2014美国数学建模大赛C题论文
2014年美赛C题翻译
This will take some skilled data extraction and modeling efforts to obtain the correct set of nodes (the Erdös coauthors) and their links (connections with one another as coauthors). 这需要熟练数据提取 并 在建模上下功夫， 以便得到正确的节点和边
Once built, analyze the properties of this network. 建完后分析网络性能(Again, do not include Erdös --- he is the most infnodes in the network. In this case, it’s co-authorship with him that builds the network, but he is not part of the network or the analysis.)
One of the techniques to determine influence of academic research is to build and measure properties of citation or co-author networks.
学术研究的技术来确定影响之一是构建和引文或合著网络的度量属性。
Google Scholar is also a good data tool to use for network influence or impact data collection and analysis.
谷歌学术搜索也是一个好的数据工具用于网络数据收集和分析影响或影响。
美国大学生数学建模比赛2014年B题
Team # 26254
Page 2 oon ............................................................................................................................................................. 3 2. The AHP .................................................................................................................................................................. 3 2.1 The hierarchical structure establishment ....................................................................................................... 4 2.2 Constructing the AHP pair-wise comparison matrix...................................................................................... 4 2.3 Calculate the eigenvalues and eigenvectors and check consistency .............................................................. 5 2.4 Calculate the combination weights vector ..................................................................................................... 6 3. Choosing Best All Time Baseball College Coach via AHP and Fuzzy Comprehensive Evaluation ....................... 6 3.1 Factor analysis and hierarchy relation construction....................................................................................... 7 3.2 Fuzzy comprehensive evaluation ................................................................................................................... 8 3.3 calculating the eigenvectors and eigenvalues ................................................................................................ 9 3.3.1 Construct the pair-wise comparison matrix ........................................................................................ 9 3.3.2 Construct the comparison matrix of the alternatives to the criteria hierarchy .................................. 10 3.4 Ranking the coaches .....................................................................................................................................11 4. Evaluate the performance of other two sports coaches, basketball and football.................................................... 13 5. Discuss the generality of the proposed method for Choosing Best All Time College Coach ................................ 14 6. The strengths and weaknesses of the proposed method to solve the problem ....................................................... 14 7. Conclusions ........................................................................................................................................................... 15
2014年美国大学生数学建模竞赛A题论文综述
数学建模综述2014年美国大学生数学建模竞赛A题论文综述我们小组精读两篇14年美赛A题论文，选择了其中一篇来进行学习，总结。
1、问题分析The Keep-Right-Except-To-Pass Rule除非超车否则靠右行驶的交通规则问题：建立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的表现。
这条规则在提升车流量的方面是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替代品（包括完全没有这种规律）并加以分析。
在一些国家，汽车靠左形式是常态，探讨你的解决方案是否稍作修改即可适用，或者需要一些额外的需要。
最后，以上规则依赖于人的判断，如果相同规则的交通运输完全在智能系统的控制下，无论是部分网络还是嵌入使用的车辆的设计，在何种程度上会修改你前面的结果论文：基于元胞自动机和蒙特卡罗方法,我们建立一个模型来讨论“靠右行”规则的影响。
首先,我们打破汽车的运动过程和建立相应的子模型car-generation的流入模型,对于匀速行驶车辆，我们建立一个跟随模型,和超车模型。
然后我们设计规则来模拟车辆的运动模型。
我们进一步讨论我们的模型规则适应靠右的情况和,不受限制的情况, 和交通情况由智能控制系统的情况。
我们也设计一个道路的危险指数评价公式。
我们模拟双车道高速公路上交通(每个方向两个车道,一共四条车道),高速公路双向三车道（总共6车道)。
通过计算机和分析数据。
我们记录的平均速度,超车取代率、道路密度和危险指数和通过与不受规则限制的比较评估靠右行的性能。
我们利用不同的速度限制分析模型的敏感性和看到不同的限速的影响。
左手交通也进行了讨论。
根据我们的分析,我们提出一个新规则结合两个现有的规则(靠右的规则和无限制的规则)的智能系统来实现更好的的性能。
该论文在一开始并没有作过多分析，而是一针见血的提出了自己对于这个问题的做法。
由于题目给出的背景只有一条交通规则，而且是题目很明确的提出让我们建立模型分析。
数学建模C题论文
191])()([),(20200y y x x r z y x z -+--=c y b x a y x y x z +⋅+⋅++=22),(4753⨯41i D i D 20.000160.001162021421339915152112032534791410.1 6660.1 2.5 2.666.11212.12525.16060.1/mcm05/probX 53⨯47Y 53⨯47k n m Z ⨯53⨯47 k n m Z ⨯~53⨯47i n m k H ⨯m m n k n 21n +120i n m k S ⨯i D126 18319719141164512X Y⎪⎪⎪⎭⎫ ⎝⎛=⨯⨯⨯⨯⨯⨯47532531534712111..................x x x x x x X ⎪⎪⎪⎭⎫⎝⎛⨯⨯⨯⨯⨯⨯47532531534712111..................y y y y y y),(y x Z =mnk ⎪⎪⎪⎭⎫⎝⎛⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯⨯),(...),,(),,(............),(...),,(),,(4753475325325315315347147121211111y x f y x f y x f y x f y x f y x f ⎪⎪⎪⎭⎫⎝⎛⨯⨯⨯⨯⨯⨯47532531534712111..................Z Z Z Z Z Z 1=imnk Z ~⎪⎪⎪⎪⎭⎫ ⎝⎛⨯⨯⨯⨯⨯⨯47532531534712111~...~~............~...~~Z Z Z Z Z Z i imnkH ∆mnk Z i mnk Z ~⎪⎪⎪⎭⎫⎝⎛⨯⨯⨯⨯⨯⨯ii i i i i h h h h h h 47532531534712111............... (2)i mnkS∆∑∑=⨯=⨯4712531)(47531j i ji i hi D ∆∑=16411641i mnk S 4i i imnk H 5347imnk S mnk H i D 41 2),(y x Z = ),(y x Z =i D nk m ⨯ i mnk H mnk Z i mnk Z ~1~mnk Z 2~mnk Z 1mnk H 2mnk H imnkS∆∑∑=⨯=⨯4712531)(47531j ij i i h1mnk S 2mnk S⑤ 用i D ∆∑=16411641i mnk S 计算出1D 与2D ，则1D 和2D 的值较小者为最优方案.3 主要程序及结论通过数据处理与分析我们认为预测方法一比预测方法二好.所得计算结果值分别为：（1）不同时段的两种方法的实测与预测值的均方差：1mnkS =[0.9247218269e-1, .165797962696, 0.9247218269e-1,0.9247218269e-1, .2586806182, .2586806182, .2586806182, 2.791713932, .2474029514, .2539943168, .2715902174, .2715902174182, .2586806182, 2.791713932, .2474029514, .2539943168, .2715902174]2mnkS := [0.921412432e-1, .1098068392, 0.2234955063e-1,0.1592933205e-1, .2851304286, .2851304286, .2851304286, 2.792910527, .2612701098, .2381007694, .2613774987, 0.5183032655e-1,.2851304286,2.792810527, .2612701098, .2381007694, .2613774987] （2） 方法一的均方差为：1D := .8311398371方案二的均方差： 2D = .8417760978得1D <2D .主要程序与运行结果为： （1） 局域曲面拟合程序> solve({0.3=0.6-r*(0.045^2+0.042^2)},{r});> z1:=0.6-79.17656374*[(x-120.2500)^2+(y-33.7667)^2];> z2:=0.6-79.17656374*[(x-120.2500)^2+(y-33.7667)^2];> z3:=0.6-79.17656374*[(x-120.2500)^2+(y-33.7667)^2];> z4:=0.6-79.17656374*[(x-120.2500)^2+(y-33.7667)^2];> solve({0.15=0.3-r*(0.045^2+0.042^2)},{r});> z4:=0.3-39.58828187*[(x-118.1833)^2+(y-31.0833)^2];> solve({5.1=10.2-r*(0.045^2+0.042^2)},{r});> z1:=10.2-1346.001584*[(x-120.3167)^2+(y-31.5833)^2];> z2:=10.2-1346.001584*[(x-120.3167)^2+(y-31.5833)^2];> z3:=10.2-1346.001584*[(x-120.3167)^2+(y-31.5833)^2];> z4:=10.2-1346.001584*[(x-120.3167)^2+(y-31.5833)^2];> solve({0.1=0.2-r*(0.045^2+0.042^2)},{r});> z4:=0.2-26.39218791*[(x-118.4000)^2+(y-30.6833)^2];>z4:=solve({118.9833^2+30.6167^2+a*118.9833+b*30.6167+c=0.7000,118.5833^ 2+30.0833^2+a*118.5833+b*30.0833+c=1.8000,119.4167^2+30.8833^2+a*119.41 67+b*30.8833+c=0.5});> solve({0.05=0.1-r*(0.045^2+0.042^2)},{r});> z1:=0.1-13.19609396*[(x-119.4167)^2+(y-30.8833)^2];>> solve({2.9=5.8-r*(0.045^2+0.042^2)},{r});> z4:=0.1-765.3734495*[(x-118.2833)^2+(y-29.7167)^2];（2）均方差求值程序：>sq1:=[0.09247218269,0.165797962696,0.09247218269,0.09247218269,0.258680 6182,0.2586806182,0.2586806182,2.791713932,0.2474029514,0.2539943168,0. 