1.Introduction 21.1Restatement of the Problem (2)1.2Our Approach (2)2.Assumptions 23.Notations 34.The Optimal Investment Model 44.1Analytic 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 Model125.1Error Analysis (12)5.2Stability Analysis (13)6.Results136.1Results of Analytic Hierarchy Process (13)6.2Results of Return On Investment Model (14)7.Strengths and Weaknesses157.1Strengths (15)7.2Weaknesses (16)References16 Appendix A Letter to the Chief Financial Officer, Mr. Alpha Chiang.171.Introduction1.1Restatement of the ProblemIn order to help improve educational performance of undergraduates attending colleges and universities in the US, the Goodgrant Foundation intends to donate a total of $100,000,000 to an appropriate group of schools per year, for five years, starting July 2016. We are to develop a model to determine an optimal investment strategy that identifies the school, 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. Considering that they don’t want to duplicate the investments and focus of other large grant organizations, we interpret optimal investment as a strategy that maximizes the ROI on the premise that we help more students attend better colleges. So the problems to be solved are as follows:1.How to prioritize the schools by optimization level.2.How to measure ROI of a school.3.How to measure investment amount of a specific school.1.2Our ApproachWe offer a model of optimal investment which takes a great many factors in the College Scorecard Data Set into account. To begin with, we make a 1 to N optimized and prioritized candidate list of school we are recommending for investment by the AHP model. For the sake that we invest more students to better school, several factors are considered in the AHP model, such as SAT score, ACT score, etc. And then, we set investment amount of each university in the order of the list according to the standard of maximized ROI. The implement details of the model will be described in section 4.2.AssumptionsWe make the following basic assumptions in order to simplify the problem. And each of our assumptions is justified.1.Investment amount is mainly used for tuition and fees. Considering that theincome of an undergraduate is usually much higher than a high school students, we believe that it’s necessary to help more poor students have a chance to go to college.2.Bank rates will not change during the investment period. The variation ofthe bank rates have a little influence on the income we consider. So we make this assumption just to simplify the model.3.The employment rates and dropout rates will not change, and they aredifferent for different schools4.For return on investment, we only consider monetary income, regardlessof the intangible income.3.NotationsWe use a list of symbols for simplification of expression.4.The Optimal Investment ModelIn this section, we first prioritize schools by the AHP model (Section 4.1), and then calculate ROI value of the schools (Section 4.2). Ultimately, we identify investment amount of every candidate schools according to ROI (Section 4.3).4.1Analytic Hierarchy Process ModelIn order to prioritize schools, we must consider each necessary factor in the College Scorecard Data Set. For each factor, we calculate its weight value. And then, we can identify the investment necessity of each school. So, the model can be developed in 3 steps as follows:4.1.1Constructing the HierarchyWe consider 19 elements to measure priority of candidate schools, which can be seen in Fig 1. The hierarchy could be diagrammed as follows:Fig.1AHP for the investment decisionThe goal is red, the criteria are green and the alternatives are blue. All the alternatives are shown below the lowest level of each criterion. Later in the process, each alternatives will be rated with respect to the criterion directly above it.As they build their hierarchy, we should investigate the values or measurements of the different elements that make it up. If there are published fiscal policy, for example, or school policy, they should be gathered as part of the process. This information will be needed later, when the criteria and alternatives are evaluated.Note that the structure of the investment hierarchy might be different for other foundations. It would definitely be different for a foundation who doesn't care how much his score is, knows he will never dropout, and is intensely interested in math, history, and the numerous aspects of study[1].4.1.2Constructing the Judgement MatrixHierarchy reflects the relationship among elements to consider, but elements in the Criteria Layer don’t always weigh equal during aim measure. In deciders’ mind, each element accounts for a particular proportion.To incorporate their judgments about the various elements in the hierarchy, decision makers compare the elements “two by two”. The fundamental scale for pairwise comparison are shown in Fig 2.Fig 2Right now, let's see which items are compared. Our example will begin with the six criteria in the second row of the hierarchy in Fig 1, though we could begin elsewhere if we want. The criteria will be compared as to how important they are to the decisionmakers, with respect to the goal. Each pair of items in this row will be compared.Fig 3 Investment Judgement MatrixIn the next row, there is a group of 19 alternatives under the criterion. In the subgroup, each pair of alternatives will be compared regarding their importance with respect to the criterion. (As always, their importance is judged by the decision makers.) In the subgroup, there is only one pair of alternatives. They are compared as to how important they are with respect to the criterion.Things change a bit when we get to the alternatives row. Here, the factor in each group of alternatives are compared pair-by-pair with respect to the covering criterion of the group, which is the node directly above them in the hierarchy. What we are doing here is evaluating the models under consideration with respect to score, then with respect to Income, then expenditure, dropout rate, debt and graduation rate.The foundation can evaluate alternatives against their covering criteria in any order they choose. In this case, they choose the order of decreasing priority of the covering criteria.Fig 4 Score Judgement MatrixFig 5 Expenditure Judgement MatrixFig 6 Income Judgement MatrixFig 7 Dropout Judgement MatrixFig 8 Debt Judgement MatrixFig 9 Graduation Matrix4.1.3 Hierarchical RankingWhen the pairwise comparisons are as numerous as those in our example, specialized AHP software can help in making them quickly and efficiently. We will assume that the foundation has access to such software, and that it allows the opinions of various foundations to be combined into an overall opinion for the group.The AHP software uses mathematical calculations to convert these judgments to priorities for each of the six criteria. The details of the calculations are beyond the scope of this article, but are readily available elsewhere[2][3][4][5]. The software also calculates a consistency ratio that expresses the internal consistency of the judgments that have been entered. In this case the judgments showed acceptable consistency, and the software used the foundation’s inputs to assign these new priorities to the criteria:Fig 10.AHP hierarchy for the foundation investing decision.In the end, the AHP software arranges and totals the global priorities for each of the alternatives. Their grand total is 1.000, which is identical to the priority of the goal. Each alternative has a global priority corresponding to its "fit" to all the foundation's judgments about all those aspects of factor. Here is a summary of the global priorities of the alternatives:Fig 114.2 ROI Model4.2.1 Overview of the investment strategyConsider a foundation making investment on a set of N geographically dispersed colleges and university in the United States, D = {1, 2, 3……N }. Then we can select top N schools from the candidate list which has been sorted through analytic hierarchy process. The total investment amount is M per year which is donated by the Goodgrant Foundation. The investment amount is j m for each school j D ∈, satisfying the following balance constraint:j j D mM ∈=∑ (1)W e can’t invest too much or too little money to one school because we want to help more students go to college, and the student should have more choices. Then the investment amount for each school must have a lower limit lu and upper limit bu as follows:j lu m bu ≤≤ (2)The tuition and fees is j p , and the time duration is {1,2,3,4}j t ∈. To simplify ourmodel, we assume that our investment amount is only used for freshmen every year. Because a freshmen oriented investment can get more benefits compared with others. For each school j D ∈, the number of the undergraduate students who will be invested is j n , which can be calculated by the following formula ：,jj j j m n j D p t =∈⨯ (3)Figure12The foundation can use the ROI model to identify j m and j t so that it canmaximize the total net income. Figure1 has shown the overview of our investment model. We will then illustrate the principle and solution of this model by a kind of nonlinear programming method.4.2.2 Analysis of net income and investment costIn our return on investment model, we first focus on analysis of net income and investment cost. Obviously, the future earnings of undergraduate students are not only due to the investment itself. There are many meaning factors such as the effort, the money from their parents, the training from their companies. In order to simplify the model, we assume that the investment cost is the most important element and we don’t consider other possible influence factors. Then we can conclude that the total cost of the investment is j m for each school j D ∈.Figure 13For a single student, the meaning of the investment benefits is the expected earnings in the future. Assuming that the student is not going to college or university after graduating from high school and is directly going to work. Then his wage base is 0b as a high school graduate. If he works as a college graduate, then his wage base is 0a . Then we can give the future proceeds of life which is represented symbolically by T and we use r to represent the bank rates which will change over time. We assume that the bank rates will not change during the investment period. Here, we use bank rates in 2016 to represent the r . The future proceeds of life of a single undergraduate student will be different due to individual differences such as age, physical condition environment, etc. If we consider these differences, the calculation process will be complicated. For simplicity’s sake, we uniform the future proceeds of life T for 20 years. Then we will give two economics formulas to calculate the total expected income in the next T years for graduates and high school graduates:40(1)Tk k a u r +==+∑(4) 40(1)T kk b h r +==+∑(5) The total expected income of a graduate is u , and the total expected income of a highschool graduate is h .Then, we continue to analyze the net income. The net income can be calculated by the following formula:os NetIncome TotalIncome C t =- (6) For each school j D ∈, the net income is j P , the total income is j Q , and the cost is j m . Then we will get the following equation through formula (6):j j j P Q m =- (7)Therefore, the key of the problem is how to calculate j Q . In order to calculate j Q, weneed to estimate the number of future employment j ne . The total number of the invested is j n , which has been calculated above. Considering the dropout rates j α and the employment rates j β for each school j , we can calculate the number of future employment j ne through the following formula:(4)(1)jt j j j j n e n βα-=⨯⨯- (8)That way, we can calculate j Q by the following formula:()j j Q ne u h =⨯- (9)Finally, we take Eq. (2) (3) (4) (7) (8) into Eq. (6), and we will obtain Eq. (9) as follows:4(4)00400(1)()(1)(1)j TT t j j j j j k kk k j jm a b P m p t r r βα+-+===⨯⨯-⨯--⨯++∑∑ (10) We next reformulate the above equation of j P for concise presentation:(4)(1)j t j jj j j jc m P m t λα-⨯⨯=⨯-- (11)where jj j p βλ= and 400400(1)(1)TT k kk k a b c r r ++===-++∑∑ .4.2.3 Calculate Return On InvestmentROI is short of return on investment which can be determined by net income andinvestment cost [7]. It conveys the meaning of the financial assessment. For each schoolj D ∈ , the net income is j P , and the investment cost equals to j m . Then the j ROIcan be calculated by the following formula:100%j j jP ROI m =⨯ (12)We substitute Eq. (10) into Eq. (11), and we will get a new formula as follows:(4)((1)1)100%j t j j j jc ROI t λα-⨯=⨯--⨯ (13)4.2.4 Maximize the Total Net IncomeGiven the net income of each school, we formulate the portfolio problem that maximize the total net income, S=Max(4)((1))j t j jj j j j Dj Djc m P m t λα-∈∈⨯⨯=⨯--∑∑ (14)S. T.jj DmM ∈=∑,{1,2,3,4}t = ,j lu m bu ≤≤ ,Considering the constraint jj DmM ∈=∑, we can further simplify the model,S is equivalent to S’=Max(4)((1))j t j jj j j Dj Djc m P t λα-∈∈⨯⨯=⨯-∑∑ (15)S. T.jj DmM ∈=∑,{1,2,3,4t = ,j l u m b u ≤≤. By solving the nonlinear programming problem S’, we can get the sameanswer as problem S.5. Testing the Model 5.1 Error AnalysisSince the advent of analytic hierarchy process, people pay more attention to it due to the specific applicability, convenience, practicability and systematization of the method. Analytic hierarchy process has not reached the ideal situation whether in theory or application level because the results depend largely on the preference and subjective judgment. In this part, we will analyze the human error problem in analytic hierarchy process.Human error is mainly caused by human factors. The human error mainly reflects on the structure of the judgment matrix. The causes of the error are the following points:1. The number of times that human judge the factors’ importance is excessive.2. The calibration method is not perfect.Then we will give some methods to reduce errors:1. Reduce times of human judgment. One person repeatedly gave the samejudgment between two factors. Or many persons gave the same judgment between two factors one time. Finally, we take the average as result.2. Break the original calibration method. If we have defined the ranking vector111121(,...)n a a a a =between the factor 1A with others. Then we can get all theother ranking vector. For example : 12122111(,1...)na a a a a =.5.2 Stability AnalysisIt is necessary to analyze the stability of ranking result [6], because the strong subjectivefactors. If the ranking result changed a little while the judgment changed a lot, we can conclude that the method is effective and the result is acceptable, and vice versa. We assume that the weight of other factors will change if the weight of one factor changed from i ξ to i η:[8](1)(,1,2...,)(1)i j j i i j n i j ηξηξ-⨯==≠- (16)And it is simple to verify the equation:11nii η==∑ (17)And the new ranking vector ω will be:A ωη=⨯ (18)By this method, the Relative importance between other factors remain the same while one of the factor has changed.6. Results6.1 Results of Analytic Hierarchy ProcessWe can ranking colleges through the analytic hierarchy process, and we can get the top N = 20 schools as follows6.2 Results of Return On Investment ModelBased on the results above, we next use ROI model to distribute investment amountj m and time duration j t for each school j D ∈ by solving the following problem:Max (4)((1))j t j jj j j Dj Djc m P t λα-∈∈⨯⨯=⨯-∑∑S. T.jj DmM ∈=∑,{1,2,3,4t = , j l u m b u≤≤ . In order to solve the problem above, we collected the data from different sources. Inthe end, we solve the model with Lingo software. The program code is as follows:model: sets:roi/1..20/:a,b,p,m,t;endsets data:a = 0.9642 0.9250 0.9484 0.9422 0.9402 0.9498 0.90490.9263 0.9769 0.9553 0.9351 0.9123 0.9410 0.98610.9790 0.9640 0.8644 0.9598 0.9659 0.9720;b = 0.8024 0.7339 0.8737 0.8308 0.8681 0.7998 0.74920.6050 0.8342 0.8217 0.8940 0.8873 0.8495 0.87520.8333 0.8604 0.8176 0.8916 0.7527 0.8659;p = 3.3484 3.7971 3.3070 3.3386 3.3371 3.4956 3.22204.0306 2.8544 3.1503 3.2986 3.3087 3.3419 2.78452.9597 2.92713.3742 2.7801 2.5667 2.8058;c = 49.5528;enddatamax=@sum(roi(I):m(I)/t(I)/p(I)*((1-b(I))^4)*c*(1-a(I)+0.05)^(4-t(I)));@for(roi:@gin(t));@for(roi(I):@bnd(1,t(I),4));@for(roi(I):@bnd(0,m(I),100));@sum(roi(I):m(I))=1000;ENDFinally, we can get the investment amount and time duration distribution as follows:7.Strengths and Weaknesses7.1Strengths1.Fixing the bank rates during the investment period may run out, but it will haveonly marginal influences.2.For return on investment, we only consider monetary income, regardless of the3.intangible income. But the quantization of these intangible income is very importantand difficult. It needs to do too much complicated technical analysis and to quantify 4.too many variables. Considering that the investment persists for a short time, thiskind of random error is acceptable.5.Due to our investment which is freshmen oriented, other students may feel unfair.It is likely to produce adverse reaction to our investment strategy.6.The cost estimation is not impeccable. We only consider the investment amount andignore other non-monetary investment.5. AHP needs higher requirements for personnel quality.7.2Weaknesses1.Our investment strategy is distinct and clear, and it is convenient to implement.2.Our model not only identifies the investment amount for each school, but alsoidentifies the time duration that the organization’s money should be provide d.3.Data processing is convenient, because the most data we use is constant, average ormedian.4.Data sources are reliable. Our investment strategy is based on some meaningful anddefendable subset of two data sets.5.AHP is more simple, effective and universal.References[1] Saaty, Thomas L. (2008). Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World. Pittsburgh, Pennsylvania: RWS Publications. ISBN 0-9620317-8-X.[2] Bhushan, Navneet, Kanwal Rai (January 2004). Strategic Decision Making: Applying the Analytic Hierarchy Process. London: Springer-Verlag. ISBN 1-8523375-6-7.[3] Saaty, Thomas L. (2001). Fundamentals of Decision Making and Priority Theory. Pittsburgh, Pennsylvania: RWS Publications. ISBN 0-9620317-6-3.[4] Trick, Michael A. (1996-11-23). "Analytic Hierarchy Process". Class Notes. Carnegie Mellon University Tepper School of Business. Retrieved 2008-03-02.[5] Meixner, Oliver; Reiner Haas (2002). Computergestützte Entscheidungs-findung: Expert Choice und AHP – innovative Werkzeuge zur Lösung komplexer Probleme (in German). Frankfurt/Wien: Redline Wirtschaft bei Ueberreuter. ISBN 3-8323-0909-8.[6] Hazelkorn, E. The Impact of League Tables and Ranking System on Higher Education Decision Making [J]. Higher Education Management and Policy, 2007, 19(2), 87-110.[7] Leslie: Trainer Assessment: A Guide to Measuring the Performance of Trainers and Facilitors, Second Edition, Gower Publishing Limited, 2002.[8] Aguaron J, Moreno-Jimenea J M. Local stability intervals in the analytic hierarchy process. European Journal of Operational Research. 2000Letter to the Chief Financial Officer, Mr. Alpha Chiang. February 1th, 2016.I am writing this letter to introduce our optimal investment strategy. Before I describe our model, I want to discuss our proposed concept of a return-on-investment (ROI). And then I will describe the optimal investment model by construct two sub-model, namely AHP model and ROI model. Finally, the major results of the model simulation will be showed up to you.Considering that the Goodgrant Foundation aims to help improve educational performance of undergraduates attending colleges and universities in the US, we interpret return-on-investment as the increased income of undergraduates. Because the income of an undergraduate is generally much higher than a high school graduate, we suggest all the investment be used to pay for the tuition and fees. In that case, if we take both the income of undergraduates’ income and dropout rate into account, we can get the return-in-investment value.Our model begins with the production of an optimized and prioritized candidate list of schools you are recommending for investment. This sorted list of school is constructed through the use of specification that you would be fully qualified to provided, such as the score of school, the income of graduate student, the dropout rate, etc. With this information, a precise investment list of schools will be produced for donation select.Furthermore, we developed the second sub-model, ROI model, which identifies the investment amount of each school per year. If we invest more money in a school, more students will have a chance to go to college. However, there is an optimal investment amount of specific school because of the existence of dropout. So, we can identify every candidate school’s in vestment amount by solve a nonlinear programming problem. Ultimately, the result of the model simulation show that Washington University, New York University and Boston College are three schools that worth investing most. And detailed simulation can be seen in our MCM Contest article.We hope that this model is sufficient in meeting your needs in any further donation and future philanthropic educational investments within the United States.。

2016 年全国大学生英语竞赛样题（C 级）2016 National English Competition for College Students(Level C - Sample)（Total: 150 marks Time: 120 minutes）Part I Listening Comprehension (30 marks)Section A (5 marks)In this section, you will hear five short conversations. Each conversation will be read only once. At the end of each conversation, there will be a twenty- second pause. During the pause, read the question and the four choices marked A, B, C and D, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the centre.1.How will the man go to the ski slopes after his air journey?A.He will fly another short journey.B.The travel agency booked him a coach ticket.C.A friend will provide him with a lift.D.The man would like to take a taxi.2.What is the woman蒺s opinion towards e-learning?A.She is in favour of it.B.The woman doesn蒺t like it.C.Nobody knows what it is.D.E-learning will encourage people reading more.3.Which topic are they going to choose for their project?A. Recycling.B. Greenhouse effect.C. Environment.D. Pollution.4.What is the man planning to do next week?A.Hold a small business expo.B.Visit an expo and meet specialists.C.Register a computer training course.D.Represent the company to attend an expo.5.What is the relationship between the two speakers probably?A. Doctor a nd patient.B. Professor and student.C. Mother and son.D. Teacher and colleague.- 1 -Section B (10 marks)In this section, you will hear two long conversations. Each conversation will be read only once. At the end of each conversation, there will be a one-minute pause. During the pause, read the questions and the four choices marked A, B, C and D, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the centre. Conversation One6.Why is Rachel coming to see Dr. Jones?A.Dr Jones needs her further explanation of an extension for her essay.B.She happened to meet him and stopped to have a chat.C.Rachel needs some suggestions from Dr. Jones.D.They had an appointment to talk about her degree.7.What is Rachel 蒺s decision on her topic of the essay?A.Environmental conditions in 19th century factories.B.Working conditions of hospitals in 19th century northern towns.C.Pros and Cons of changing working conditions in 19th century.D.How to improve working conditions in southern towns in 19th c entury.8.Why did Rachel choose the topic at last?A.There are lots of sources that she can refer to.B.No one else chose the topic as it is a rare one.C.That is the topic Dr. Jones recommended to her.D.She can finish the project on the internet.9.What is Dr. Jones蒺attitude toward Racher蒺s essay?A.He would rather her choosing another topic.B.The essay is only 80 percent completed.C.She needs to rewrite it because he was too down about it.D.There are still much further editing job to do.10.Which part of Rachel 蒺s essay did Dr. Jones appreciate m ost?A. The introduction.B. The middle part.C. The end of it.D. The bibliography.Conversation Two11.What is Glaeser蒺s opinion towards cities?A.It is very dirty and no longer good to live in cities.B.They are too crowded with exploded population.C.Cities are extraordinary in creating opportunities.D.We need to save the industry and garments in cities.- 2 -12.What did globalization bring to older cities, such as New York, in 1970s?A. New technologies and prosperity.B. The rising of garment industry.C. Reductions in population.D. A severe depression.13.What is the current role of cities in the world?A.Cities are more and more important.B.They are less important than before.C.People believe cities are always the heart of manufacturing.D.There are advantages in cities in market opportunities.14.What is the main focus of Glaeser蒺s book Triumph of the City?A.Techniques of looking for jobs in cities.B.His legend in travelling around the world.C.Pleasure and prospects of living in cities.parisons between living in cities and countryside.15.According to Glaeser, what is the advantage of countries with more than half populationliving in urban areas comparing to those with less than half population living in urban areas?A. Less happier.B. Much richer.C. More relaxed.D. Very depressed.Section C (5 marks)In this section, you will hear five short news items. After each item, which will be read only once, there will be a twenty- second pause. During the pause, read the question and the four choices marked A, B, C and D, and decide which is the best answer. Then mark the corre 原sponding letter on the answer sheet with a single line through the centre.16.Where is the Consumer Electronics Show held each year?A. New York.B. Las Vegas.C. WashingtonD.C. D. Around the world.17.What is the side effect of convertional three-balde wind turbines?A.The blades are easily broken.B.They are slow in catching wind.C.They cause serious pollution.D.They kill lots of birds while rotating.18.Why bicycles-riding accidents increase in big cities?A.As there are no bicycle lanes in most cities.B.Because riders sometimes distract attention from riding.C.Because of riders 蒺lack of maps and navigation in the dark.D.Due to riders 蒺always making phone calls while riding.- 3 -19.Which of the following is mentioned to be an importanted part of October celebration?A. B. C. D.20.What are scientists going to do with the tiny clumps of organic matter drifting in the ocean?A.To do the research on food chain in the ocean.B.To collect samples of new species in the ocean.C.To predict future changes in our climate.D.To calculate certain sensitive instruments.Section D (10 marks)In this section, you will hear a short passage. There are 10 missing words or phrases. Fill in the blanks with the exact words or phrases you hear. The passage will be read twice. Remember to write the answers on the answer sheet.Barcelona, Spain in a privileged position on the northeastern coast of the Iberian peninsula andthe shores of the Mediterranean, Barcelona is the 21. city in Spain in both size and population. It is also the capital of Catalonia, an Autonomous Community within Spain. There are two official languages spoken in Barcelona: Catalan, generally spoken in all of Catalonia, and Castillian Spanish. The city of Barcelona has a population of 1.510.000, but this number 22. more than 4.000.000 if the outlying areas are also included. The capital of Cataloniais unequivocally a Mediterranean city, not only because of its 23. but also and above all because of its history, tradition and 24. . The documented history of the city 25. the founding of a Roman colony on its soil in the second century B.C. Modern Barcelona experienced spectacular growth and 26. at the onset of industrialization during the second half of the 19th century. The 1888 World蒺s Fair became a symbol of the capacity for hard work and the international outlook projected for the city. Culture and the arts 27.Barcelona and in all of Catalonia; the splendor achieved by Catalonian modernism is one of the most patent displays.Barcelona, more than just a single city, is really a collection of 28. cities. The visitor unfamiliar with its history might be surprised by the fact that such a 29. city preserves its historic Gothic center almost intact, or by the curious contrast between the maze of narrow streets and the grid -like layout of the Eixample, the urban planning“Enlargement” project of the end of the 19th century; or that beside a modern high-rise, we can also find a quaint square where the most outstanding decorative element is 30. , an echo of the old factories that were installed there in the past.- 4 -Part II Vocabulary, Grammar & Culture (15 marks)There are 15 incomplete sentences in this section. For each blank there are four choices marked A, B, C and D. Choose the one that best completes the sentence. Then mark the corre 原sponding letter on the answer sheet with a single line through the centre.Section A Vocabulary and Grammar (10 marks)31.Most elderly people have to live the money they when they were working.A. off; laid upB. up; set upC. on; p ut asideD. by; put back32.It is certain that American English has very influenced British English, e speciallyin the last quarter of the century.A. extremelyB. numerouslyC. excessivelyD. considerably33.—Why doesn 蒺t Janet stay with her relatives in New York?—She in Boston.A. has o nly relativesB. has relatives onlyC. only has relativesD. relatives has only34.The Mayor and his fellow were for some way of ridding the town of Rats.A. at their wit蒺s endB. at their wits endC. in their wit蒺s endD. for their wits end35.Scientists will have to come new methods of increasing the world蒺s food supply.A. up withB. down withC. up forD. down to36.When shopping in a supermarket, people just put items they like into the basketand then pay them at the entrance.A. that; ofB. Which; forC. Whichever; beforeD. Whatsover; off37. in a worldwide competition, the two students were awarded scholarships totaling$ 30,000.A. To be judged the bestB. Having judged the bestC. Judged the bestD. Judging the best38.They continue to buy proper books, too, on good paper and bound hardcovers.A. printed; betweenB. planned; inC. arranged; ofD. published; among39.—Listen! Do you feel like going out for Greek food tonight?—Well, I have exams tomorrow, Thursday and Friday.—That蒺s too bad, Well, maybe next week.A. I was thinking about 6:00.B. How about French food?C. I can蒺t make it this week.D. I can蒺t agree with you more.- 5 -40.—Anna, I wanted to ask you about my marketing report. I蒺m not sure about it ...—That蒺s OK, Leo. .—Choose a product or service then compare two organisations that produce it. I蒺m doing in原stant coffee.A. Would you like coffee or tea?B. So what would you have to do?C. Any hints for the project?D. How much have you actually written?Section B Culture (5 marks)41.The annual between Oxford and Cambridge universities on the river Thames is,however, one of the most popular sporting events of the year.A. Motor-cycling RaceB. Boat RaceC. Swimming RaceD. Waterball Race42.The Statue of Liberty is a colossal neoclassical sculpture on Liberty Island in New YorkHarbor in New York City, in the United States. The statue was a gift to the United States from the people of .A. the U.K.B. FranceC. ItalyD. Germany43.The Nobel Prize in Literature 2015 was awarded to Svetlana Alexievich“for her polyphonicwr i ti ng s,a m o nu m en t t o s u ff e r i n g a nd c o u r age i n ou r ti me”.S ve tl an a i s a B e l a r u s i an investigative journalist and non-fiction prose writer who writes in .A. RussianB. EnglishC. SwdishD. German44.Built in ancient times to keep invading Mongols out, is a historical treasure forChina. Stretching for thousands of kilometers across northern China, the World Heritage site is a marvel that attracts tens of thousands of tourists every year.A. the StonehengeB. the Forbidden CityC. the Great WallD. the Summer Palace45.Thanksgiving Day is a national holiday celebrated in and the United States as a dayof giving thanks for the blessing of the harvest and of the preceding year.A. CanadaB. IrelandC. ScotlandD. the U. K.Part III Cloze (10 marks)Read the following passage and fill in each blank with one word. Choose the correct word in one of the following three ways: according to the context, by using the correct form of the givenword, or by using the given letter (s) of the word. Remember to write the answers on the answer sheet.The latest issue of the Proceeding of the National Academy of Sciences reports that Asians and Westerners in fact view the world differently.- 6 -The study, led by Hannah -Faye Chua,Juilie Boland and Richard Nisbett, tracked theeye 46. (move) of students when lookingat a picture. The students i nvolved in the study47. in 25 European Americans and 27native Chinese. The researchers found thatAsian students spent more time studying thebackground of the picture. In 48. , theEuropean American students concentrated on the foreground of the picture.It has been observed that Westerners attend more to focal objects, whereas Asians attend more to contextual 49. inf . In this study, the researchers examined the differences in cognitive processing styles between Asians and Westerners. They showed the difference between the two races are cultural, which dates 50. thousands of years.The key to Chinese culture is 51. har . Successful rice farmers in Asia long ago relied on close bonds with other farmers. The farmers often shared water and new techniques. Meanwhile, the West focuses on ways to get things done, while paying little attention to 52.. Asians live in a more socially complicated world than Westerners do, so they are inclined to pay more attention to others whereas Westerners are 53. (individual). Reinforcing the belief that the perceptual differences are cultural, Asians raised in North America viewed the pictures similarly to those of Westerners 54. des .In this issue, there are other studies that have shown differences between Asians and European Americans when reading and writing. The studies, though, do not suggest that a particular race is more advanced 55. (intellect). Rather, they confirm that people from one culture do better on some tasks while people from other cultures do better on different tasks. Therefore, it would be hard to argue that one culture is generally outperforming the other.Part IV Reading Comprehension (35 marks)Section A (5 marks)A lot of people in the world today are used to working, going on holiday, and having money - but many of them aren蒺t happy. Yet other people seem to be really happy, even if they are poor, or have no job, or are surrounded by problems. Why?Professor Mihaly Csikszentmihalyi, from the University of Chicago, has interviewed thousands of people who have a happy life to find out how they do it. ‘I蒺ve been studying happiness for over 30 years,’says Csikszentmihalyi. ‘My interest in the subject came from my own experience as a child during World War II, when I saw many adults destroyed by the terrible events. But there were always a few who kept their courage, helped others, and were able to give a sense of purpose and meaning to their lives. I wanted to find out how a person could build a fulfilling and enjoyable life.- 7 -In general, his research showed that people were unhappy doing nothing. The professor stresses that happy people don蒺t waste time, either at work or when they蒺re free. ‘Many people feel that the time they spend at work or at school is wasted. But often their free time is also wasted.’Many people are used to doing passive things - watching television, for example - without using any skills. As a result, life goes past in a series of boring experiences.But it doesn 蒺t have to be this way. Theprofessor has found that people are happy whent he y ge t i n t o so m e t h i n g h e ca lls‘fl ow’.W henpeople get very involved in a task that they havechosen, and which is well -defined andch a ll e n g i ng,t he y e xpe r i ence‘fl ow’,a s t a tewhere they don蒺t notice time passing.They also experience enjoyment. ProfessorCsikszentmihalyi makes a contrast between enjoyment and pleasure. ‘I used to think they were the same thing - but they蒺re not! Pleasureis a bit bowl of ice cream, or taking a hot bath on a cold day - nothing bad at all! But enjoyment is about doing something and achieving something. It isn蒺t really important what we do, it蒺s more important to do something, and feel positive about it, and to try to do it well.’People who are not used to happiness can learn how to be happy, says the professor, if they constantly get into‘flow’states. Is happiness as easy as that? Perhaps it is. Questions 56—60Decide the following statements are true (T) or false (F) according to the passage.56.Professor Csikszentmihalyi has been studying happiness for more than 30 years.57.Professor Csikszentmihalyi thinks that many people use their free time well.58.As Csikszentmihalyi stated, watching TV in your free time is a passive thing.59.We can experience ‘flow’when we do things that are impossible for us and people in‘flow’can easily forget what time it is.60.Enjoyment and pleasure are the same and they are both positive according to ProfessorCsikszentmihalyi.Section B (10 marks)Questions 61—65 are based on the following passage.61. The type and amount of food that we usually eat is known as our diet. Eating a healthy, raried diet will help keep you strong and fit throughout your life. On the other hand, an unhealthy diet can lead to many problems and even shorten your life.62.Your body cannot make most of these nutrients, so you have to get them from the food you eat. The exact amount you need depends on your age, your size, how- 8 -much you are growing, whether you are a boy ora girl, and how active you are.63.But you also needenergy for things that you rarely think about,such as breathing, digestion, keeping your heartbeating, and fueling your brain. The energy infood is measured in units called calories. A sliceand a half of bread contains about 100 calories. Any calories that your body does not use are stored as fat.64.The most important thing is making sure you get a balanced diet.A balanced diet provides you with just the right amount of nutrients and calories. Because just one food cannot give you all the nutrients you need, the best way to make sure you get enough nutrients you need, the best way to make sure you get enough nutrients is to eat a variety of different kinds of food. No foods are “good”or “bad”in themselves. The key is to get a balance.Food are classified into five different groups, based on the nutrients they provide. These are: bread, other cereals, and potatoes; fruits and vegetables; milk and dairy foods; meat, fish and alternatives; fatty and sugary foods.65.By following these guidelines and making sure you have a good breakfast, lunch, and dinner each day, you should get a healthy, balanced diet. You can also eat t w o o r t h r ee sm a ll s nack s a d ay―j u s t b e s u r e t h a t t h e y a r e h ea l t hy one s a nd no t“j un k f ood”. Questions 61—65Complete the article with the following sentences. There are two extra sentences that you do not need to use.A.Your body uses the food you eat to help you grow, to provide you with energy, and tohelp you fight against infection and disease.B.Another important task of food is to provide your body with energy, which you need foractivities such as walking, swimming, skating, and dancing.C.In order to live, you need nutrients ―n ourishing substances that enable the cells ofyour body to work.D. People蒺s diet varies greatly throughout the world.E.If you eat foods from each of the first five four groups (not the fatty and sugary foods)everyday, you should have no problem staying healthy.F.A diet that gives you the right amount of nutrients and calories is a balanced diet.G.How should we get all the nutrients we need in a day?- 9 -Section C (10 marks)Questions 66—70 are based on the following passage.Photography is enthralling because it is both anart and a science. It is an art over which thephotographer has creative control but only to acertain extent: unlike a painter, you can onlytake photographs of what is there. If the sun isnot shining, you cannot photograph sunlight. Soyou need to find a subject. But the greatestphotographs are of subjects that most people would have walked past without noticing. The truly great photographers are those who can see,in their mind蒺s eye, the photograph that they can create through their vision, artistry and skill.Vision comes first. If you cannot see the potential, you can never be a true photographer. Artistry, by contrast, can be photographer. Artistry, by contrast, can be learned and developed;you can read a book or you take lessons. You can learn from a great practitioner. Perhaps the simplest aspect to describe is framing. The human eye has a huge field of view, stretching from horizon to horizon. The lens of a camera, by contrast, has a very restricted field of view. This isboth a curse and a blessing. Try as you might, you cannot capture the sheer scale of the human perspective of the world. But you can, and must, select the image that you are attempting to capture -or rather, to create. Look through the viewfinder: learn to see the world through the lens. Understand the difference it makes when you remove the irrelevant and select only what really matters. This is artistry.Then comes skill. This is the technical part. Skill is exercised long before you even start to look for a subject: first you must select the kind and model of camera you will use. Will it have advanced features, inter-changeable lenses, a motor-wind, a build-in flash, automatic focusing?How much do you want to do manually every time you wish to take a photograph, and how much will you leave to the electronics inside? Then you must choose a make and speed of film.The actual taking of the picture requires choices about exposure and shutter speed. After takingthe shot, there are more decisions about developing and printing; every decision makes an enormous difference. Experience teaches you about all of these; there is no other way to learnthan to try, possibly to fail, but to learn from the experience and improve. This is what marksout the photographer from those who merely take snapshots. There is always a better photographthat could have been taken-the ultimate photograph, if you like. All photographers pursue thisgoal of perfection. In the process, though, they take some beautiful photographs that bring themjoy thereafter.- 10 -Questions 66—70Answer the following questions according to the passage.66.What do true photographers differ from others?67.How can a photographer achieve the goal of artistry?68.What is artistry according to the writer?69.How can a photographer be skillful?70.What marks out the photographer from those ordinary ones?Section D (10 marks)Questions 71—75 are based on the following passage.Have you heard about the great flood? Perhaps you have heard about a man named Noah who built a huge boat to escape the flood. In this legend of the great flood, water covered all the land, killing most of the people and animals on Earth. Only Noah蒺s immediate family, including his wife, three sons, and the sons蒺wives, survived the flood along with all of the animals on his boat. After the flood waters receded, the people and animals on Noah 蒺s boat set about repopulating the Earth. This legend of Noah and his family is familiar to many people. But it is not the only legend about a great flood. Actually, many cultures have similar stories about a great flood that wiped out almost everyone on Earth.In the Jewish, Muslim, and Christian legend of the flood, Noah was warned by God that a great flood would kill every human and animal on land. God told Noah to construct the boat that would save his family and two of every animal. In a Hindu legend of the flood, a fish warned a man about the flood, and only the man was saved. Then the gods made a woman for this man, and the man and woman had many children. The Greek, Roman, and Chinese legends of the flood say only people on the highest mountain survived the flood. In Scandinavian and Celtic legends, the water of the flood was actually the blood of a giant. When the giant was killed, its body became the Earth, and its blood covered all of the land. There are also Incan, Mayan, and American Indian legends about a great flood. In each a of these legends, a few people live through the flood by climbing mountains or by constructing boats.Many people today believe the great flood is only a legend. However, other people say that the striking similarities among all of theflood legends suggest a real flood coveredthe Earth at some point long ago. In fact,some scientists speculate that the ancientflood waters are now frozen in glaciers atthe poles of the Earth. But why do thelegends disagree with each other? The floodhappened long before humans could write,- 11 -so the story of the flood could only be passed down through generations by oral retellings. As the story was passed by words of mouth, it may have changed as various cultures learned the story. That may explain why some parts of the legends differ. Through careful examinations of the similar elements in these legends, however, certain facts about an ancient catastrophic flood may be revealed.Questions 71—75Complete the summary with words from the passage, changing the form where necessary, with only one word for each blank.Many 71.cultures around the world have legends that describe a great flood in the past. At the time of the flood, only a few people escaped, either by climbing a high mountain or by 72. a boat. However, various legends differ between cultures on certain elements. For example, in the Scandinavian and Celtic legends, the flood was not water but blood from a giant. Although the legends may not 73. on all p oints, some people say striking 74. across cultures suggest that real flood happened longago. In fact, according to some scientists蒺75. that water from the flood is frozen in glaciers today.Part V Translation (15 marks)Section A (5 marks)Translate the following paragraph into Chinese. Remember to write the answers on the answer sheet.cation will lead to better life for the people; and it is through education that civilisationsustains itself. Every family wishes to have good education for its children. Knowledge gives one more opportunities in life, sustains civilisations and ensures that ethical norms are observed. To maintain sustainable growth, improve people蒺s lives and promote social equity are the three major goals of this government. Equity in education gives everyone a fair chance at the beginning of life and therefore constitutes an important foundation of social equity.Section B (10 marks)Translate the following sentences into English by using the hints given in brackets. Rememberto write the answers on the answer sheet.77.我不反对再听一遍你的解释。