2715902174,0.2715902174182,0.2586806182,2.791713932,0.2474029514,0.2539 943168,0.2715902174];> sum1:=add(i,i=sq1);> ave1:=sum1/17;>ve1:=[.5222900020,.5222900020,.5222900020,.5222900020,.5222900020,.5222 900020,.5222900020,.5222900020,.5222900020,.5222900020,.5222900020,.522 2900020,.5222900020,.5222900020,.5222900020,.5222900020,.5222900020,.52 22900020];>sq2:=[0.0921412432,0.1098068392,0.022********,0.01592933205,0.285130428 6,0.2851304286,0.2851304286,2.792910527,0.2612701098,0.2381007694,0.261 3774987,0.0518*******,0.2851304286,2.792810527,0.2612701098,0.238100769 4,0.2613774987];（2）数据模拟图程序：> with(linalg):> l:=matrix(91,7,[58138,32.9833,118.5167, 0.0000, 5.0000, 0.2000, 0.0000, 58139, 33.3000,118.8500, 0.0000, 3.9000, 0.0000, 0.0000,58141, 33.6667,119.2667, 0.0000, 0.0000, 0.0000, 0.0000,58143, 33.8000,119.8000, 0.0000, 0.0000, 0.0000, 0.0000,58146, 33.4833,119.8167, 0.0000, 0.0000, 0.0000, 0.0000,58147, 33.0333,119.0333, 0.0000, 6.0000, 1.4000, 0.0000,58148, 33.2333,119.3000, 0.0000, 1.1000, 0.3000, 0.0000,58150, 33.7667,120.2500, 0.0000, 0.0000, 0.0000, 0.1000,58154, 33.3833,120.1500, 0.0000, 0.0000, 0.0000, 0.0000,58158, 33.2000,120.4833, 0.0000, 0.0000, 0.0000, 0.0000,58230, 32.1000,118.2667, 3.3000,20.7000, 6.6000, 0.0000,58236, 32.3000,118.3000, 0.0000, 8.2000, 3.6000, 1.4000,58238, 32.0000,118.8000, 0.0000, 0.0000, 0.0000, 0.0000,58240, 32.6833,119.0167, 0.0000, 3.0000, 1.4000, 0.0000,58241, 32.8000,119.4500, 0.1000, 1.4000, 1.5000, 0.1000,58243, 32.9333,119.8333, 0.0000, 0.7000, 0.4000, 0.0000,58245, 32.4167,119.4167, 0.3000, 2.7000, 3.8000, 0.0000,58246, 32.3333,119.9333, 7.9000, 2.7000, 0.1000, 0.0000,58249, 32.2000,120.0000,12.3000, 2.4000, 5.6000, 0.0000,58251, 32.8667,120.3167, 5.2000, 0.1000, 0.0000, 0.0000, 58252, 32.1833,119.4667, 0.4000, 3.2000, 4.8000, 0.0000, 58254, 32.5333,120.4500, 0.0000, 0.0000, 0.0000, 0.0000, 58255, 32.3833,120.5667, 1.1000,18.5000, 0.5000, 0.0000, 58264, 32.3333,121.1833,35.4000, 0.1000, 0.2000, 0.0000, 58265, 32.0667,121.6000, 0.0000, 0.0000, 0.0000, 0.0000, 58269, 31.8000,121.6667,31.3000, 0.7000, 2.8000, 0.1000, 58333, 31.9500,118.8500, 8.2000, 8.5000,16.9000, 0.1000, 58334, 31.3333,118.3833, 4.9000,58.1000, 9.0000, 0.1000, 58335, 31.5667,118.5000, 5.4000,26.0000,11.0000, 0.8000, 58336, 31.7000,118.5167, 3.6000,27.8000,15.3000, 0.6000, 58337, 31.0833,118.1833, 7.0000, 6.4000,15.3000, 0.2000, 58341, 31.9833,119.5833,11.5000, 5.4000,16.1000, 0.0000, 58342, 31.7500,119.5500,32.6000,37.9000, 5.8000, 0.0000, 58343, 31.7667,119.9333,20.7000,24.3000, 5.3000, 0.0000, 58344, 31.9500,119.1667,12.4000, 5.9000,16.3000, 0.0000, 58345, 31.4333,119.4833,21.8000,18.1000, 9.8000, 0.1000, 58346, 31.3667,119.8167, 0.1000,12.7000, 5.1000, 0.2000, 58349, 31.2667,120.6333, 1.1000, 5.1000, 0.0000, 0.0000, 58351, 31.8833,120.2667,22.9000,15.5000, 6.2000, 0.0000, 58352, 31.6500,120.7333,15.1000, 5.4000, 2.4000, 0.0000, 58354, 31.5833,120.3167, 0.1000,12.5000, 2.4000, 0.0000, 58356, 31.4167,120.9500, 5.1000, 4.9000, 0.4000, 0.0000, 58358, 31.0667,120.4333, 2.4000, 3.4000, 0.0000, 0.8000, 58359, 31.1500,120.6333, 1.5000, 3.8000, 0.5000, 0.1000, 58360, 31.9000,121.2000, 5.6000, 3.2000, 2.9000, 0.1000, 58361, 31.1000,121.3667, 3.5000, 0.6000, 0.2000, 0.7000, 58362, 31.4000,121.4833,33.0000, 4.1000, 0.9000, 0.0000, 58365, 31.3667,121.2500,17.7000, 2.2000, 0.1000, 0.0000, 58366, 31.6167,121.4500,75.2000, 0.4000, 1.5000, 0.0000, 58367, 31.2000,121.4333, 7.2000, 2.8000, 0.2000, 0.2000, 58369, 31.0500,121.7833, 3.2000, 0.3000, 0.0000, 0.3000, 58370, 31.2333,121.5333, 7.0000, 3.4000, 0.2000, 0.2000, 58377, 31.4667,121.1000, 7.8000, 7.2000, 0.3000, 0.0000, 58426, 30.3000,118.1333, 0.0000, 0.0000,17.6000, 6.2000, 58431, 30.8500,118.3167, 5.1000, 2.3000,16.5000, 0.1000, 58432, 30.6833,118.4000, 3.6000, 1.4000,20.5000, 0.2000, 58433, 30.9333,118.7500, 2.1000, 3.4000, 8.5000, 0.2000, 58435, 30.3000,118.5333, 0.0000, 0.0000,13.6000, 8.5000, 58436, 30.6167,118.9833, 0.0000, 0.0000, 5.3000, 0.5000, 58438, 30.0833,118.5833, 0.0000, 0.0000,27.6000,21.8000, 58441, 30.8833,119.4167, 0.1000, 1.6000, 1.6000, 1.0000, 58442, 31.1333,119.1833, 3.0000, 8.8000, 5.4000, 0.2000, 58443, 30.9833,119.8833, 0.1000, 2.7000, 0.1000, 0.9000,58446, 30.9667,119.6833, 0.0000, 0.1000, 5.1000, 2.5000, 58448, 30.2333,119.7000, 0.0000, 0.0000,15.1000, 6.9000, 58449, 30.0500,119.9500, 0.0000, 0.0000,23.5000, 8.2000, 58450, 30.8500,120.0833, 0.0000, 0.7000, 0.0000, 4.1000, 58451, 30.8500,120.9000, 0.5000, 0.1000, 0.0000, 3.8000, 58452, 30.7833,120.7333, 0.3000, 0.0000, 0.0000, 3.0000, 58453, 30.0000,120.6333, 0.0000, 0.0000, 0.0000,18.2000, 58454, 30.5333,120.0667, 0.0000, 0.0000, 0.5000, 4.9000, 58455, 30.5167,120.6833, 0.0000, 0.0000, 0.0000, 4.6000, 58456, 30.6333,120.5333, 0.0000, 0.0000, 0.0000, 4.2000, 58457, 30.2333,120.1667, 0.0000, 0.0000, 2.0000,12.6000, 58459, 30.2000,120.3167, 0.0000, 0.0000, 0.0000,15.0000, 58460, 30.8833,121.1667, 1.2000, 0.1000, 0.0000, 2.3000, 58461, 31.1333,121.1167, 4.0000, 1.4000, 0.4000, 0.2000, 58462, 31.0000,121.2500, 2.7000, 0.3000, 0.4000, 1.7000, 58463, 30.9333,121.4833, 1.7000, 0.1000, 0.0000, 0.8000, 58464, 30.6167,121.0833, 0.0000, 0.0000, 0.0000, 3.6000, 58467, 30.2667,121.2167, 0.0000, 0.0000, 0.0000, 1.8000, 58468, 30.0667,121.1500, 0.0000, 0.1000, 5.1000, 2.5000, 58472, 30.7333,122.4500, 0.3000, 0.6000, 0.0000, 4.9000, 58477, 30.0333,122.1000, 0.0000, 0.0000, 0.0000, 0.0000, 58484, 30.2500,122.1833, 0.0000, 0.0000, 0.0000, 0.0000, 58530, 29.8667,118.4333, 0.0000, 0.0000,27.5000,23.6000, 58531, 29.7167,118.2833, 0.0000, 0.0000, 3.7000,11.5000, 58534, 29.7833,118.1833, 0.0000, 0.0000, 9.3000, 6.5000, 58542, 29.8167,119.6833, 0.0000, 0.0000, 0.0000,27.6000, 58550, 29.7000,120.2500, 0.0000, 0.0000, 0.0000, 4.9000, 58562, 29.9667,121.7500, 0.0000, 0.0000, 0.0000, 0.9000]);> lat:=col(l,2);> lon:=col(l,3); > sd1:=col(l,4);> sd2:=col(l,5); > sd3:=col(l,6); > sd4:=col(l,7);> abc1:=seq([lat[i],lon[i],sd1[i]],i=1..91);> abc2:=seq([lat[i],lon[i],sd2[i]],i=1..91);> abc3:=seq([lat[i],lon[i],sd3[i]],i=1..91);> abc4:=seq([lat[i],lon[i],sd4[i]],i=1..91);> with(plots):> pointplot3d([abc1],color=green,axes=boxed);> surfdata([abc1],labels=["x","y","z"],axes=boxed);> with(stats):> with(fit):> with(plots):fx1:=leastsquare[[x,y,z],z=x^3+y^3+a*x^2+b*y^2+c*x*y+d*x+e*y+f,{a,b,c,d ,e,f}]([abc1]);> plot3d(fx1,x=25..35,y=119..135);> pointplot3d([abc2],color=blue,axes=boxed);> surfdata([abc2],labels=["x","y","z"],axes=boxed);>fx2:=leastsquare[[x,y,z],z=x^3+y^3+a*x^2+b*y^2+c*x*y+d*x+e*y+f,{a,b,c,d ,e,f}]([abc2]);> plot3d(fx2,x=25..35,y=119..135);> pointplot3d([abc3],color=red,axes=boxed)> surfdata([abc3],labels=["x","y","z"],axes=boxed);>fx3:=leastsquare[[x,y,z],z=x^3+y^3+a*x^2+b*y^2+c*x*y+d*x+e*y+f,{a,b,c,d ,e,f}]([abc3]);> surfdata([abc4],labels=["x","y","z"],axes=boxed);>fx4:=leastsquare[[x,y,z],z=x^3+y^3+a*x^2+b*y^2+c*x*y+d*x+e*y+f,{a,b,c,d ,e,f}]([abc4]);五.