2016年美赛A题热水澡一个人用热水通过一个水龙头来注满一个浴缸，然后坐在在浴缸中，清洗和放松。

不幸的是，浴缸不是一个带有二次加热系统和循环喷流的温泉式浴缸，而是一个简单的水容器。

过一会儿，洗澡水就会明显地变凉，所以洗澡的人需要不停地将热水从水龙头注入，以加热洗浴水。

该浴缸的设计是以这样一种方式，当浴缸里的水达到容量极限，多余的水通过溢流口泄流。

考虑空间和时间等因素，建立一个浴缸的水温模型，以确定最佳的策略，使浴缸里的人可以用这个模型来让整个浴缸保持或尽可能接近初始的温度，而不浪费太多的水。

使用你的模型来确定你的策略对浴缸的形状和体积，浴缸里的人的形状、体积、温度，以及浴缸中的人的运动等因素的依赖程度。

如果这个人一开始用了一种泡泡浴剂加入浴缸，以协助清洗，这会怎样影响你的模型的结果？除了要求的一页MCM摘要提交之外，你的报告必须包括一页的为浴缸用户准备的非技术性的说明书来阐释你的策略，同时解释为什么洗澡水的温度得到均衡地保持是如此之难。

2016年美赛B题太空垃圾在地球轨道上的小碎片的数量已引起越来越多的关注。

据估计，目前有超过500，000块的空间碎片，也被称为轨道碎片，由于被认为对空间飞行器是潜在的威胁而正在被跟踪。

2009年2月10日，俄罗斯卫星kosmos-2251和美国卫星iridium-33相撞之后，该问题受到了新闻媒体更广泛的讨论。

一些消除碎片方法已经被提出。

这些方法包括使用微型的基于太空的喷水飞机和高能量的激光来针对一些特定的碎片和设计大型卫星来清扫碎片。

碎片按照大小和质量分步，从刷了油漆的薄片到废弃的卫星都有。

碎片在轨道上的高速度飞行使得捕捉十分困难。

建立一个以时间为考量的模型，以确定最佳的方法或系列方法，为一个私营企业提供商机，以解决空间碎片问题。

你的模型应该包括定量和定性的对成本，风险，收益的估计，并考虑其他的一些重要因素。

你的模型应该能够评估某种方法，以及组合的系列方法，并能够研究各种重要的假设情况。

For office use only T1T2T3T4T eam Control Number42939Problem ChosenCFor office use onlyF1F2F3F42016Mathematical Contest in Modeling(MCM)Summary Sheet (Attach a copy of this page to each copy of your solution paper.)SummaryIn order to determine the optimal donation strategy,this paper proposes a data-motivated model based on an original definition of return on investment(ROI) appropriate for charitable organizations.First,after addressing missing data,we develop a composite index,called the performance index,to quantify students’educational performance.The perfor-mance index is a linear composition of several commonly used performance indi-cators,like graduation rate and graduates’earnings.And their weights are deter-mined by principal component analysis.Next,to deal with problems caused by high-dimensional data,we employ a lin-ear model and a selection method called post-LASSO to select variables that statis-tically significantly affect the performance index and determine their effects(coef-ficients).We call them performance contributing variables.In this case,5variables are selected.Among them,tuition&fees in2010and Carnegie High-Research-Activity classification are insusceptible to donation amount.Thus we only con-sider percentage of students who receive a Pell Grant,share of students who are part-time and student-to-faculty ratio.Then,a generalized adaptive model is adopted to estimate the relation between these3variables and donation amount.Wefit the relation across all institutions and get afitted function from donation amount to values of performance contributing variables.Then we divide the impact of donation amount into2parts:homogenous and heterogenous one.The homogenous influence is modeled as the change infit-ted values of performance contributing variables over increase in donation amount, which can be predicted from thefitted curve.The heterogenous one is modeled as a tuning parameter which adjusts the homogenous influence based on deviation from thefitted curve.And their product is increase in true values of performance over increase in donation amount.Finally,we calculate ROI,defined as increase in performance index over in-crease in donation amount.This ROI is institution-specific and dependent on in-crease in donation amount.By adopting a two-step ROI maximization algorithm, we determine the optimal investment strategy.Also,we propose an extended model to handle problems caused by time dura-tion and geographical distribution of donations.A Letter to the CFO of the Goodgrant FoundationDear Chiang,Our team has proposed a performance index quantifying the students’educational per-formance of each institution and defined the return of investment(ROI)appropriately for a charitable organization like Goodgrant Foundation.A mathematical model is built to help predict the return of investment after identifying the mechanism through which the donation generates its impact on the performance.The optimal investment strategy is determined by maximizing the estimated return of investment.More specifically,the composite performance index is developed after taking all the pos-sible performance indicators into consideration,like graduation rate and graduates’earnings. The performance index is constructed to represents the performance of the school as well as the positive effect that a college brings to students and the community.From this point of view, our definition manages to capture social benefits of donation.And then we adopt a variable selection method tofind out performance contributing vari-ables,which are variables that strongly affect the performance index.Among all the perfor-mance contributing variables we select,three variables which can be directly affected by your generous donation are kept to predict ROI:percentage of students who receive a Pell Grant, share of students who are part-time and student-to-faculty ratio.Wefitted a relation between these three variables and the donation amount to predict change in value of each performance contributing variable over your donation amount.And we calculate ROI,defined as increase in the performance index over your donation amount, by multiplying change in value of each performance contributing variable over your donation amount and each performance contributing variable’s effect on performance index,and then summing up the products of all performance contributing variables.The optimal investment strategy is decided after maximizing the return of investment according to an algorithm for selection.In conclusion,our model successfully produced an investment strategy including a list of target institutions and investment amount for each institution.(The list of year1is attached at the end of the letter).The time duration for the investment could also be determined based on our model.Since the model as well as the evaluation approach is fully data-motivated with no arbitrary criterion included,it is rather adaptable for solving future philanthropic educational investment problems.We have a strong belief that our model can effectively enhance the efficiency of philan-thropic educational investment and provides an appropriate as well as feasible way to best improve the educational performance of students.UNITID names ROI donation 197027United States Merchant Marine Academy21.85%2500000 102711AVTEC-Alaska’s Institute of Technology21.26%7500000 187745Institute of American Indian and Alaska Native Culture20.99%2000000 262129New College of Florida20.69%6500000 216296Thaddeus Stevens College of Technology20.66%3000000 229832Western Texas College20.26%10000000 196158SUNY at Fredonia20.24%5500000 234155Virginia State University20.04%10000000 196200SUNY College at Potsdam19.75%5000000 178615Truman State University19.60%3000000 199120University of North Carolina at Chapel Hill19.51%3000000 101648Marion Military Institute19.48%2500000187912New Mexico Military Institute19.31%500000 227386Panola College19.28%10000000 434584Ilisagvik College19.19%4500000 199184University of North Carolina School of the Arts19.15%500000 413802East San Gabriel Valley Regional Occupational Program19.09%6000000 174251University of Minnesota-Morris19.09%8000000 159391Louisiana State University and Agricultural&Mechanical Col-19.07%8500000lege403487Wabash Valley College19.05%1500000 Yours Sincerely,Team#42939An Optimal Strategy of Donation for Educational PurposeControl Number:#42939February,2016Contents1Introduction51.1Statement of the Problem (5)1.2Baseline Model (5)1.3Detailed Definitions&Assumptions (8)1.3.1Detailed Definitions: (8)1.3.2Assumptions: (9)1.4The Advantages of Our Model (9)2Addressing the Missing Values93Determining the Performance Index103.1Performance Indicators (10)3.2Performance Index via Principal-Component Factors (10)4Identifying Performance Contributing Variables via post-LASSO115Determining Investment Strategy based on ROI135.1Fitted Curve between Performance Contributing Variables and Donation Amount145.2ROI(Return on Investment) (15)5.2.1Model of Fitted ROIs of Performance Contributing Variables fROI i (15)5.2.2Model of the tuning parameter P i (16)5.2.3Calculation of ROI (17)5.3School Selection&Investment Strategy (18)6Extended Model186.1Time Duration (18)6.2Geographical Distribution (22)7Conclusions and Discussion22 8Reference23 9Appendix241Introduction1.1Statement of the ProblemThere exists no doubt in the significance of postsecondary education to the development of society,especially with the ascending need for skilled employees capable of complex work. Nevertheless,U.S.ranks only11th in the higher education attachment worldwide,which makes thefinancial support from large charitable organizations necessary.As it’s essential for charitable organizations to maximize the effectiveness of donations,an objective and systematic assessment model is in demand to develop appropriate investment strategies.To achieve this goal,several large foundations like Gates Foundation and Lumina Foundation have developed different evaluation approaches,where they mainly focus on spe-cific indexes like attendance and graduation rate.In other empirical literature,a Forbes ap-proach(Shifrin and Chen,2015)proposes a new indicator called the Grateful Graduates Index, using the median amount of private donations per student over a10-year period to measure the return on investment.Also,performance funding indicators(Burke,2002,Cave,1997,Ser-ban and Burke,1998,Banta et al,1996),which include but are not limited to external indicators like graduates’employment rate and internal indicators like teaching quality,are one of the most prevailing methods to evaluate effectiveness of educational donations.However,those methods also arise with widely acknowledged concerns(Burke,1998).Most of them require subjective choice of indexes and are rather arbitrary than data-based.And they perform badly in a data environment where there is miscellaneous cross-section data but scarce time-series data.Besides,they lack quantified analysis in precisely predicting or measuring the social benefits and the positive effect that the investment can generate,which serves as one of the targets for the Goodgrant Foundation.In accordance with Goodgrant Foundation’s request,this paper provides a prudent def-inition of return on investment(ROI)for charitable organizations,and develops an original data-motivated model,which is feasible even faced with tangled cross-section data and absent time-series data,to determine the optimal strategy for funding.The strategy contains selection of institutions and distribution of investment across institutions,time and regions.1.2Baseline ModelOur definition of ROI is similar to its usual meaning,which is the increase in students’educational performance over the amount Goodgrant Foundation donates(assuming other donationsfixed,it’s also the increase in total donation amount).First we cope with data missingness.Then,to quantify students’educational performance, we develop an index called performance index,which is a linear composition of commonly used performance indicators.Our major task is to build a model to predict the change of this index given a distribution of Goodgrant Foundation$100m donation.However,donation does not directly affect the performance index and we would encounter endogeneity problem or neglect effects of other variables if we solely focus on the relation between performance index and donation amount. Instead,we select several variables that are pivotal in predicting the performance index from many potential candidates,and determine their coefficients/effects on the performance index. We call these variables performance contributing variables.Due to absence of time-series data,it becomes difficult tofigure out how performance con-tributing variables are affected by donation amount for each institution respectively.Instead, wefit the relation between performance contributing variables and donation amount across all institutions and get afitted function from donation amount to values of performance contribut-ing variables.Then we divide the impact of donation amount into2parts:homogenous and heteroge-nous one.The homogenous influence is modeled as the change infitted values of performance contributing variables over increase in donation amount(We call these quotientsfitted ROI of performance contributing variable).The heterogenous one is modeled as a tuning parameter, which adjusts the homogenous influence based on deviation from thefitted function.And their product is the institution-specific increase in true values of performance contributing variables over increase in donation amount(We call these values ROI of performance contributing vari-able).The next step is to calculate the ROI of the performance index by adding the products of ROIs of performance contributing variables and their coefficients on the performance index. This ROI is institution-specific and dependent on increase in donation amount.By adopting a two-step ROI maximization algorithm,we determine the optimal investment strategy.Also,we propose an extended model to handle problems caused by time duration and geographical distribution of donations.Note:we only use data from the provided excel table and that mentioned in the pdffile.Table1:Data SourceVariable DatasetPerformance index Excel tablePerformance contributing variables Excel table and pdffileDonation amount PdffileTheflow chart of the whole model is presented below in Fig1:Figure1:Flow Chart Demonstration of the Model1.3Detailed Definitions&Assumptions 1.3.1Detailed Definitions:1.3.2Assumptions:A1.Stability.We assume data of any institution should be stable without the impact from outside.To be specific,the key factors like the donation amount and the performance index should remain unchanged if the college does not receive new donations.A2.Goodgrant Foundation’s donation(Increase in donation amount)is discrete rather than continuous.This is reasonable because each donation is usually an integer multiple of a minimum amount,like$1m.After referring to the data of other foundations like Lumina Foundation,we recommend donation amount should be one value in the set below:{500000,1000000,1500000, (10000000)A3.The performance index is a linear composition of all given performance indicators.A4.Performance contributing variables linearly affect the performance index.A5.Increase in donation amount affects the performance index through performance con-tributing variables.A6.The impact of increase in donation amount on performance contributing variables con-tains2parts:homogenous one and heterogenous one.The homogenous influence is repre-sented by a smooth function from donation amount to performance contributing variables.And the heterogenous one is represented by deviation from the function.1.4The Advantages of Our ModelOur model exhibits many advantages in application:•The evaluation model is fully data based with few subjective or arbitrary decision rules.•Our model successfully identifies the underlying mechanism instead of merely focusing on the relation between donation amount and the performance index.