如何在评价方法中考虑公众感受的数学模型建立.1660.1 2.5 2.666.11212.12525.16060.1z } 1.00 {0≤≤=z z R } 5.21.0 {1≤≤=z z R } 66.2 {2≤≤=z z R } 121.6 {3≤≤=z z R } 251.12 {4≤≤=z z R } 601.25 {5≤≤=z z R } 1.60 {6≥=z z R 0ˆR 1ˆR 2ˆR 3ˆR 4ˆR 5ˆR 6ˆR } 1)( {ˆ000R z z z R ∈≤=，μ} 1)( {ˆ111R z z z R ∈≤=，μ} 1)( {ˆ222R z z z R ∈≤=，μ } 1)( {ˆ333R z z z R ∈≤=，μ} 1)( {ˆ444R z z z R ∈≤=，μ} 1)( {ˆ555R z z z R ∈≤=，μ } 1)( {ˆ666R z z z R ∈≤=，μ)(z i μ i 1z ∈i R i R )(z i μ i 16i R ˆ i 1 2)(z i μ i 1⎩⎨⎧≤<+-≤≤=1.006.0 , 5.22506.00, 1)(0z z z z μ)(1z μ] 2369277587.0e [2369277587.0112)3.1(----z 5.21.0≤≤z )(2z μ] 20555762126.0e [20555762126.0112)3.4(----z 66.2≤≤z)(3z μ] 2287787270.0e [2287787270.0119.5)05.9(2----z 121.6≤≤z )(4z μ] 70397557815.0e[70397557815.0119.12)55.18(2----z 251.12≤≤z)(5z μ] 00475951221.0e[00475951221.011100)55.42(2----z 601.25≤≤z)(6z μ2)]5.60(5 [11--+z 1.60≥z 74)(z i μ及iR ˆ i =0，1，…,6合并可得} 0 {≥=z z R 上的模糊集合} , 1)( {ˆR z z z R∈≤=μ.其中R 是论域,)(z μ是模糊集合R ˆ的隶属函数，由)(z i μ分段合)(z μ小雨的隶属函数图特大暴雨隶属函数图大暴雨隶属函数图暴雨隶属函数图⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧>≤<≤<≤<≤<≤<≤≤=60)(6025)(2512)(126)(65.2)(5.21.0)(1.00)()(6543210z z z z z z z z z z z z z z t μμμμμμμμ 5 353⨯47imnkZ ~)(z μ53⨯47=M mnk⎪⎪⎪⎭⎫⎝⎛⨯⨯⨯⨯⨯⨯47532531534712111..................μμμμμμ=M imnk~⎪⎪⎪⎭⎫⎝⎛⨯⨯⨯⨯⨯⨯47532531534712111~...~~............~...~~μμμμμμi ),(y x Z =i mnk ∏∆mnk M =M i mnk~⎪⎪⎪⎪⎭⎫ ⎝⎛⨯⨯⨯⨯⨯⨯i i i i i i 47532531534712111..................λλλλλλ 6imnkΓ∆∑∑=⨯=⨯4712531)(47531j i j i i λ i Ω∆∑=16411641i imnkΓ 8 i 2i i i mnk ∏5347imnk Γi mnk ∏i Ω411Ω2Ω 1Ω2Ω1D 2D19811999。
2014MCM-B优秀论文
2014MCM-B-优秀论文美赛丛书目录（考虑）1. 问题2. 问题背景与问题分析3. 评价指标体系选哪些指标？理由何在？如何度量？4. 排名模型（权重模型）5. 时间因素处理6. 模型检验7. 问题综合分析与进一步研究8. 优秀论文A-26911-东南大学9. 优秀论文B - 30680-美国-北卡26160-重庆大学摘要：灰色与模糊评价模型，另外考虑了性别与时间因素。
AHP筛选特征因子，7个因子，灰色相关模型，模糊综合评价模型，灰色模型略强，时间因素对前十人选影响较小。
26160-重庆大学.pdf评价：除结果图外，乏善可陈，时间因素影响的结论有误。
26636-外经贸大学摘要：灰色相关模型，依据专家意见选择了四个评价指标：NCAA冠军，Pct，胜场数，教练报酬。
模糊相容矩阵确定各个评价指标的权值，结果与ESPN作比较。
最后讨论了时间因素，发现规律：“从前”的教练的胜率要远远高于“现在”的教练，但其他三个指标所受到的影响很小。
引入滑动平均方法，将时间因素纳入胜率计算模型中，这是本文的一个亮点。
Shannon熵用于评价稳定性。
讨论了参数敏感性。
便利与普适是我们模型的最大优点，但存在指标选择的主观性。
26636-外经贸.pdf评价：指标体系以及评价模型一般，有点投机，时间因素讨论、模型结果检验以及敏感性检验是亮点，结果对比表达清晰明了，可信度高。
缺假设与“conclusion”，是硬伤。
26911-东南大学三阶段全面评价模型，指标体系（胜率，稳定性，获得冠军数量，个人报酬，点击率，个人荣誉，职业联赛排名），谷歌趋势统计方法，线性拟合方法，加权和模型，AHP+最大熵模型，灰色相关分析，综合排名26911-东南大学.pdf评价：非常全面，思路很清晰，表达很简洁，值得效仿。
具体说：指标意义讨论充分；指标取值实用、合理；时间因素考虑到位；权重确定有技术含量；结果表达清晰；文章节奏把握好。
如果按更高标准衡量，第二种权重体系中GRA的作用不大显著。
HIMCM 2014美国中学生数学建模竞赛试题
HIMCM 2014美国中学生数学建模竞赛试题Problem A: Unloading Commuter TrainsTrains arrive often at a central Station, the nexus for many commuter trains from suburbs of larger cities on a “commuter” line. Most trains are long (perhaps 10 or more cars long). The distance a passenger has to walk to exit the train area is quite long. Each train car has only two exits, one near each end so that the cars can carry as many people as possible. Each train car has a center aisle and there are two seats on one side and three seats on the other for each row of seats.To exit a typical station of interest, passengers must exit the car, and then make their way to a stairway to get to the next level to exit the station. Usually these trains are crowded so there is a “fan” of passengers from the train trying to get up the stairway. The stairway could accommodate two columns of people exiting to the top of the stairs.Most commuter train platforms have two tracks adjacent to the platform. In the worst case, if two fully occupied trains arrived at the same time, it might take a long time for all the passengers to get up to the main level of the station.Build a mathematical model to estimate the amount of time for a passenger to reach the street level of the station to exit the complex. Assume there are n cars to a train, each car has length d. The length of the platform is p, and the number of stairs in each staircase is q. Use your model to specifically optimize (minimize) the time traveled to reach street level to exit a station for the following:问题一:通勤列车的负载问题在中央车站,经常有许多的联系从大城市到郊区的通勤列车“通勤”线到达。
利用网络模型测定节点影响力与重要_省略_年美国大学生数学建模竞赛C题为例_杨红卫
第３卷第２期２ ０ １ ４年６月数学建模及其应用Ｍａｔｈｅｍａｔｉｃａｌ Ｍｏｄｅｌｉｎｇ ａｎｄ Ｉｔｓ ＡｐｐｌｉｃａｔｉｏｎｓＶｏｌ．３Ｎｏ．２Ｊｕｎ．２０１４檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺檺殣殣殣殣竞赛论坛利用网络模型测定节点影响力与重要性———以２０１４年美国大学生数学建模竞赛Ｃ题为例杨红卫１，２，靳姗姗１，常正波１，２（１．山东科技大学数学与系统科学学院，山东青岛２６６５９０；２．山东科技大学数学建模研究中心，山东青岛２６６５９０）摘 要：介绍了２０１４年美国大学生数学建模竞赛Ｃ题的背景与立意，针对６篇获得Ｏｕｔｓｔａｎｄｉｎｇ奖的论文的解题思路与方法进行了归纳与总结，指出了学生答卷中的亮点与不足，并给出了建议和改进方案。
关键词：网络模型；节点影响力与重要性；ＰａｇｅＲａｎｋ算法；权威人气模型中图分类号：Ｏ２４１．３ 文献标志码：Ａ 文章编号：２０９５－３０７０（２０１４）０２－００７２－０３收稿日期：２０１４－０５－１４基金项目：山东科技大学教育教学研究“群星计划”项目（ｑｘ２０１３２２６）通讯作者：杨红卫，Ｅ－ｍａｉｌ：ｈｗｙａｎｇ１９７９＠１６３．ｃｏｍ１ Ｃ题的背景与立意你相信世界上任意的２个人能够通过至多６个人建立起联系吗？美国电影《六度分离》告诉我们，只要找到正确的媒介，任意两个看上去不相关的实体之间，即使是美国总统与威尼斯的船夫也能建立联系。
事实上我们知道，上述问题可以归结为近年来新兴的一个研究领域：复杂网络。
复杂网络产生之初就受到人们的广泛关注。
现实世界中存在着许多复杂网络，例如计算机网络、社会网络等等。
在学术领域也存在着这样的复杂网络，其中最著名的例子就是数学家Ｐａｕｌ Ｅｒｄｏｓ。
Ｅｒｄｏｓ有５００多个合著论文者，发表了１ ４００余篇研究论文，形成了一个复杂的论文合著网络，每一位数学家都以自己在Ｅｒｄｏｓ合著网络中与Ｅｒｄｏｓ的距离较小以及在网络中有显著影响力为荣。
第二届研究生数学建模竞赛C题优秀论文(1)
城市出租车交通规划综合模型一、问题重述城市中出租车的需求随着经济发展、城市规模扩大及居民生活方式改变而不断变化。
目前某城市中出租车行业管理存在一定的问题，城市居民普遍反映出租车价格偏高，另一方面，出租车司机却抱怨劳动强度大，收入相对来说偏低，整个出租车行业不景气，长此以往将影响社会稳定。
现为了配合该城市发展的战略目标，最大限度地满足城市中各类人口的出行需要，并协调市民、出租车司机和社会三者的关系，实现该城市交通规划可持续发展，需解决以下的问题：（1）从该城市当前经济发展、城市规模及总体人口规划情况出发，类比国内城市情况，预测该城市居民的出行强度和出行总量，这里的居民指的是该城市的常住人口。
同时结合人口出行特征，进一步给出该城市当前与今后若干年乘坐出租车人口的预测模型。
（2）根据该城市的公共出行情况与出租车主要状况，建立出租车最佳数量预测模型。
（3）油价调整（3.87元/升与4.30元/升）会影响城市居民与出租车司机的双方的利益关系，给出能够使双方都满意的价格调节最优方案。
（4）针对当前的数据采集情况，提出更合理且实际可行的数据采集方案。
（5）从公用事业管理部门的角度考虑出租车规划的问题，写一篇短文介绍自己的方案。
二、模型假设1．常住人口和暂住人口的出行特征相近，划分为第一类人，在所有分析过程中假设其出行特征完全一样。
而短期及当日进出人口为第二类。
2．由于短期及当日进出人口情况复杂，假设第二类人口在于乘坐出租车方面相关出行特征（如乘车出行强度等）在未来几年内保持不变。
3．由于城市地理状况和居民的生活习惯在短时期内不易改变，所以在各交通小4．假设居民中出行人口占总人口数的比例不变。
5．假设对于出行人口而言，在出行方式选择方面的比例与出行人次的比例一样。
6．假设在未来几年内，出租车固定营运成本不变。
7．由于每次一起打车的人数，与居民的生活习惯相关，所以假设出租车每趟载客人次不变，即不受出租车数目和收费方案的不同而改变。
2014美国数学建模C题ICM附件中Erdos 1 合作者人名---全部大写人名
ABBOTT, HARVEY LESLIE 1974 HANSON, DENISMEIR, AMRAMMOON, JOHN W.MOSER, LEO*SAUER, NORBERT W.SIMMONS, GUSTAVUS J.SUBBARAO, MATUKUMALLI VENKATA* ACZEL, JANOS D. 1965RENYI, ALFRED A.*STRAUS, ERNST GABOR*AGOH, TAKASHI 1997GRANVILLE, ANDREW JAMES AHARONI, RON 1988HAJNAL, ANDRASHOFFMAN, ALAN JEROMEHOLZMAN, RONKOMJATH, PETERKRIVELEVICH, MICHAELLINIAL, NATHANLOEBL, MARTINMAGIDOR, MENACHEMMILNER, ERIC CHARLES*SHELAH, SAHARONTHOMASSEN, CARSTENAIGNER, MARTIN S. 1987GRIESER, DANIELKLEITMAN, DANIEL J.PRINS, GEERT CALEB ERNST*TUZA, ZSOLTWEST, DOUGLAS BRENTAJTAI, MIKLOS 1981ALON, NOGA M.BABAI, LASZLOCHVATAL, VACLAV (VASEK)KOMLOS, JANOSLINIAL, NATHANRODL, VOJTECHSCHULMAN, LEONARD J. Y.SPENCER, JOEL HAROLDSZEMEREDI, ENDREALAOGLU, LEONIDAS* 1944: 2 ALAVI, YOUSEF 1987: 8BEHZAD, MEHDI^1BOALS, ALFRED JOHNCHARTRAND, GARY THEODORECHUNG, FAN RONG KING (GRAHAM) GRAHAM, RONALD LEWISLICK, DON RAYMONDLIU, JIUQIANGMALDE, PARESH J.MCCANNA, JOSEPH E.OELLERMANN, ORTRUD R.SCHWENK, ALLEN JOHN CARLSWART, HENDRIKA CORNELIA SCOTT (HENDA) THOMASSEN, CARSTENWANG, JIAN FANGALLADI, KRISHNASWAMI 1977: 5GORDON, BASILHOGGATT, VERNER EMIL, JR.*VAALER, JEFFREY DAVIDALON, NOGA M. 1985: 5AJTAI, MIKLOSARONOV, BORISBABAI, LASZLOBARAK, AMNON B.BOLLOBAS, BELACHUNG, FAN RONG KING (GRAHAM)COLBOURN, CHARLES JOSEPHDUKE, RICHARD ALTERFAUDREE, RALPH JASPER, JR.FRANKL, PETERFREIMAN, GREGORY A.FUREDI, ZOLTANGRAHAM, RONALD LEWISGUNDERSON, DAVID SHANEGYARFAS, ANDRASGYORI, ERVINHAJNAL, ANDRASHAMBURGER, PETERHOLZMAN, RONJANSON, SVANTEKIERSTEAD, HENRY A.KLEITMAN, DANIEL J.KOHAYAKAWA, YOSHIHARUKOSTOCHKA, ALEXANDR V.KRIVELEVICH, MICHAELLEFMANN, HANNOLEHEL, JENOLINIAL, NATHANLOVASZ, LASZLOLUCZAK, TOMASZMAUDUIT, CHRISTIANMOLLOY, MICHAEL SEAN O'BRIENNATHANSON, MELVYN BERNARDNESETRIL, JAROSLAVPACH, JANOSPOMERANCE, CARL BERNARDRODL, VOJTECHRUSZINKO, MIKLOSRUZSA, IMRE Z.SAKS, MICHAEL EZRASPENCER, JOEL HAROLDSZEGEDY, MARIOSZEKELY, LASZLO A.SZEMEREDI, ENDRETETALI, PRASAD VENKATA SITARAMA VARA THOMASSEN, CARSTENTROTTER, WILLIAM THOMAS, JR.TUZA, ZSOLTWEST, DOUGLAS BRENTWINKLER, PETER MANNWORMALD, NICHOLAS CHARLES ANDERSON, JAMES MILNE 1985CLUNIE, JAMES G.FUCHS, WOLFGANG HEINRICH JOHANNES* NEWMAN, DONALD JOSEPH*PINKUS, ALLAN M.RUBEL, LEE ALBERT*SHAPIRO, HAROLD SEYMOURSHIELDS, ALLEN LOWELL*SHISHA, OVED*ANDRASFAI, BELA 1974SOS, VERA TURANANKENY, NESMITH CORNETT* 1954CHOWLA, SARVADAMAN D. S.*ROGERS, CLAUDE AMBROSE*ANNING, NORMAN H.* 1945 ARKIN, JOSEPH* 1996ARNEY, DAVID CHRISTOPHERBURR, STEFAN ANDRUSHOGGATT, VERNER EMIL, JR.*POLLACK, RICHARD M.STRAUS, ERNST GABOR*ARNEY, DAVID CHRISTOPHER 1996ARKIN, JOSEPH*BURR, STEFAN ANDRUSJACOBSON, MICHAEL SCOTTARONOV, BORIS 1994ALON, NOGA M.GODDARD, WAYNE DEANKLEITMAN, DANIEL J.KLUGERMAN, MICHAEL RICHARDPACH, JANOSSCHULMAN, LEONARD J. Y.ASH, J. 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R.BOES, DUANE CHARLES 1981DARST, RICHARD BRIANBOLLOBAS, BELA 1962: 18ALON, NOGA M.CATLIN, PAUL ALLEN*CHUNG, FAN RONG KING (GRAHAM)CLARK, LANE HENRYDAYKIN, DAVID E.FAUDREE, RALPH JASPER, JR.GUY, RICHARD KENNETHGYARFAS, ANDRASGYORI, ERVINHARARY, FRANK*HEGYVARI, NORBERTHELL, PAVOLHOBBS, ARTHUR M.JANSON, SVANTEJIN, GUO PINGKOHAYAKAWA, YOSHIHARUKOSTOCHKA, ALEXANDR V.KRIVELEVICH, MICHAELLEHEL, JENOLOVASZ, LASZLOLUCZAK, TOMASZMCKAY, BRENDAN DAMIENMEIR, AMRAMMILNER, ERIC CHARLES*NESETRIL, JAROSLAVPALMER, EDGAR MILANRODL, VOJTECHROSENFELD, MOSHE^1ROUSSEAU, CECIL CLYDESAKS, MICHAEL EZRASARKAR, AMITESSAUER, NORBERT W.SCHELP, RICHARD H.SIMONOVITS, MIKLOSSOS, VERA TURANSPENCER, JOEL HAROLDSTRAUS, ERNST GABOR*SZEMEREDI, ENDRETHOMASSEN, CARSTENWEST, DOUGLAS BRENTWINKLER, PETER MANNWORMALD, NICHOLAS CHARLES BONAR, DANIEL DONALD 1977 CARROLL, FRANCIS WIILLIAMPIRANIAN, GEORGE*BONDY, JOHN ADRIAN 1973: 2 CHVATAL, VACLAV (VASEK)ENTRINGER, ROGER CHARLESFAJTLOWICZ, SIEMIONHELL, PAVOLHEMMINGER, ROBERT LOUISLOVASZ, LASZLOSIMONOVITS, MIKLOSSTATON, WILLIAM A., IIIBONNET, ROBERT 1974SHELAH, SAHARONBOROSH, ITSHAK 1978CHUI, CHARLES KAM-TAIFRAENKEL, AVIEZRI SIEGMUNDHOBBS, ARTHUR M.BOSAK, JURAJ 1971NESETRIL, JAROSLAVROSA, ALEXANDERBOVEY, JOHN D. 1975NIVEN, IVAN MORTON*WILLIAMSON, ALAN GLYNNE BRENNER, JOEL LEE* 1987BEASLEY, LEROY B.BOAS, RALPH PHILIP, JR.*BROWN, WILLIAM G.MAYS, MICHAEL ELLSWORTHSZALAY, MIHALYWILLIAMSON, ALAN GLYNNE BRILLHART, JOHN DAVID 1983BLECKSMITH, RICHARD FREDMONTGOMERY, PETER L.MORTON, PATRICKODLYZKO, ANDREW MICHAELSELFRIDGE, JOHN L.WAGSTAFF, SAMUEL STANDFIELD, JR. 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CLARK, BRENT N. 1985COLBOURN, CHARLES JOSEPHCLARK, LANE HENRY 1993BOLLOBAS, BELAENTRINGER, ROGER CHARLESMCCANNA, JOSEPH E.MEIR, AMRAMMOON, JOHN W.SUN, HUI CHENGSZEKELY, LASZLO A.TUZA, ZSOLTWORMALD, NICHOLAS CHARLES CLARKSON, JAMES ANDREW* 1943 CLUNIE, JAMES G. 1967ANDERSON, JAMES MILNEEDREI, ALBERT*KOVARI, TAMASRUBEL, LEE ALBERT*COHEN, STEPHEN D. 1976NATHANSON, MELVYN BERNARD COLBOURN, CHARLES JOSEPH 1985 ALON, NOGA M.CLARK, BRENT N.DE CAEN, DOMINIQUE*DRAKE, DAVID ALLYNMCKAY, BRENDAN DAMIENMULLIN, RONALD C.PHELPS, KEVIN THOMASRODL, VOJTECHROSA, ALEXANDERSIRAN, JOZEFSTINSON, DOUGLAS ROBERTWINKLER, PETER MANNWORMALD, NICHOLAS CHARLES CONWAY, JOHN HORTON 1979CROFT, HALLARD T.GUY, MICHAEL J. T.GUY, RICHARD KENNETHODLYZKO, ANDREW MICHAEL COPELAND, ARTHUR HERBERT, SR.* 1946 HARARY, FRANK*CROFT, HALLARD T. 1979GUY, RICHARD KENNETHCSAKI, ENDRE 1985GRILL, KARLKOMLOS, JANOSREVESZ, PALVINCZE, ISTVAN*CSISZAR, IMRE 1965KOMLOS, JANOSLOVASZ, LASZLOCZIPSZER, JANOS* 1962FREUD, GEZA*HAJNAL, ANDRASRENYI, ALFRED A.*DARLING, DONALD A. 1956: 2KAC, MARK*DARST, RICHARD BRIAN 1981BOES, DUANE CHARLESPOLLARD, HARRY STRANGE* DAVENPORT, HAROLD* 1936: 7CHOWLA, SARVADAMAN D. S.*HEILBRONN, HANS ARNOLD*LEVEQUE, WILLIAM JUDSON*MAHLER, KURT*ROGERS, CLAUDE AMBROSE*SCHINZEL, ANDRZEJ BOBOLA MARIA DAVIES, ROY O. 1975CHVATAL, VACLAV (VASEK)HARARY, FRANK*ROGERS, CLAUDE AMBROSE*TAYLOR, SAMUEL JAMESDAYKIN, DAVID E. 1976: 2BOLLOBAS, BELACAMERON, PETER J.CHEN, CHUAN CHONGFRANKL, PETERKLEITMAN, DANIEL J.LOVASZ, LASZLOSHENG, TSENG KUOWEST, DOUGLAS BRENTDE BRUIJN, NICOLAAS GOVERT 1948: 6 SZEKERES, GEORGE*VAN LINT, JACOBUS HENDRICUS*DE CAEN, DOMINIQUE* 1986COLBOURN, CHARLES JOSEPHFON-DER-FLAASS, DMITRI G.FUREDI, ZOLTANGODSIL, CHRISTOPHER DAVIDWORMALD, NICHOLAS CHARLESDE KONINCK, JEAN-MARIE 1981GALAMBOS, JANOSIVIC, ALEKSANDARKATAI, IMRELUCA, FLORIANSUBBARAO, MATUKUMALLI VENKATA*TENENBAUM, GERALDDEBOSE, YOLANDA 1996HOBBS, ARTHUR M.DEHEUVELS, PAUL 1987GRILL, KARLREVESZ, PALDELEGLISE, MARC 1999NICOLAS, JEAN-LOUISDENES, JOZSEF 1969HARARY, FRANK*TURAN, PAL*DESHOUILLERS, JEAN-MARC 1976: 2 BALOG, ANTALFREIMAN, GREGORY A.GRANVILLE, ANDREW JAMESLEV, VSEVOLOD F.LUCA, FLORIANMELFI, GIUSEPPEPOMERANCE, CARL BERNARDSARKOZY, ANDRASSOS, VERA TURANTENENBAUM, GERALDDEUBER, WALTER A.* 1997BERGELSON, VITALYGRAHAM, RONALD LEWISGUNDERSON, DAVID SHANEHINDMAN, NEIL B.KOSTOCHKA, ALEXANDR V.LEFMANN, HANNOMEYER, ANJA GABRIELEROTHSCHILD, BRUCE LEESACHS, HORSTSIMONOVITS, MIKLOSSOS, VERA TURANDEZA, MICHEL-MARIE 1975: 4AVIS, DAVID MICHAELBABAI, LASZLOCAMERON, PETER J.FRANKL, PETERMULLIN, RONALD C.DIACONIS, PERSI W. 2004CHUNG, FAN RONG KING (GRAHAM)GRAHAM, RONALD LEWISJANSON, SVANTEDIAMOND, HAROLD GEORGE 1978: 3 BATEMAN, PAUL TREVIERMONTGOMERY, HUGH LOWELLPOMERANCE, CARL BERNARDRUBEL, LEE ALBERT*VAALER, JEFFREY DAVIDDIRAC, GABRIEL ANDREW* 1963SCHUSTER, SEYMOURTHOMASSEN, CARSTENDIXMIER, JACQUES 1987NICOLAS, JEAN-LOUISDOWKER, YAEL NAIM 1959 DRAKE, DAVID ALLYN 1990CAMERON, PETER J.COLBOURN, CHARLES JOSEPHFUREDI, ZOLTANLARSON, JEAN ANNDUDLEY, UNDERWOOD 1983 DUKE, RICHARD ALTER 1977: 8ALON, NOGA M.BURR, STEFAN ANDRUSFOWLER, JOEL CHRISTOPHERHARARY, FRANK*LEFMANN, HANNOPHELPS, KEVIN THOMASRODL, VOJTECHWINKLER, PETER MANNDVORETZKY, ARYEH* 1950: 8HANANI, HAIM*KAKUTANI, SHIZUO*ROGERS, CLAUDE AMBROSE*TAYLOR, SAMUEL JAMESECKLUND, EARL F., JR. 1974: 2EGGLETON, ROGER BENJAMINSELFRIDGE, JOHN L.EDREI, ALBERT* 1985CLUNIE, JAMES G.FUCHS, WOLFGANG HEINRICH JOHANNES* SZEGO, GABOR*EGGLETON, ROGER BENJAMIN 1972: 7 ECKLUND, EARL F., JR.FRAENKEL, AVIEZRI SIEGMUNDGUY, RICHARD KENNETHHOLTON, DEREK ALLANSELFRIDGE, JOHN L.SKILTON, DONALD K.EL-ZAHAR, MOHAMED H. 1985SAUER, NORBERT W.ELEKES, GYORGY 1981: 2HAJNAL, ANDRASKOMJATH, PETERNATHANSON, MELVYN BERNARDRUZSA, IMRE Z.SIMONOVITS, MIKLOSELLIOTT, PETER D. 