•Our model takes both homogeneity and heterogeneity into consideration.•Our model makes full use of the cross-section data and does not need time-series data to produce reasonable outcomes.2Addressing the Missing ValuesThe provided datasets suffer from severe data missing,which could undermine the reliabil-ity and interpretability of any results.To cope with this problem,we adopt several different methods for data with varied missing rate.For data with missing rate over50%,any current prevailing method would fall victim to under-or over-randomization.As a result,we omit this kind of data for simplicity’s sake.For variables with missing rate between10%-50%,we use imputation techniques(Little and Rubin,2014)where a missing value was imputed from a randomly selected similar record,and model-based analysis where missing values are substituted with distribution diagrams.For variables with missing rate under10%,we address missingness by simply replace miss-ing value with mean of existing values.3Determining the Performance IndexIn this section,we derive a composite index,called the performance index,to evaluate the educational performance of students at every institution.3.1Performance IndicatorsFirst,we need to determine which variables from various institutional performance data are direct indicators of Goodgrant Foundation’s major concern–to enhance students’educational performance.In practice,other charitable foundations such as Gates Foundation place their focus on core indexes like attendance and graduation rate.Logically,we select performance indicators on the basis of its correlation with these core indexes.With this method,miscellaneous performance data from the excel table boils down to4crucial variables.C150_4_P OOLED_SUP P and C200_L4_P OOLED_SUP P,as completion rates for different types of institutions,are directly correlated with graduation rate.We combine them into one variable.Md_earn_wne_p10and gt_25k_p6,as different measures of graduates’earnings,are proved in empirical studies(Ehren-berg,2004)to be highly dependent on educational performance.And RP Y_3Y R_RT_SUP P, as repayment rate,is also considered valid in the same sense.Let them be Y1,Y2,Y3and Y4.For easy calculation and interpretation of the performance index,we apply uniformization to all4variables,as to make sure they’re on the same scale(from0to100).3.2Performance Index via Principal-Component FactorsAs the model assumes the performance index is a linear composition of all performance indicators,all we need to do is determine the weights of these variables.Here we apply the method of Customer Satisfaction Index model(Rogg et al,2001),where principal-component factors(pcf)are employed to determine weights of all aspects.The pcf procedure uses an orthogonal transformation to convert a set of observations of pos-sibly correlated variables into a set of values of linearly uncorrelated variables called principal-component factors,each of which carries part of the total variance.If the cumulative proportion of the variance exceeds80%,it’s viable to use corresponding pcfs(usually thefirst two pcfs)to determine weights of original variables.In this case,we’ll get4pcfs(named P CF1,P CF2,P CF3and P CF4).First,the procedure provides the linear coefficients of Y m in the expression of P CF1and P CF2.We getP CF1=a11Y1+a12Y2+a13Y3+a14Y4P CF2=a21Y1+a22Y2+a23Y3+a24Y4(a km calculated as corresponding factor loadings over square root of factor k’s eigenvalue) Then,we calculate the rough weights c m for Y m.Let the variance proportions P CF1and P CF2 represent be N1and N2.We get c m=(a1m N1+a2m N2)/(N1+N2)(This formulation is justifiedbecause the variance proportions can be viewed as the significance of pcfs).If we let perfor-mance index=(P CF 1N 1+P CF 2N 2)/(N 1+N 2),c m is indeed the rough weight of Y m in terms of variance)Next,we get the weights by adjusting the sum of rough weights to 1:c m =c m /(c 1+c 2+c 3+c 4)Finally,we get the performance index,which is the weighted sum of the 4performance indicator.Performance index= m (c m Y m )Table 2presents the 10institutions with largest values of the performance index.This rank-ing is highly consistent with widely acknowledged rankings,like QS ranking,which indicates the validity of the performance index.Table 2:The Top 10Institutions in Terms of Performance IndexInstitutionPerformance index Los Angeles County College of Nursing and Allied Health79.60372162Massachusetts Institute of Technology79.06066895University of Pennsylvania79.05044556Babson College78.99269867Georgetown University78.90468597Stanford University78.70586395Duke University78.27719116University of Notre Dame78.15843964Weill Cornell Medical College 78.143341064Identifying Performance Contributing Variables via post-LASSO The next step of our model requires identifying the factors that may exert an influence on the students’educational performance from a variety of variables mentioned in the excel table and the pdf file (108in total,some of which are dummy variables converted from categorical variables).To achieve this purpose,we used a model called LASSO.A linear model is adopted to describe the relationship between the endogenous variable –performance index –and all variables that are potentially influential to it.We assign appropriate coefficient to each variable to minimize the square error between our model prediction and the actual value when fitting the data.min β1J J j =1(y j −x T j β)2where J =2881,x j =(1,x 1j ,x 2j ,...,x pj )THowever,as the amount of the variables included in the model is increasing,the cost func-tion will naturally decrease.So the problem of over fitting the data will arise,which make the model we come up with hard to predict the future performance of the students.Also,since there are hundreds of potential variables as candidates.We need a method to identify the variables that truly matter and have a strong effect on the performance index.Here we take the advantage of a method named post-LASSO (Tibshirani,1996).LASSO,also known as the least absolute shrinkage and selection operator,is a method used for variableselection and shrinkage in medium-or high-dimensional environment.And post-LASSO is to apply ordinary least squares(OLS)to the model selected byfirst-step LASSO procedure.In LASSO procedure,instead of using the cost function that merely focusing on the square error between the prediction and the actual value,a penalty term is also included into the objective function.We wish to minimize:min β1JJj=1(y j−x T jβ)2+λ||β||1whereλ||β||1is the penalty term.The penalty term takes the number of variables into con-sideration by penalizing on the absolute value of the coefficients and forcing the coefficients of many variables shrink to zero if this variable is of less importance.The penalty coefficient lambda determines the degree of penalty for including variables into the model.After min-imizing the cost function plus the penalty term,we couldfigure out the variables of larger essence to include in the model.We utilize the LARS algorithm to implement the LASSO procedure and cross-validation MSE minimization(Usai et al,2009)to determine the optimal penalty coefficient(represented by shrinkage factor in LARS algorithm).And then OLS is employed to complete the post-LASSO method.Figure2:LASSO path-coefficients as a function of shrinkage factor sFigure3:Cross-validated MSEFig2.displays the results of LASSO procedure and Fig3displays the cross-validated MSE for different shrinkage factors.As specified above,the cross-validated MSE reaches minimum with shrinkage factor between0.4-0.8.We choose0.6andfind in Fig2that6variables have nonzero coefficients via the LASSO procedure,thus being selected as the performance con-tributing variables.Table3is a demonstration of these6variables and corresponding post-LASSO results.Table3:Post-LASSO resultsDependent variable:performance_indexPCTPELL−26.453∗∗∗(0.872)PPTUG_EF−14.819∗∗∗(0.781)StudentToFaculty_ratio−0.231∗∗∗(0.025)Tuition&Fees20100.0003∗∗∗(0.00002)Carnegie_HighResearchActivity 5.667∗∗∗(0.775)Constant61.326∗∗∗(0.783)Observations2,880R20.610Adjusted R20.609Note:PCTPELL is percentage of students who receive aPell Grant;PPTUG_EF is share of students who are part-time;Carnegie_HighResearchActivity is Carnegie classifica-tion basic:High Research ActivityThe results presented in Table3are consistent with common sense.For instance,the pos-itive coefficient of High Research Activity Carnegie classification implies that active research activity helps student’s educational performance;and the negative coefficient of Student-to-Faculty ratio suggests that decrease in faculty quantity undermines students’educational per-formance.Along with the large R square value and small p-value for each coefficient,the post-LASSO procedure proves to select a valid set of performance contributing variables and describe well their contribution to the performance index.5Determining Investment Strategy based on ROIWe’ve identified5performance contributing variables via post-LASSO.Among them,tu-ition&fees in2010and Carnegie High-Research-Activity classification are quite insusceptible to donation amount.So we only consider the effects of increase in donation amount on per-centage of students who receive a Pell Grant,share of students who are part-time and student-to-faculty ratio.We denote them with F1,F2and F3,their post-LASSO coefficients withβ1,β2andβ3.In this section,wefirst introduce the procedure used tofit the relation between performance contributing variables and donation amount.Then we provide the model employed to calcu-latefitted ROIs of performance contributing variables(the homogenous influence of increase in donation amount)and the tuning parameter(the heterogenous influence of increase in dona-tion amount).Next,we introduce how to determine stly,we show how the maximiza-tion determines the investment strategy,including selection of institutions and distribution of investments.5.1Fitted Curve between Performance Contributing Variables and Donation AmountSince we have already approximated the linear relation between the performance index with the3performance contributing variables,we want to know how increase in donation changes them.In this paper,we use Generalized Adaptive Model(GAM)to smoothlyfit the relations. Generalized Adaptive Model is a generalized linear model in which the dependent variable depends linearly on unknown smooth functions of independent variables.Thefitted curve of percentage of students who receive a Pell Grant is depicted below in Fig4(see the other two fitted curves in Appendix):Figure4:GAM ApproximationA Pell Grant is money the U.S.federal government provides directly for students who needit to pay for college.Intuitively,if the amount of donation an institution receives from other sources such as private donation increases,the institution is likely to use these donations to alleviate students’financial stress,resulting in percentage of students who receive a Pell Grant. Thus it is reasonable to see afitted curve downward sloping at most part.Also,in commonsense,an increase in donation amount would lead to increase in the performance index.This downward sloping curve is consistent with the negative post-LASSO coefficient of percentage of students who receive a Pell Grant(as two negatives make a positive).5.2ROI(Return on Investment)5.2.1Model of Fitted ROIs of Performance Contributing Variables fROI iFigure5:Demonstration of fROI1Again,we usefitted curve of percentage of students who receive a Pell Grant as an example. We modeled the bluefitted curve to represent the homogeneous relation between percentage of students who receive a Pell Grant and donation amount.Recallfitted ROI of percentage of students who receive a Pell Grant(fROI1)is change in fitted values(∆f)over increase in donation amount(∆X).SofROI1=∆f/∆XAccording to assumption A2,the amount of each Goodgrant Foundation’s donation falls into a pre-specified set,namely,{500000,1000000,1500000,...,10000000}.So we get a set of possible fitted ROI of percentage of students who receive a Pell Grant(fROI1).Clearly,fROI1is de-pendent on both donation amount(X)and increase in donation amount(∆X).Calculation of fitted ROIs of other performance contributing variables is similar.5.2.2Model of the tuning parameter P iAlthough we’ve identified the homogenous influence of increase in donation amount,we shall not neglect the fact that institutions utilize donations differently.A proportion of do-nations might be appropriated by the university’s administration and different institutions allocate the donation differently.For example,university with a more convenient and well-maintained system of identifying students who needfinancial aid might be willing to use a larger portion of donations to directly aid students,resulting in a lower percentage of under-graduate students receiving Pell grant.Also,university facing lower cost of identifying and hiring suitable faculty members might be inclined to use a larger portion of donations in this direction,resulting in a lower student-to-faculty ratio.These above mentioned reasons make institutions deviate from the homogenousfitted func-tion and presents heterogeneous influence of increase in donation amount.Thus,while the homogenous influence only depends on donation amount and increase in donation amount, the heterogeneous influence is institution-specific.To account for this heterogeneous influence,we utilize a tuning parameter P i to adjust the homogenous influence.By multiplying the tuning parameter,fitted ROIs of performance con-tributing variables(fitted value changes)convert into ROI of performance contributing variable (true value changes).ROI i=fROI i·P iWe then argue that P i can be summarized by a function of deviation from thefitted curve (∆h),and the function has the shape shown in Fig6.The value of P i ranges from0to2,because P i can be viewed as an amplification or shrinkage of the homogenous influence.For example,P i=2means that the homogeneous influence is amplified greatly.P i=0means that this homogeneous influence would be entirely wiped out. The shape of the function is as shown in Fig6because of the following reasons.Intuitively,if one institution locates above thefitted line,when deviation is small,the larger it is,the larger P i is.This is because the institution might be more inclined to utilize donations to change that factor.However,when deviation becomes even larger,the institution grows less willing to invest on this factor.This is because marginal utility decreases.The discussion is similar if one institution initially lies under thefitted line.Thus,we assume the function mapping deviation to P i is similar to Fig6.deviation is on the x-axis while P i is on the y-axis.Figure6:Function from Deviation to P iIn order to simplify calculation and without loss of generality,we approximate the function。

2010年全国大学生英语竞赛C类试题参考答案及作文评分标准2010 National English Contest for College Students (Level C - Preliminary)Part I Listening Comprehension (30 marks)Section A (5 marks)1. B2. C3. A4. C5. CSection B (10 marks)6. B7. C8. A9. A 10. B 11. A 12. C 13. B 14. C 15. ASection C (5 marks)16. C 17. C 18. A 19. B 20. BSection D (10 marks)21. train sets 22. the under-fives 23. month 24. packaging 25. five 26.storage 27. November 3rd 28. drivers 29. production lines 30. shiftPart II Vocabulary and Structure (15 marks)31. D 32. C 33. A 34. C 35. B 36. D 37. A 38. C 39. C 40. B 41. A 42. A 43. B 44. B 45. DPart III Cloze (10 marks)46.adaptation 47. in 48. ignored 49. from 50.deny 51. spinning 52. representing 53.However 54. that/which 55. talePart IV Reading Comprehension (40 marks)Section A (10 marks)56. F 57. F 58. T 59. Dwyfach Coggages 60. The beachSection B (10 marks)61. threatened 62. move 63. bamboo 64. habitats 65. includingSection C (10 marks)66. C 67. D 68. C 69. A 70. BSection D (10 marks)71. give an indication signal 72. breathing 73. lack of eye contace 74. their internal world 75. BPart V Translation (20 marks)Section A (10 marks)76. 奥巴马政府在新预算中承认了这个问题，该预算包括了一个五千万美元的预防性方案.。