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(WILLIAM)* 1949CHUNG, KAI-LAI*POLLARD, HARRY STRANGE* FELZENBAUM, ALEXANDER GERSH 1988 BERGER, MARC ARONFRAENKEL, AVIEZRI SIEGMUNDHOLZMAN, RONKLEITMAN, DANIEL J.FEW, LEONARD 1964ROGERS, CLAUDE AMBROSE* FISHBURN, PETER C. 1991: 9BECK, ISTVANBEJLEGAARD, NIELSCHUNG, FAN RONG KING (GRAHAM)GRAHAM, RONALD LEWISODLYZKO, ANDREW MICHAELSPENCER, JOEL HAROLDTETALI, PRASAD VENKATA SITARAMA VARA TROTTER, WILLIAM THOMAS, JR.WINKLER, PETER MANNFODOR, GEZA* 1956: 3HAJNAL, ANDRASMATE, ATTILAFON-DER-FLAASS, DMITRI G. 1992CAMERON, PETER J.DE CAEN, DOMINIQUE*KOSTOCHKA, ALEXANDR V.NESETRIL, JAROSLAVTUZA, ZSOLTWEST, DOUGLAS BRENTFOWLER, JOEL CHRISTOPHER 1985: 2 DUKE, RICHARD ALTERPHELPS, KEVIN THOMASSOS, VERA TURANWILSON, RICHARD MICHAELFOWLER, THOMAS GEORGE 1999 FRAENKEL, AVIEZRI SIEGMUND 1988BERGER, MARC ARONBOROSH, ITSHAKEGGLETON, ROGER BENJAMINFELZENBAUM, ALEXANDER GERSHGILLIS, JOSEPH E.*GORDON, BASILHARARY, FRANK*HOLZMAN, RONLOEBL, MARTINNESETRIL, JAROSLAVSOS, VERA TURANSTRAUS, ERNST GABOR*FRANKL, PETER 1978: 6ALON, NOGA M.BABAI, LASZLOBURR, STEFAN ANDRUSCAMERON, PETER J.CHUNG, FAN RONG KING (GRAHAM)DAYKIN, DAVID E.DEZA, MICHEL-MARIEFISHBURN, PETER C.FUREDI, ZOLTANGRAHAM, RONALD LEWISKLEITMAN, DANIEL J.ODLYZKO, ANDREW MICHAELPACH, JANOSRODL, VOJTECHRUZSA, IMRE Z.SAKS, MICHAEL EZRASINGHI, NAVIN MADHAVPRASADSOS, VERA TURANSZEKELY, LASZLO A.WILSON, RICHARD MICHAELFREEDMAN, ALLEN R. 1990BROWN, THOMAS CRAIGFREIMAN, GREGORY A. 1990ALON, NOGA M.DESHOUILLERS, JEAN-MARCHERZOG, MARCELRUZSA, IMRE Z.SCHONHEIM, JOHANANSOS, VERA TURANFREUD, GEZA* 1974CZIPSZER, JANOS*NEWMAN, DONALD JOSEPH*REDDY, A. 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JOSEPHTHOMASSEN, CARSTENTUZA, ZSOLTGINZBURG, ABRAHAM 1961: 2ZIV, ABRAHAMGODDARD, WAYNE DEAN 1994ARONOV, BORISCHARTRAND, GARY THEODORECHEN, HANGCHUNG, FAN RONG KING (GRAHAM)ENTRINGER, ROGER CHARLESFAUDREE, RALPH JASPER, JR.HAMBURGER, PETERHATTINGH, JOHANNES HENDRIKHEDETNIEMI, STEPHEN TRAVISHENNING, MICHAEL ANTHONYKLEITMAN, DANIEL J.KLUGERMAN, MICHAEL RICHARDKUBICKA, EWA MARIEKUBICKI, GRZEGORZLASKAR, RENU CHAKRAVARTIMCCANNA, JOSEPH E.OELLERMANN, ORTRUD R.PACH, JANOSPIPPERT, RAYMOND ELMERSCHULMAN, LEONARD J. Y.SWART, HENDRIKA CORNELIA SCOTT (HENDA) GODSIL, CHRISTOPHER DAVID 1988DE CAEN, DOMINIQUE*HOLTON, DEREK ALLANKRANTZ, STEVEN GEORGEMCKAY, BRENDAN DAMIENNESETRIL, JAROSLAVPARSONS, TORRENCE DOUGLAS* GOLDBERG, MARK K. 1988FABER, VANCEPACH, JANOSSPENCER, JOEL HAROLDGOLOMB, MICHAEL* 1955 GOODMAN, ADOLPH W.* 1966POSA, LAJOSGORDON, BASIL 1964ALLADI, KRISHNASWAMIBERTRAM, EDWARD ARTHURFRAENKEL, AVIEZRI SIEGMUNDRUBEL, LEE ALBERT*STRAUS, ERNST GABOR*GOULD, RONALD J. 1987: 4BURR, STEFAN ANDRUSCHARTRAND, GARY THEODORECHEN, GUANTAOFAUDREE, RALPH JASPER, JR.FUREDI, ZOLTANGUNDERSON, DAVID SHANEGYARFAS, ANDRASJACOBSON, MICHAEL SCOTTKOSTOCHKA, ALEXANDR V.KUBICKA, EWA MARIEKUBICKI, GRZEGORZLEHEL, JENOLICK, DON RAYMONDLUCZAK, TOMASZRODL, VOJTECHROUSSEAU, CECIL CLYDESCHELP, RICHARD H.WEST, DOUGLAS BRENTGRAHAM, RONALD LEWIS 1972: 28 ALAVI, YOUSEFALON, NOGA M.BABAI, LASZLOBOLLOBAS, BELABROWN, THOMAS CRAIGBURR, STEFAN ANDRUSCHARTRAND, GARY THEODORECHINN, PHYLLIS ZWEIGCHUNG, FAN RONG KING (GRAHAM)DEUBER, WALTER A.*DIACONIS, PERSI W.ENTRINGER, ROGER CHARLESFISHBURN, PETER C.FRANKL, PETERFUREDI, ZOLTANHARARY, FRANK*HELL, PAVOLHOFFMAN, ALAN JEROMEHOGGATT, VERNER EMIL, JR.*KLEITMAN, DANIEL J.LI, WEN-CH'ING WINNIELOVASZ, LASZLOLUCZAK, TOMASZMONTGOMERY, PETER L.NESETRIL, JAROSLAVODLYZKO, ANDREW MICHAELOELLERMANN, ORTRUD R.RODL, VOJTECHROTHSCHILD, BRUCE LEERUZSA, IMRE Z.SAKS, MICHAEL EZRASIMMONS, GUSTAVUS J.SIMONOVITS, MIKLOSSOS, VERA TURANSPENCER, JOEL HAROLDSTRAUS, ERNST GABOR*SZEMEREDI, ENDRETAYLOR, HERBERTULAM, STANISLAW MARCIN*VAN LINT, JACOBUS HENDRICUS*WILSON, RICHARD MICHAELWINKLER, PETER MANNYAO, FOONG FRANCESGRAHAM, SIDNEY WEST 1996IVIC, ALEKSANDARKOLESNIK, GRIGORI ABRAMOVICHPOMERANCE, CARL BERNARDVAALER, JEFFREY DAVIDGRANVILLE, ANDREW JAMES 1990: 2 AGOH, TAKASHICALKIN, NEIL JAMESCANFIELD, EARL RODNEYDESHOUILLERS, JEAN-MARCHILDEBRAND, ADOLF J.MAIER, HELMUTMULLIN, RONALD C.POMERANCE, CARL BERNARDSHALLIT, JEFFREY OUTLAWSPIRO-SILVERMAN, CLAUDIA A.TETALI, PRASAD VENKATA SITARAMA VARA VAUGHAN, ROBERT CHARLESGRIESER, DANIEL 1987AIGNER, MARTIN S.GRILL, KARL 1987CSAKI, ENDREDEHEUVELS, PAULREVESZ, PALGRUBER, PETER MANFRED 1989HAMMER, JOSEPHGRUNBAUM, BRANKO 1973: 2BURR, STEFAN ANDRUSKLAMKIN, MURRAY SEYMOUR*ROSENFELD, MOSHE^1GRUNWALD, GEZA* 1938: 3TURAN, PAL*GUNDERSON, DAVID SHANE 1995: 3 ALON, NOGA M.DEUBER, WALTER A.*FUREDI, ZOLTANGOULD, RONALD J.HINDMAN, NEIL B.KOSTOCHKA, ALEXANDR V.MEYER, ANJA GABRIELEMOLLOY, MICHAEL SEAN O'BRIENRODL, VOJTECHSAUER, NORBERT W.GUPTA, HANSRAJ* 1976CHOWLA, SARVADAMAN D. 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T.HANANI, HAIM*HARARY, FRANK*LACAMPAGNE, CAROLE B.MILNER, ERIC CHARLES*MOON, JOHN W.SELFRIDGE, JOHN L.GYARFAS, ANDRAS 1988: 15 ALON, NOGA M.BIALOSTOCKI, ARIEBOLLOBAS, BELABURR, STEFAN ANDRUSCHEN, GUANTAOCHUNG, FAN RONG KING (GRAHAM) FAUDREE, RALPH JASPER, JR.FUREDI, ZOLTANGERENCSER, LASZLOGOULD, RONALD J.JACOBSON, MICHAEL SCOTTJAGOTA, ARUN KUMARKLEITMAN, DANIEL J.KOHAYAKAWA, YOSHIHARUKOMLOS, JANOSKRATSCH, DIETERLEHEL, JENOLUCZAK, TOMASZNESETRIL, JAROSLAVORDMAN, EDWARD THORNEPYBER, LASZLORODL, VOJTECHROUSSEAU, CECIL CLYDERUSZINKO, MIKLOSSARKOZY, GABOR N.SCHELP, RICHARD H.SELKOW, STANLEY M.SZEMEREDI, ENDRETROTTER, WILLIAM THOMAS, JR.TUZA, ZSOLTWEST, DOUGLAS BRENTZALCSTEIN, YECHEZKELGYORI, ERVIN 1992: 2ALON, NOGA M.BOLLOBAS, BELAFAUDREE, RALPH JASPER, JR.KOSTOCHKA, ALEXANDR V.LEHEL, JENOLUCZAK, TOMASZMILNER, ERIC CHARLES*PACH, JANOSROTHSCHILD, BRUCE LEESARKOZY, ANDRASSCHELP, RICHARD H.SIMONOVITS, MIKLOS。
2014美赛A题论文
For office use onlyT1________________ T2________________ T3________________ T4________________Team Control Number27400Problem ChosenAFor office use onlyF1________________F2________________F3________________F4________________2014 Mathematical Contest in Modeling (MCM) Summary Sheet(Attach a copy of this page to your solution paper.)Type a summary of your results on this page. Do not includethe name of your school, advisor, or team members on this page.SummaryThe aim of this paper is to evaluate the performance of the changing lane rule named Keep-Right-Except-To-Pass and compare other rules we’ve constructed with the given one. The performance of changing lane rules mainly manifest in safety and traffic flow. Meanwhile, safety is influenced by posted speed limits and traffic density and traffic flow is influenced by average speed.First we construct Model 1 to describe the relationship between posted speed limits, traffic density and safety, noting that safety has negative correlation with collision times and can be fully expressed by it. Therefore we use Matlab to imitate the changing lane and collision process. Then we construct Model 2 to describe the relationship between traffic flow and average speed. Combining the result of Model 1and 2, we can conclude that the higher the posted speed limits and the lower the traffic density, the higher level safety an traffic flow could reach, and the Keep-To-Right-Except-To-Pass rule has the best performance.Then we construct Model 3 to compare some normal changing lane rules with the given one and with each other. Thus we imitate all the rules using algorithm given by model 1. We introduce a new concept named Standard Time to express traffic flow and still collision times to express safety. The result is that when a freeway road contains 2 lanes, the given rule shows the best performance. And when the number of lanes becomes 3, then the Choose-Speed rule, a very common traffic rule acts the best.As for the left-driving countries, we first choose the best rules and mirror symmetrically modify them. Then use the method of Model 2 to imitate performances of these rules. We have observed that these two best rules can be simply carried over.Finally, we have a short discussion about the intelligent system. Since speed can be fastest and changing lanes can be well planned, we regard this system as absolutely safe traffic which has the largest traffic flow.Team #27400 Page 1 of 161.Introduction1.1 Analysis to the problemThis problem can be divided into 4 requirements that we must meet, listed as follows:(1)Build a mathematical model to demonstrate the essence of Keep-Right-Except-To-Pass rule in light and heavy traffic;(2)Show the effects of other reasonable changing-lane rules or conditions by using themodified model built in the former requirement;(3)Determine whether the left-side-driving countries can use the same rule(s) withsimple mirror symmetric modification, or must add some requirements to guaranteethe safety or traffic flow;(4)Construct an intelligent traffic system which does not depend on humans’ compliance,and then compare the effects with earlier analysis.Therefore, this problem requires us to evaluate the performances of several changing-lane rules, especially the Keep-Right-Except-To-Pass rule while performances mainly manifest in traffic flow and safety. It is obvious that speed limit and the number of cars influent cars’ speed and then the performances of those rules.To solve requirement (2), we will use the same method as above. But all rules weconstructed should be discussed, imitated and compare with each other.To discuss the left-driving countries, we will conclude the best rules from requirement2 and apply to those countries. Then compare results with that of right-driving countries.If the results are totally the same, then those rules can be simply carried over with simple change. If not, additional requirement are needed.As for the intelligent system, we assume no collision will happen. So a simplediscussion is feasible.1.2 Crucial method for the problemTo imitate the process of changing lanes and collision, we will construct an algorithm named Changing-line and Collision. This will show the state of a number of car on the same stretch of freeway road, including going straight, changing lane to pass and traffic collision. The imitation process will be delivered on Matlab;2.Symbols and definitionSymbol Definition UnitσStandard Deviation of Speed miles/hmiles/hV85% Percentile of Normal85Distributionmiles/hV70% Percentile of Normal70DistributionDENS Traffic Density (Note: expressed by thenumber of cars) ST Standard Time \FLO Traffic Flow \CT Collision Times \3.General hypotheses for all models(1) All freeway roads contain either two or three lanes.(2) Overtaking Principle: the latter car must change lane and overtake the car right in front it if its speed is faster.(3) No violation of the rules.(4) The intelligent traffic system has no collision.(5) Road indicates one direction of the road.(6) Each cars remains constant speed no matter it goes straight or change lane.(7) Changing lane doesn’t cost time.(8) Given a traffic density, the average speed of cars is constant.(9) All discussions are confined to one stretch of road that is long enough to allow a series of cars to go across.4.Model establishment4.1 PreparationFirst, we must discuss what “changing-lane” is. For a two-lane road, if one car is going to change its lane to the left, then the right side lane “loses” one car and the left side lane “acquires” one, and vice versa. If the road contains three lanes, we can regard it as two “two-lane road”. This property also holds for an n-lane (n>2) road, which means we could regard it as (n-1) two-lane road. Therefore, changing-lane is the relation between two lanes. We just need to analyze a two-lane road to uncover the principle of changing lane and collision.Second, influence relationship figures are given below. In these figures, factors at lower level influence those at upper level. Safety will be expressed by collision times( ).Figure 1. General influence relationshipThird, we have constructed three additional changing-lane rules and shall describe these five rules in mathematical language. The original Keep-Right-Except-To-Pass rule is denoted Rule 1.Rule 1: Keep-Right-Except-To-Pass. If A B v v >, then car A goes left, overtakes car B and then gets back to the right lane.Figure 2. Rule one: Keep-Right-Except-To-PassRule 2: Free-Overtaking. If A B v v > and A C v v >, then car A changes lane to the left, passing B, and then to the right, passing C. And if there still exists a car D in front of A and A D v v >, car A will change to the left lane, pass D and then go straight. The following figure shows the case when the number of lanes is two, and it is identical for the case of 3 lanes.Figure 3. Rule 2: Free-OvertakingRule 3: Pass-Left. For a three-lane freeway road, if B A C v v v >>, then car A changes to the middle lane, and car B to the left lane, and finally they should get back to their original lane.Figure 4. Rule 3: Pass-LeftRule 4: Choose-Speed. Each lane of the road has a posted speed limit interval. We denote the left lane fast lane, right one slow lane and the middle one mid-lane. Drivers should choose lane according to their cars ’ speed.4.2 Model 1: Changing Lane and Collision Algorithm 4.2.1 Flow Diagram*To check Matlab code, please refer to Appendix 1. Note: we only use collision times to express safety.Figure 5. Flow Diagram of the Changing Lane and Collision Algorithm Comments:(1) The 1000*2 matrix stands for a stretch freeway road that contains two lanes;(2) Speed of cars is a series of random numbers which stands for the units they are to go forward each time;(3) Cars enter the road from the right lane.