Contents1.Introduction (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 Filter data (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)1 Introduction1.1 BackgroundThe 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 organi zation’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 bas ed 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 & ROIFoundation (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 durati on that the organization’s money should be provided to have thehighest 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 describesthe optimal investment strategy3 Fundamental assumptions1) The indexes of GRA (such as ACT 、SA T 、Pell Grant 、Graduation Rate 、Retention Rate 、Graduates income)are the most influential factor that affect the use potential of school funds, what’s more, the indexes have the same weight2) For four-year universities, their C200_L4_POOLED_SUPP 、RET_FTL4、RET_PTL4 arezero; For two-year colleges, their C150_4_POOLED_SUPP 、RET_FT4、RET_PT4 are zero3) For public institutions ，their NPT4_PRIV 、NPT41_PRIV 、NPT42_PRIV 、NPT43_PRIV 、NPT44_PRIV 、NPT45_PRIV are zero; For private for-profit and nonprofit institutions, their NPT4_PUB 、NPT41_PUB 、NPT42_PUB 、NPT43_PUB 、NPT44_PUB 、NPT45_PUB are zero4) We define “NULL” appears in the data except appears in 3) as the average of that series5) Ignore the influence of degree-conferring situation, race, religion, region6) Schools’ data of SA T and ACT d evelop in a linear trend4 Definitions and NotationsTable A: The Excel which contain the IPEDS UID for Potential Candidate SchoolsTable B: The Excel which contain the Most Recent Cohorts Data (Scorecard Elements) : The weight of the first k index)(k iξ: Grey relational coefficient r i : Grey weight relation: Standardized index value: Index value: Sample average: Sample standard deviation:Standardized index vector:The correlation coefficient y i: Main components : Rate of contribution:The cumulative contribution rate : The comprehensive scorek w ~a ij a ij j μj s ~x jr ijb j pαZ5 Models5.1 Filter dataBecause the topic has a large number of additional data, we should classify the data based on the College Scorecard Data Dictionary which we can find from the official website .And then, according to the flow diagram5.1.1 as follow, we can filtering data. By using that flow diagram, we set up limits to filter the data circularly. We use SPSS to achieve above purpose, after that we get the valid data of 2936 potential candidate schools.InputTable A,TableBBased on the ID in TableA, merge Table A and BTable A has theID which TableB don’tDelete that IDin Table AOutputTable AOutputTableAFigure 5.1.1 Flow Diagram5.2 Object Selection Model (Grey Relational Analysis)5.2.1 Model analysisNot only there is a large amounts of missing in the original data, but also even after a preliminary screening, the data volume is still very large. We find there are more than 50 factors which affect us optimizing the school , what ’s more, the link between each factor we can't find accurately. So the normal model has no use to predict and evaluate the data .But Grey correlation analysis method is both suitable for irregular data and normal data. The quantitative results are consistent with qualitative analysis perfectly. Therefore, we choose that method to further narrowing the scope of the data.Grey correlation analysis is based on the similarity degree of various factors ’ changing curve , it can judge the correlation degree of each index .Through the quantitative analysis of the dynamic process, we can get the geometrical relationship of statistical data in the system and the grey correlation degree between the reference sequence and compare sequence. The greater the comparative sequence ’s correlation degree is , the closer the relationship between the reference sequence and compare sequence will be.The basic idea is to standardized the original observation and calculate the correlation coefficient, correlation degree. And then rank the indexes according to the size of the correlation. The application of GRA involves many fields, especially in the field of social economy, such as the ROI of the national economy departments , analyzing regional economic advantages , industrial structure adjustment, GRA has a good application effect.5.2.2 Model solution1) We have 2936 objects （potential candidate schools ）and 7 evaluation indexes （ACT 、SAT 、Pell Grant 、Graduation Rate 、Retention Rate 、Graduates income ），the reference sequence is}7,...,2,1|)({00==k k x x , the compare sequence is 2936,...,2,1},7,...,2,1|)({===i k k x i i x ；2) The weight of every index is ],...,[71w w w =，)7,...,2,1(=k w k means the first k index ’sweight , in that model we assume every index ’s weight is equal.3) |)()(|max max |)()(||)()(|max max |)()(|min min )(0000t x t x t x k x t x t x t x t x k s t s i s t s s t s i-+--+-=ρρξ 4) )(71k i k i i w r ξ∑==5) By using MATLAB, we can finish above data calculation process ,and then we can makethe figure of each evaluation objects’ grey weight relatio n as follow:Figure 5.2.1 Distribution Diagram of Grey Weight Relation According to Figure 5.2.1,we find that 90% objects’grey weight relation is under 0.60.We use MA TLAB to rank the evaluation objects, because the greater the grey weight relation is, the better the evaluation result is. We choose the first 300 objects as the new potential candidate schools.But during the process of GRA, the weight of evaluation indexes has deviation, we can’t get the accurate solution, so we need build another model to analyze in detail.5.3ROI Model (Principal Component Analysis)5.3.1 Model analysisAccording to the topic’s requirements, we should choose the potential candidate schools by their money using ability, but there are so many indexes influence the resul t, we can’t get reliable evaluation only by one factor.In the study of that practical problem, in order to comprehensively and systematically analyze problems, we must consider many factors. These involved factors generally referred to the index, also known as a variable in the multivariate statistical analysis. Because each variable reflects some information of the research question and all of them has a certain correlation , the information one index reflects may overlap another.PCA is to use less variables to explain most variables of the original data, it transforms many high correlation variables into uncorrelated variables. Usually the number of new variables is smaller than the original variables, we call it principal component and use it to explain the comprehensive index.This method simplify the problem, at the same time make the result more scientific and effectiveTherefore ,it seems easier to use PCA solving the Optimization problem. By reducing dimension, we transform many indexes(such as Net Price, Repayment of Debt, Repayment Rate, Graduates Income) into a few principal components.5.3.2 Model solution1) Standardized the original data,15,...,2,1,300,...,2,1,~==-=j i s j j ij ij a a μ;15,...,2,1,)(13001,3001300123001=--==∑∑==j a a i j ij j i ij j s μμ 15,...,2,1,~=-=j s x x j j jjμ2) Calculate the correlation coefficient matrix,15*15)(r ij R =，15,...,2,1,,1300*~3001~=-=∑=j i a a r kj k ki ij3) Calculate the eigenvalue and the feature vectors,By using SPSS, we calculate the eigenvalue of R ,0...1521≥≥≥≥λλλ，And the standardized feature vector ,,...,,1521μμμby using the feature vector, we get 15 newindexes ，,......,,...,...~151515~2215~111515~15152~222~1122~15151~221~1111x x x x x x x x x y yyμμμμμμμμμ+++=+++=+++= 4) Choose P （15≤P ）principal component ，calculate the comprehensive score①Calculate the contribution rate of )15,...,2,1(=j j λ and cumulative contribution rate∑∑====151151,j j p k k j j b b αλλ By using SPSS, we get the contribution rate of 15 eigenvalue as follow:Table 5.3.1 Contribution RateAnalyzing Table 5.3.1，we find the cumulative contribution rate of the first three eigenvalue is more than 90%, the model has a well result.②Choose the first three principal component for a comprehensive evaluation,y b j p j j Z ∑==1By using SPSS, we get the feature vectors of the first three characteristic root,shows in Table 5.3.2Table 5.3.2 The Feature VectorsWe make the first three principal components ’ contribution rate as weight, build up the principal component comprehensive evaluation model,y y y Z 3211031.01153.06892.0++= Put every optimized school’s three principal components into above equation ，we get the comprehensive evaluation result of 300 new potential candidate schools, shows in figure5.3.3 ，Fac_1 on behalf ofy 1，Fac_2 on behalf of y 2,Fac_3 on behalf of y 3， Total onbehalf of Z ，Figure 5.3.3 Comprehensive evaluation result of 300 schoolsWe choose the first 40 schools as the final potential candidates list ，the comprehensive evaluation result shows in figure 5.3.4，Figure 5.3.4 Comprehensive evaluation result of 40 final potential schoolsBecause the indexes (such as Net Price, Repayment of Debt, Repayment Rate, Graduates Income) of this model are closely related to ROI, we use the comprehensive score to evaluate schools’ ROI. We ranked it in Table 5.3.3,Table 5.3.3 Rank5.4 Verify the possibility5.4.1 ComparisonThrough comparison we found that many famous universities such as Harvard University does not appear in our preferred list, this can’t help but let us create confusion, what is the reason causes this kind of phenomenon ?Considering that phenomenon, we analyze from the model itself. The topic asks us to optimize the school list which is based on the potential of fund using .We've learned from the related literature , there is a positive correlation between the income of graduate individual and donation. As their income level become higher, the possibility and amount of donation is greater. According to statistics, every 1% increase in income, the possibility to donation increase 0.35% ~ 0.5%; when the personal income increased $10000, donation amount can increased 2%; per $10000 increase in household income, donation amount can increased 9%.So at the beginning, we choose Net Price, Repayment of Debt, Repayment Rate, Graduates Income as evaluation indexes.We standardized the indexes, and then compare the data of final potential schools with Harvard University, the result shows in Figure 5.4.1Figure 5.4.1 ComparisonAccording to Figure 5.4.1, we find the average net price and the monthly repayment of the debt are significantly less than final potential schools. The bigger the average net price and the monthly repayment of the debt are, the higher the students’ needs for money are, so the school has high potential to use the fund.Like Harvard University, there are many famous foundations invest it, its students have enough funds ,so there is no doubt that it has low average net price and monthly repayment of the debt. That is the reason which makes Harvard University get low comprehensive score in our model.5.4.2 External factorBecause the Goodgrant Foundation do not want to duplicate the investments and focus of other large grant organizations, we check out the Gates foundation's donation list of schools and compare it with the potential candidates list which we get in Figure 5.3.4, what’s more, we eliminate repetitive schools to get the final candidates list, shows in Table 5.4.2(the red name means that school should remove from the potential candidates list),Table 5.4.2 Real rank5.5 Investment Forecast Model5.5.1 Linear Regression Forecasting Model1)We find previous years’ (09-13years) Reference data which is closely related to students’performance(such as ACT，SAT, Enrollment of undergraduate degree-seeking students) from “https:///ipeds/datacenter/Default.aspx”.According to Table 5.4.2,we use that 36 schools’ data to do the linear regression prediction.2)There are many schools’ data lost in the table,so how to deal with those “NULL”?We choose other years data of that school, doing the linear regression prediction, and then getthe data of that year. If other years data have also lost , we take the average data of other schools as the lost data.3)Because the data we can use is limited(no more than 5 years),we can’t doing theComplex