(4) If two cars collide, their speed will become zero but will not affect other cars. Accordingly, the position of collision will be valuated zero.To show how this algorithm works, we now give an example of a road, length 7 and five carswith different speed:Figure 6. An Example of the Algorithm4.2.2 Relationship between Average Speed, Standard Deviation of Speed and Posted Speed LimitsWe have mentioned in the last section that the speed of cars obeys normal distribution [3]. Now we deduce the relationship between ,μσ and PSL .Figure 7. Speed of cars obey normal distributionWe know from reference [4](page 15) that:857.6570.98V PSL =+⋅①The above foemula can be applied to all types of roads. Equation ② from reference [5](page 53):70-6.541+2.4V σ=⋅②Referring to the table of standard normal distribution, we have70V μσ-=0.52③ 85V μσ-=1.04④Considering formula ②③, we have=1.88-6.541μσ⑤Considering formula ①④, we have7.657+0.98=1.04PSL μσ-⑥Considering formula ⑤⑥, we have14.198+0.98=2.92PSLσ⑦0.98*=13.6012PSL μ-⑧Formula ⑦⑧ explains that the higher the posted speed limits, the greater the variance of speed and same to the average speed.0.9813.6012MU PSL =-⑨4.2.3 Process of ImitationWe now use control-variable method to describe the impact of traffic density and posted speed limits on safety. Therefore, we consider:(1) Traffic density being constant, the impact of variation of posted speed limits on safety; (2) Posted speed limits being constant, the impact of variation of traffic density on safety.When traffic density is constant:Table 1.Variation of Posted Speed LimitsPSL 50 60 70 80 90 100 μ 34.1481 40.4577 46.7673 53.0769 59.3865 65.6961 σ21.6432 24.9993 28.3555 31.7116 35.0678 38.424Figure 8. Variation of μ and σ along with Variation of PSLNote: SIGMA=σ, MU=μWhen posted speed limits is constant:Table 2.Variation of the number of carsThe number of cars 5 10 20 30 40 50Therefore we will acquire 6*6 groups of data when PSL is constant and 6*6 groups of data when traffic density is constant.4.3 Model 2: Relationship between Traffic Flow and Average SpeedIt is obvious that traffic flow is the function of average.We denote:=⋅+>FLO k MU c k(0)4.4 Model 3: Rules and Performances4.4.1 AnalysisIn section 4.1 we have listed four changing lane rules. Now we need to compare their effect and evaluate which rule has the best performance.According to the establishment of model 1, performances are fully expressed by safety and traffic flow, and safety has negative correlation with collision times. We can acquire the related data by imitation like model 1. However, since rules have changed, average speed of the road under different rules is different and is merely decided by PSL.Thus we introduce a new concept, namely, Standard Time(ST). Definition: time cost by each move of cars is called standard time. With this concept, we don’t need to calculate the real time cost by cars when going across a stretch of road, but count how many moves cars should make. Standard time has positive correlation with traffic flow, and we can denote:ST k FLO k=⋅>(0)4.4.2 Imitation ProcessConstruct a matrix. If the road contains two lanes, then the matrix size is 150*2; if it contains three lanes, then the size is 150*3. Arrange 40 random positions for each column vectors, and the numbers, as described before, obey normal distribution. Let other variables be constant, we discuss the impact of different rules on safety and traffic flow.Operations are as follows:(1) Distribute a series positions(40 for each column vector as described) for the matrix.(2) Valuate each position a number that obey normal distribution.(3) Apply one of the rules to the matrix. Those numbers will either “collide ” or “keep moving ” until all the position are valuated zero. (4) Record collision times and the spent standard time.(5) Apply another rule to the matrix, repeat steps (1) through (4).Statistically analyzing the data acquired and comparing the performances of different rules, we can decide advantages and disadvantages of each rule.4.4.3 Use the Method of 4.4.2 to Estimate Left-driving CountriesWe will conclude the best two rules and then apply the methods in section 4.4.2 to the left-driving country and estimate the performance of the two rules. Operation steps:(1) Mirror symmetrically modify the chosen rules; (2) Refer to the steps in section 4.4.2; (3) Compare with the results in 4.4.2.5. Model solution5.1 Model 1During the imitation process, we do the experiment for times for each case and then analyze all the results. We will show part of our statistical data. To view full data, please refer to Appendix 2.(1) Given DENS=30, the result is as follows:Table 3.Relationship between Changing Lane Times, Collision Times and PSL when DENS=30PSL Changing-lane times Average Collision TimesAverag-Line chart:Figure 9. Variation of Changing Lane Times and Collision Times along with Variation ofPSL(2) Given PSL=70, the result is as follows:Table 4.Relationship between Changing Lane Times, Collision Times and Number of Times whenPSL=70NumberChanging Lane Times Average Collision Time Average Line chart:Figure 10. Variation of Changing Lane Times and Collision Times along with Variation ofnumber of cars5.2 Model 2We know from formula ⑨, section 4.2.2 that0.9813.6012MU PSL =-Considering formula ⑨ and formula in 4.3, we have:0.9813.6012FLO k PSL k c =⋅-+5.3 Model 3The result of section 4.4.2 is given below:Table 5.Collision Times and Standard Time of each ruleRule →Rule 1 Rule 2(2Rule 3 Rule 2(3 Rule 4Extract the row of Average ST and Average CTTable 6.Average Collision Times and Average Standard Time of each rule The result of 4.4.3 is given below:Table 7.Collision Times and Standard Time of Rule 1 and Rule 4 Applied to Left-driving Countries6.Conclusion6.1 Conclusion of model 1 and 2We can conclude from model 1 that safety will decrease along with the growth oftraffic density. Safety will also decrease while the posted speed limits(PSL) is raised.However, comparing to PSL, traffic density has greater impact on safety while PSL can hardly influence safety.From model 2, we can conclude that traffic flow has liner growth along with the raise of PSL.The following table has summed up model 1 and 2.Table . 8Evaluation of Rule Performances in Different Road conditions6.2 Conclusion of model 3We can know from table 6 that when the number of lanes is 2, rule 1 is not very different from rule 2 in terms of traffic flow but is much safer than rule 2. When the number of lanes is 3, rule 3 is safest rule, but rule 4 will become both safe and efficient. Meanwhile, Free-Overtaking rule, actually meaning no rule, is most dangerous. Therefore, we have chosen rule 1 and rule 4 as the best rules.Result of section 4.4.3 is showed below. Note that original rules are listed on the left and modified on the right.Table .9Comparison between the Modified Rules and the OriginalFrom the table above, we can conclude that no difference between left-driving and right-driving countries. Therefore, those rules can be simply carried over with simple mirror symmetric modification.6.2 Conclusion of intelligent systemSince all the cars are controlled by a high-tech computer, we assume this system will never have an accident until the computer crashes. So every car reach their fastest speed, the order of overtaking can be calculated to avoid collision. Therefore, safety and traffic flow reach the highest level.7. References[1] Mark M. Meerschaert. Mathematical Modelling (Third Edition). Beijing: China Machine Press, 2008.12[2] Solomon. Accidents on Main Rural Highways Re la ted to Speed, Driver, and Vehicle[R]. Washing ton D. C: Federal Highway Administration, 1964[3] Lu Jian, Sun Xinglong, Daiyue. Regression analysis on speed distribution characteristics of ordinary road. Nanjing: Journal of Southeast University(Natural Science Edition), 2012.2 (in Chinese).