forecast. We choose Linear Regression prediction, by analyzing the variation trend of 36 schools’ data and forecast 2016~2020 years’ ACT and SCT . Based on forecast data, We make the diagram of 2016 ~ 2020 data variation trend which shows as Figure 5.5.1 and Figure 5.5.2 ,analyze the development of student performance primarily.Figure 5.5.1 Figure 5.5.25.5.2 School potential Prediction (TOPSIS)1)Based on forecast data which we get from Linear Regression Forecasting Model, we useTOPSIS method to evaluate the effect which The Goodgrant Foundation’s investment can takes in the future 5years.2)We take five factors (such as ACT and SAT mark、the growing trend of the mark and thegrowing trend of undergraduate degree-seeking students’ number) as indexes, evaluate the potential of its annual school development . We calculate the comprehensive evaluation score, and then sorting every candidate school by score.3)According to the influence the five factors have, we define the weight of every factor asfollow: ACT mark--0.25, SAT mark--0.25,both the growing trend of ACT and SAT are0.2, the growing trend of undergraduate degree-seeking students’ number--0.1.4)We use MA TLAB to calculate the comprehensive evaluation score and show the result inFigure 5.4.3,analyze the Figure, we find between 2016 and 2020 every school’s score changes little, it means every school’s development capacity is stable. What’s more, the score of the first 20 schools which get the higher score in 2016 are always higher than other school from 2017 to 2020,so we choose those 20 schools as the reliable potentialcandidate list, we think those school both has the better ROI and development potential.Figure 5.5.3 ScoreThe score of those 30 schools from2016 to 2020 is showed in Table 5.5.1ID Z[SP]_2016Z[SP]_2017Z[SP]_2018Z[SP]_2019Z[SP]_2020 1213090.581 0.653 0.591 0.595 0.600 1226120.574 0.609 0.575 0.576 0.577 1229310.684 0.656 0.683 0.682 0.681 1311590.543 0.527 0.526 0.518 0.511 1523180.543 0.490 0.616 0.610 0.604 1630460.628 0.490 0.512 0.509 0.506 1649880.520 0.571 0.561 0.555 0.550 1656620.574 0.725 0.601 0.598 0.596 1666560.607 0.497 0.639 0.645 0.652 1791590.548 0.551 0.534 0.528 0.523 1868670.734 0.734 0.737 0.739 0.740 1912410.611 0.549 0.602 0.598 0.594 1939000.694 0.585 0.683 0.678 0.673 1948240.556 0.524 0.549 0.547 0.544 2024800.584 0.594 0.583 0.582 0.582 2112910.624 0.526 0.613 0.607 0.602 2114400.740 0.654 0.737 0.735 0.732 2165970.601 0.488 0.587 0.580 0.573 2174930.546 0.483 0.535 0.530 0.525 2232320.611 0.595 0.607 0.605 0.603Table 5.5.1 Z[SP]5.5.3 Final investment (TOPSIS)5.5.3.1 Model AnalysisAccording to 5.5.2，we get the final 20 candidate school list, after that ,we will undertake the key process--investment allocation.There are many factors affect investment, but through the step-by-step modeling process, those factors finally can be summed up as follow : The comprehensive score of ROI model(Z[ROI]) ;The comprehensive score of School potential Prediction(Z[SP]) ;Percent of all federal undergraduate students receiving a federal student loan(PCTFLOAN);Median debtof the student (MD);The number of undergraduates(NG).Because TOPSIS method allows us to analyze the scheme by our own ideas which give us enough free space, what’s more,the result of TOPSIS method is clear, it has well operational flexibility, so we choose that to solve our problem.Weight distribution: all of the factors in 1) have great effects on investment, but both PCTFLOAN and MD belong to debt ,those share the weight of debt, so we can distribute the weight as follow:Z[ROI]--0.25,Z[SP]--0.25,NG--0.25,PCTFLOAN--0.125,MD--0.1255.5.3.2Model SolutionNG is changing with time ,we show it in Table 5.5.2,id NG_2016NG_2017NG_2018NG_2019NG_20201213092597263326692705274112261270777304753077577983122931551755795642570457671311597159725073427434752615231824102497258526722759163046414142004260431943791649881657016587166041662216639165662393740104083415642291666565866655172377923860817915985708711885389949136186867294430433142324133401912418505857886518724879719390022951231832341623648238811948245177514051045067503020248083688528868888489009211291348934853481347734732114405977601460506087612321659768916891689168916891217493203620482061207320862232321394914218144861475415023Table 5.5.2 NGWe can also get Z[ROI],PCTFLOAN,MD from previous data,ID Z[ROI]PCTFLOAN MD1213090.73034350.641249511226120.802319610.5115250001229310.765134390.3726205001311590.786649810.460323500152318 1.004578520.5776270001630460.845330140.5407270001649880.854815810.4235270001656620.924753020.567823312166656 1.112655080.783250001791590.808487460.348250001868670.785503970.6589270001912410.811966360.5467250001939000.982760460.4131232501948240.916736310.586627835.52024800.747331260.6791268632112910.767629720.4098270002114400.854345660.3964250002165970.771433880.435627000217493 1.154260170.390726024.52232320.825762390.491625281Table 5.5.3By using MATLAB, we calculate the final comprehensive score (Z [FN]) of the 20 candidate schools. According to the score, we decide how much money The Goodgrant Foundation should invest for each school. But Z[SP] is changing every year，so the investment to each school is changing. The final comprehensive score and investment from 2016 to 2020 is showed as follow table:ID Z[FN]_2016Z[FN]_2017Z[FN]_2018Z[FN]_2019Z[FN]_2020 1213090.252 0.339 0.268 0.274 0.280 1226120.280 0.343 0.292 0.298 0.303 1229310.329 0.301 0.334 0.332 0.331 1311590.211 0.225 0.206 0.204 0.203 1523180.373 0.370 0.430 0.426 0.423 1630460.366 0.288 0.281 0.281 0.282 1649880.426 0.489 0.457 0.453 0.449 1656620.304 0.460 0.337 0.336 0.336 1666560.514 0.472 0.560 0.575 0.589 1791590.264 0.293 0.262 0.261 0.261 1868670.451 0.445 0.456 0.457 0.457 1912410.351 0.317 0.347 0.344 0.342 1939000.674 0.605 0.670 0.667 0.663 1948240.367 0.371 0.366 0.365 0.364 2024800.352 0.381 0.358 0.360 0.362 2112910.311 0.250 0.304 0.299 0.295 2114400.465 0.382 0.464 0.461 0.457 2165970.321 0.269 0.312 0.307 0.302 2174930.423 0.416 0.420 0.419 0.419 2232320.437 0.446 0.442 0.444 0.446Table 5.5.4 Z[FN]ID INV_2016INV_2017INV_2018INV_2019INV_2020 121309$3,377,595$4,545,294$3,535,471$3,623,230$3,704,440 122612$3,753,266$4,594,187$3,863,051$3,934,467$4,003,692 122931$4,406,572$4,033,955$4,406,992$4,394,449$4,376,854 131159$2,817,760$3,009,942$2,716,954$2,696,351$2,682,999 152318$4,988,693$4,951,707$5,679,022$5,635,768$5,596,019 163046$4,893,351$3,860,524$3,716,334$3,720,512$3,726,668 164988$5,703,381$6,549,593$6,041,218$5,985,171$5,932,065 165662$4,069,234$6,165,503$4,455,247$4,447,100$4,439,571 166656$6,875,631$6,324,965$7,406,247$7,598,343$7,789,734 179159$3,533,653$3,922,658$3,462,914$3,456,195$3,453,114 186867$6,033,507$5,963,478$6,031,848$6,038,227$6,038,962 191241$4,695,197$4,249,163$4,587,144$4,551,653$4,517,746 193900$9,026,607$8,102,416$8,859,888$8,814,570$8,766,089 194824$4,917,651$4,973,672$4,833,172$4,824,265$4,817,097 202480$4,711,203$5,106,241$4,727,869$4,760,523$4,791,968 211291$4,167,850$3,355,796$4,021,230$3,959,898$3,900,586 211440$6,218,948$5,124,833$6,134,486$6,091,854$6,041,917 216597$4,301,641$3,607,390$4,124,471$4,055,891$3,990,970 217493$5,664,556$5,577,679$5,554,513$5,543,635$5,536,138 223232$5,843,702$5,981,004$5,841,930$5,867,899$5,893,373Table 5.5.5 INV6. ConclusionsThe candidate list of schools:Table 6.1During the evaluation of ROI Model, we get those40 schools as the first optimization list; When we compare the first optimization list with other Big Foundations’ list, the red names are deleted;During the evaluation of Investment Forecast Model, the blue names are deleted; In theend, the final candidate schools are the last 20 black names.Considering the distribution of that 40 optimized school, we can find that half of them are located in large city, the more developed the city is, the more the optimized schools locate in.Figure 6.1 LocaleThe investment list is showed in Table 6.2,We transform the data in Table 6.2 into a line chart which is showed in Figure 6.2.According to Figure 6.2 we can find , in different years The Goodgrant Foundation should undertakes different Investment strategy.Figure 6.2 INV7.Strengths and WeaknessesFor this model, we have used Grey Correlation Analysis, Principal Component Analysis, Comprehensive Evaluation Method(TOPSIS),Linear Regression Model. There are nearly 3000 schools' data with 50 index. In addition to the given data, we can't able to make a comprehensive evaluation for all university’ indexes.When we choose university at first time , the principle that according to is the ability to school’s cultivate, we can set aside most of the university due to the size of the numerical . The powerful of the university ability could be determined according to the size of the numerical. In the given index, we chose seven indicators related to the students' ability to predict the ability of university. However, these indicators without a typical distribution, so we can not use the exact formula or model to accurately judge the powerful of each university training students' ability.7.1StrengthsGrey Correlation Analysis Method, as a kind of Comprehensive Evaluation Method, it has not a exactly requirement for size of sample, also do not need the typical distribution, and the relatively small amount of calculation, the result will be the same as those of qualitative analysis, the advantages of simple and reliable. The most important thing is that it can build a relational sequence which can obtain correlation quantificationally. In this model, we can application the grey correlation method to get correlation, the size of the correlation willrepresent the strength of the school training students' ability. If size of the correlation more bigger, the evaluation results will be better.After the primary screening. we used Principal Component Analysis (PCA). Principal Component Analysis (PCA) can eliminate the mutual influence between the indexes, it also can reduce the workload of index selection, we can use a handful of composite indicator to replace the original indicators for evaluation. In this screening, we apply the indicator of return on investment regard as the university ability, we should select multiple indicators for principal component analysis, in order to determine the comprehensive variables. The return on investment required to our ability can be used a general comprehensive index to in place , according to the size of the index, we can select the list of schools that we need again. This method overcomes the defect of identified weighting, and having a standard calculation. Using the software can be implemented on the computer, the most important is that the comprehensive index value is objective and reasonable.Finally, using linear regression to forecast, then use TOPSIS to decide the last list. The reason is that we need five years list, so it must be make predictions. Linear regression method deal with multi-factor model is more simple and convenient, and the regression analysis applicable is easy to be affected by many factors. When Our model need predict index, simple easy to use regression analysis. At the end of the forecast, we using TOPSIS method to judge the development potential of the school by predict the index and the given index as influ ence factors. TOPSIS can join the evaluator’ like, it can analyze base on the director of the preference, and it can be carried out in accordance with the investors' willingness to change; The calculation results is more clear, and high maneuverability. The value that acquire by TOPSIS, can represent the development potential of the university. we can according to the size of the values to determine the amount of distribution, in order to distribution rationalization, and have a maximum functionality.7.2WeaknessesWhen we use grey correlation analysis, we should assume the value by ourselves. So it must have exist error, and the accuracy is not high.Principal component analysis model have disadvantage too. The Explain of meaning of the principal component have fuzziness, clear and exact compare with the original data.When predict date, there have a lot of missing, it must influential to forecast results.。

脑卒中发病环境因素分析及干预摘要本文主要讨论脑卒中发病环境因素分析及干预问题。

根据题中所给出的数据，利用SPSS20软件进行相关性统计分析，分别对各气象因素进行单因素分析，进而建立后退法线性回归分析模型，得到脑卒中与气压、气温、相对湿度之间的关系。

同时在广泛收集各种资料并综合考虑环境因素，对脑卒中高危人群提出预警和干预的建议方案。

首先，利用SPSS20软件,从患病人群的性别、年龄、职业进行统计分析，得到2007-2010年男性患病人数高于女性，且男性所占比例有逐年下降趋势，女性则有上升趋势，因此，性别比例呈减小趋势。

分析不同年龄段患病人数，得到患病高峰期为75-77岁之间，且青少年比例逐年呈增长趋势，可见患病比例趋于年轻化。

同时在不同的职业中，农民发病人数最多，教师，渔民，医务人员，职工，离退人员的发病人数较少。

其次，由题中所给数据先进行单因素分析，剔除对脑卒中影响不显着的因素，得出气温、气压、相对湿度对脑卒中的影响程度大小，进而采用后退法线性回归分析建立模型，利用SPSS20对数据进行分析，求得脑卒中发病率与气温、气压、相对湿度之间的关系。

即发病率与平均温度成正相关，与最高温度成负相关，发病率与平均气压成正相关，与最低气压成负相关，与平均相对湿度成负相关，与最小相对湿度成正相关。

最后，通过查找资料发现，影响脑卒中的因素有两类，一类是不可干预因素，如年龄、性别、家族史，另一类是可干预因素，如高血压、高血脂、糖尿病、肥胖、抽烟、酗酒等因素。

分析这些因素，建立双变量因素分析模型，并结合问题1和问题2，对高危人群提出预警和干预的建议方案。

关键词脑卒中单因素分析后退法线性回归分析双变量因素分析一问题的重述脑卒中（俗称脑中风）是目前威胁人类生命的严重疾病之一，它的发生是一个漫长的过程，一旦得病就很难逆转。

这种疾病的诱发已经被证实与环境因素，包括气温、湿度之间存在密切的关系。

对脑卒中的发病环境因素进行分析，其目的是为了进行疾病的风险评估，对脑卒中高危人群能够及时采取干预措施，也让尚未得病的健康人，或者亚健康人了解自己得脑卒中风险程度，进行自我保护。

2016 National English Competitionfor College Students(Level C - Sample)参考答案及评分标准Part I. Listening Comprehension（30 marks）Section A (5 marks)1—5 CBABDSection B (10 marks)6—10 CBADC 11—15 CDACBSection C (5 marks)16—20 BDBBCSection D (10 marks)23. geographic location 24. cultural influences21. second largest 22. spirals to25. dates back to 26. economic revival 27. flourished in 28. multi-faceted and diverse29. modern and enterprising 30. a chimneyPart II Vocabulary, Grammar & Culture (15 marks)Section A Vocabulary & Grammar (10marks) 31—35 CDBAA 36—40 BCACBSection B Culture (5marks) 41—45 BBACAPart III Cloze (10 marks)contrast 49. information 50. back46. movement 47. included 48.51. harmony 52. others 53. individualists 54. descent 55. intellectuallyPart IV Reading Comprehension (35 marks)Section A58. F 59. F 60. F56. T 57. FSection B61—65 ACBDE SectionC (10 marks)66.T hey notice the subjects that most people don蒺t.67.A rtistry can be learned and developed through reading or taking lessons.68.U nderstand the difference it makes when you remove the irrelevant and selectonly what really matters while taking a picture.-1 -69.T ake more exercises.70.T o learn from experience and improve marks out the photographer from others. Section D (10 marks)71. different72. constructing/building73. agree74. similarities75. speculationPart V Translation (15marks)Section A (5marks)76.教育是民生改善的来源，传承文明的载体。

A题A person fills a bathtub with hot water from a single faucet and settles into the bathtub to cleanse and relax. Unfortunately, the bathtub is not a spa-style tub with a secondary heating system and circulating jets, but rather a simple water containment vessel. After a while, the bath gets noticeably cooler, so the person adds a constant trickle of hot water from the faucet to reheat the bathing water. The bathtub is designed in such a way that when the tub reaches its capacity, excess water escapes through an overflow drain.Develop a model of the temperature of the bathtub water in space and time to determine the best strategy the person in the bathtub can adopt to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water.建立时间和空间上的关于浴缸水温度的模型，确定浴缸中的人可以采纳的最佳策略使得即便是人在浴缸中也能保持水温，且在不浪费水的同时还尽可能的接近原来的水温。

小区开放对道路通行的影响评价模型摘要本文针对小区开放对道路的影响进行了研究，建立了层次分析模型、通行能力评价模型，使用了MATLAB、EXCEL等软件，得出小区开放在不同条件下会对道路交通产生不同的影响。

首先运用层次分析法，分析得出整体一般情况下小区开放有利于周边道路交通的结论。

之后构建了不同类型的小区，并分析得出小区开放的效果与小区结构及周边道路结构、车流量有关，因此小区开放不能盲目采取，要因地制宜。

最后根据分析结果，从交通通行的角度，向城市规划和交通管理部门提出了关于小区开放的合理化建议。

本文的突出特点是使用了层次分析法定量的比较了小区开放前后道路合理性，构建了对于研究该问题具有代表性的三种类型的小区，并建立了影响评估模型，客观的对不同小区结构及周边道路结构、车辆通行的影响进行评价。

针对问题一，首先查阅相关资料选取影响道路通行的指标，并对选取的指标进行筛选，然后运用各项指标进行层次分析，通过小区开放和小区封闭对道路交通和理性的判断来分析小区开放对道路通行的影响最后得出从整体看来，小区开放有利于道路通行。

针对问题二，通过查阅有关道路通行能力的相关资料建立了通行能力评价模型，首先根据模型求出道路基本通行能力的表达式，基本通行能力是理想状态下的通行能力，与实际情况分析对比存在差异。

因此基于差异，通过各实际因素对道路通行能力的影响进行修正，得到实际道路通行能力的数据。

最终计算出小区开放前后实际通行能力的相对系数。

针对问题三，构建了三种类型的小区，不同类型的小区具有不同的结构及不同的周边道路结构、车流量，应用问题二建立的模型分别对三种小区开放和封闭条件下周边道路的实际通行能力进行了计算，通过相对系数评价不同类型的小区开放对道路通行的影响，分析得出小区开放与地理位置、内部结构等因素有关，不能一概而论。

针对问题四，结合前述模型结果分析结果，从交通出行角度对城市规划部门和交通管理部门提出了合理化意见。

小区开放要合理的实施以体现小区开放的意义。

数学建模美赛c题数学建模美赛c题是国际数学建模竞赛的一部分，旨在提升学生在数学建模方面的技能。

参赛选手在有限的时间内解决实际问题，利用自己在数学、科学和工程方面的知识。

数学建模美赛C题的官方定义是“由参赛选手根据提供的问题内容，利用数学、统计学以及相关的应用软件，用模型来表达和解释现实世界中的问题或事件”。

这恰好吻合了数学建模的定义，它是一种利用数学方法来表达现实世界中的问题和活动的技术。

参赛选手需要使用计算机分析技术，分析模型，并且根据期望得出结果，务必要及时、准确地解决实际问题。

建模的过程也可以分为两个阶段：模型建立阶段和结果验证阶段。

在模型建立阶段，参赛选手必须建立一个能够反映问题实际情况的数学模型，并通过实验收集所需要的数据，以便于参赛选手根据该模型推断问题的解决方案。

在结果验证阶段，参赛选手使用数学模型推断出的解决方案，通过与实际情况的比对，来验证推断效果，并进一步完善建模技术。

数学建模美赛C题不仅让选手在快速解决问题方面进行挑战，而且还能够让选手运用现有的数学、科学和工程知识，学习实际操作的能力。

参赛选手需要以最快的速度熟练掌握数学模型、计算机分析技术，以及统计分析软件，充分利用技术，为解决实际问题创造出更好的解决方案，还要能够及时准确地反馈给裁判长。

参赛选手还需要注意模型和结果的表达方式，使之能够更好地反映出问题本身，以方便裁判长和评委更直观地阅读，从而获得更多的有利评价。

总而言之，数学建模美赛C题的参赛要求不仅针对其解决数学问题的能力，而且还能够锻炼参赛选手的技术能力，并且能够给比赛带来实际收获。

参赛选手应该努力练习和学习，即使在比赛中遭遇挫折也要有必要的毅力和勇气，最后祝愿大家参加比赛能够取得更佳的成绩。