[4] Wang Lijin. Research on Speed Limits and Operating Speed for Freeway. Beijing: Beijing University of Technology, 2011.5 (in Chinese).8. AppendixAppendix 1. Matlab Codeclear;clc;highway=zeros(1000,2);%define road%crash_times = 0;%define collition times%change_lane_times=0;%define change lane times%num_of_car=5; %definedefine number of car%MU=84.3898;SIGMA=20.4406;randspe=[];j=1;while j<=num_of_carx=round(normrnd(MU,SIGMA,1,1));if x>0randspe(j,1)=x; %define speed and gualentee %j=j+1;endx=0;endrandpla=[];for i=1:num_of_carx=ceil(rand(1)*1000);if find(randpla==x)x=ceil(rand(1)*1000); %define location and guarantee the car located in different place%endrandpla(i,1)=x;endfor i=1:num_of_carhighway(randpla(i,1),2)=randspe(i,1); %insert every car in different speed at diferent place %speed(i,1)=0;pla(i,1)=0;endinitialr_highway=highway; %record intialr-highway statement%disp(initialr_highway)disp('Aboveis the stateof initialr highway')while sum(sum(highway))~=0i=1;speed(1)=0; pla(1)=0;for j=1:length(highway) %Store the location and speed of each carif highway(j,2)~=0 ....to pla_matrix and speed_matrix separately%speed(i)=highway(j,2);pla(i)=j;i=i+1;endendcount=length(pla);while count>1 %When the differerce of two adjacent car's speed is greater than their distance,thenif speed(count)-speed(count-1)>=abs(pla(count)-pla(count-1)) ... the later car must change lane to the left% highway(pla(count),1)=highway(pla(count),2);highway(pla(count),2)=0;change_lane_times=change_lane_times+1;endcount=count-1;endlane_changed= highway; %record lane_changed highway statement%disp(lane_changed)disp('Aboveis the state of after-changed lane highway ')k=1;pas_spe(1)=0;pas_pla(1)=0;for j=1:length(highway)if highway(j,1)~=0pas_spe(k)=highway(j,1);pas_pla(k)=j;k=k+1;endendcount=length(pas_pla); %delete crashed car%while count>1if pas_spe(count)-pas_spe(count-1)>=abs(pas_pla(count)-pas_pla(count-1))highway(pas_pla(count),1)=0;highway(pas_pla(count-1),1)=0;crash_times=crash_times+1;endcount=count-1;endaft_adjust = highway;disp(aft_adjust)disp('Above is after adjusted highway')for i=1:length(highway)for j=1:2if i-highway(i,j)>0highway(i-highway(i,j),j)=highway(i,j);%move forward%endhighway(i,j)=0;endendfor i=1:length(highway)if highway(i,1)~=0&&highway(i,2)==0%back to right%highway(i,2)=highway(i,1);highway(i,1)=0;endendback_to_right = highway; %record lane_changed highway statement%disp(back_to_right);disp('Aboveis the state of back_to_right lane highway.');pla=0;speed=0;pas_pla=0;pas_spe=0;endfprintf('change_lane_time ','\n');disp(change_lane_times)fprintf('crash_time ','\n');disp(crash_times)Appendix 2. Data of ImitationPSL Change lane times Mean Crash times MeanNumberof cars=5 50 2 2 2 2.0 0 0 0 0.0 60 3 2 3 2.7 0 0 0 0.0 70 1 0 1 0.7 0 0 0 0.0 80 2 0 1 1.0 0 0 0 0.0 90 0 0 3 1.0 0 0 0 0.0 100 1 3 2 2.0 0 0 0 0.0Numberof 50 7 5 11 7.7 0 0 0 0.0 60 8 11 8 9.0 0 1 0 0.3cars=10 70 10 6 7 7.7 1 0 1 0.780 6 7 10 7.7 0 1 1 0.790 4 7 4 5.0 1 2 0 1.0100 6 3 3 4.0 1 1 1 1.0Numberof cars=20 50 47 29 38 38.0 1 2 2 1.7 60 30 34 20 28.0 2 0 1 1.0 70 15 17 22 18.0 0 2 3 1.7 80 18 22 16 18.7 0 2 1 1.0 90 20 10 22 17.3 1 1 2 1.3 100 21 15 13 16.3 2 2 1 1.7Numberof cars=30 50 61 60 48 56.3 5 4 2 3.7 60 46 42 45 44.3 4 1 2 2.3 70 42 38 48 42.7 4 5 3 4.0 80 43 32 47 40.7 2 5 5 4.0 90 32 41 33 35.3 3 4 5 4.0 100 26 27 24 25.7 2 2 4 2.7Numberof cars=40 50 65 100 74 79.7 8 4 8 6.7 60 56 77 75 69.3 5 8 3 5.3 70 53 64 62 59.7 4 5 5 4.7 80 52 60 60 57.3 3 7 3 4.3 90 44 53 48 48.3 5 4 4 4.3 100 43 50 38 43.7 1 7 0 2.7Numberof cars=50 50 82 86 106 91.3 12 12 10 11.3 60 80 68 72 73.3 10 9 13 10.7 70 82 75 81 79.3 8 7 10 8.3 80 61 72 58 63.7 9 7 11 9.0 90 57 54 54 55.0 6 7 11 8.0 100 64 50 51 55.0 7 9 8 8.0PSL=705 1 0 1 0.7 0 0 0 0.0 10 1067 7.7 1 0 1 0.7 20 15 17 22 18.0 0 2 3 1.7 30 42 38 48 42.7 4 5 3 4.0 40 53 64 62 59.7 4 5 5 4.7 50 82 75 81 79.3 8 7 10 8.3PSL Change lanetimescollisiontimesDensityChange lanetimescollisiontimes50 56.33333333 3.666666667 5.0 0.666666667 060 44.33333333 2.333333333 10.0 7.666666667 0.666666667 70 42.66666667 4 20.0 18 1.666666667 80 40.66666667 4 30.0 42.66666667 490 35.33333333 4 40.0 59.66666667 4.666666667 100 25.66666667 2.666666667 50.0 79.33333333 8.333333333。
2014数学建模比赛C题省二等奖论文
2014高教社杯全国大学生数学建模竞赛承诺书我们仔细阅读了《全国大学生数学建模竞赛章程》和《全国大学生数学建模竞赛参赛规则》（以下简称为“竞赛章程和参赛规则”,可从全国大学生数学建模竞赛网站下载）.我们完全明白,在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题.我们知道,抄袭别人的成果是违反竞赛章程和参赛规则的,如果引用别人的成果或其他公开的资料（包括网上查到的资料）,必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出.我们郑重承诺,严格遵守竞赛章程和参赛规则,以保证竞赛的公正、公平性.如有违反竞赛章程和参赛规则的行为,我们将受到严肃处理.我们授权全国大学生数学建模竞赛组委会,可将我们的论文以任何形式进行公开展示（包括进行网上公示,在书籍、期刊和其他媒体进行正式或非正式发表等）.我们参赛选择的题号是（从A/B/C/D中选择一项填写）：C我们的报名参赛队号为（8位数字组成的编号）：所属学校（请填写完整的全名）：参赛队员(打印并签名)：1.2.3.指导教师或指导教师组负责人(打印并签名)：（论文纸质版与电子版中的以上信息必须一致,只是电子版中无需签名.以上内容请仔细核对,提交后将不再允许做任何修改.如填写错误,论文可能被取消评奖资格.）日期：2014年9月15日赛区评阅编号（由赛区组委会评阅前进行编号）：2014高教社杯全国大学生数学建模竞赛编号专用页赛区评阅编号（由赛区组委会评阅前进行编号）：全国评阅编号（由全国组委会评阅前进行编号）：生猪养殖场的经营管理数学模型摘要养猪是农村里是很平常的农活,过去的几年里,靠养猪发家致富的不胜枚举,养猪有养猪的科学,如何科学的养猪是当代农村人所关心的问题.我们根据题意,在此基础上建立了数学模型.针对问题1,我们建立了两个模型,首先查阅相关资料,结合收集到的数据,在小猪全部转化种猪和肉猪提前下,方案一从开始经营出发考虑三年生殖繁殖情况,根据达到或超过盈亏平衡点采用MATLAB编程软件计算出每头每年平均产仔量18头.方案二是考虑后备种猪(首次孕育仔猪前的种猪),其地位,孕育方式与产过小猪的母猪不一样,这里我们将种猪（后面母猪所产出）与母猪同样看待,利用母猪与公猪消耗饲料,肉猪产生利用建立方程,求得母猪每年平均产仔量.在收集的数据下求得产仔量18头.针对问题2,我们知道了母猪怀孕期114天,小猪出栏要9个月,故肉猪离出栏天数为160天,然后建立一个优化模型,确定了每天肉猪销量,每天所有母猪成本,出售肉猪价格,利用Lingo软件运行结果母猪与种猪（后面母猪所产出）之和825头.从而列出母猪与种猪的二元一次方程,得出结果最大规模下母猪的存栏数525头,小猪选为种猪的比例为1：30.针对问题3,在最大的规模下假设母猪只生出肉猪与猪苗,将三年分成四个周期,根据已知的生猪的价格曲线分析,确定每个周期肉猪与猪苗的比例,得到利润=母猪存栏数⨯每头母猪9个月产生的肉猪数量⨯每公斤的平均利润+母猪的存栏数⨯每头猪9个月产生的猪苗数量⨯每头猪苗平均重量⨯每公斤猪肉的售价.在收集的数据下求得平均利润为3281985元,并得到母猪与肉猪出栏的曲线.关键词：MATLAB软件Lingo软件周期简化一、问题重述某养猪场最多能养10000头猪,该养猪场利用自己的种猪进行繁育.养猪的一般过程是：母猪配种后怀孕约114天产下乳猪,经过哺乳期后乳猪成为小猪.小猪的一部分将被选为种猪（其中公猪母猪的比例因配种方式而异）,长大以后承担养猪场的繁殖任务；有时也会将一部分小猪作为猪苗出售以控制养殖规模；而大部分小猪经阉割后养成肉猪出栏（见图1）.母猪的生育期一般为3～5年,失去生育能力的公猪和母猪将被无害化处理掉.种猪和肉猪每天都要消耗饲料,但种猪的饲料成本更高一些.养殖场根据市场情况通过决定留种数量、配种时间、存栏规模等优化经营策略以提高盈利水平.请收集相关数据,建立数学模型回答以下问题：图1.猪的繁殖过程1.假设生猪养殖成本及生猪价格保持不变,且不出售猪苗,小猪全部转为种猪与肉猪,要达到或超过盈亏平衡点,每头母猪每年平均产仔量要达到多少2.生育期母猪每头年产2胎左右,每胎成活9头左右.求使得该养殖场养殖规模达到饱和时,小猪选为种猪的比例和母猪的存栏数,并结合所收集到的数据给出具体的结果.3.已知从母猪配种到所产的猪仔长成肉猪出栏需要约9个月时间.假设该养猪场估计9个月后三年内生猪价格变化的预测曲线如图2所示,请根据此价格预测确定该养猪场的最佳经营策略,计算这三年内的平均年利润,并给出在此策略下的母猪及肉猪存栏数曲线.图2三年价格预测曲线横坐标说明：以开始预测时为第一年,D2表示第二年,依次类推.二、问题分析在问题1中,解题思路比较简单,算出盈亏平衡点,如果我们按照养猪达到平衡时来算,则只盈利不亏本[1],从而我们很难找出盈亏平衡点,故我们可以从开始养猪时算起,并假设出公母猪配种比例,种猪肉猪分配比例,猪一年所吃的饲料等多方面对其进行假设,在网络,相关书籍杂志中收集相关数据,在生猪养殖成本及生猪价格保持不变,猪卖出周期为3年的情况下,对其进行建立模型即可.在问题2中,利用Lingo软件解决优化问题,并列出母猪与种猪的二元一次方程,生猪养猪场达到饱和时,在不赔本的情况下,肉猪每天的销售总价与种猪和肉猪每天的成本花销之差最小.在问题3中,该问题刚开始接触不好下手,因为题目只给出该养猪场9个月后,三年内生猪价格变化如此曲线,由此价格预测确定的这养猪场的养殖策略,缺少不少信息,如生猪成本信息,生猪出栏头数等.生猪成本信息,可以假设或通过查资料得到,关键是生猪出栏头数如何确定,另外母猪生母猪,母猪再生母猪,如此如此,导致关系异常复杂,经过反复思考,母猪所产小猪,全部转化肉猪或猪苗,不再产生种猪,这样的问题得到极大的简化,母猪繁育可看成周期性的,母猪从配种到养猪场出栏9个月,三年刚好4个周期,另外,母猪受孕到肉猪出栏中,母猪完全可以再次受孕,中间有重叠交叉.联想到,第一问,第二问,母猪每年产2胎左右,在求每头母猪每年平均产仔时,不考虑具体胎数,此处也可按周期或按年考虑,应当可行.三、问题假设三个问题总假设1.不考虑固定成本(如地皮成本,建筑物,猪排泄物,无害处理成本等)2.种猪为自然受精,公猪:母猪配种比例为1：30问题1的假设1.假设猪的存活率为100%;2.预留种(肉)猪身体全部正常,生猪的生长速度一致,其中种猪都能良好的繁衍下一代,不考虑近亲繁殖而导致的品种品质退化问题.3.种猪不管是公猪还是母猪养殖成本相同,只是饲料不同;4.肉猪9个月出栏问题2的假设1.种猪没有因为死亡,生病,无生育能力等原因而被淘汰.2.养猪场基数较大,而公猪,猪苗存在的数量少之又少,故可以忽略公猪,猪苗数量.问题3的假设1.饱和时小猪全部被选为肉猪和猪苗,不考虑转化为种猪.r1：1.2.第1个9月,我们把小猪选为肉猪与猪苗的比例为=1r3：7.第2个9月,小猪选为肉猪与猪苗的比例为=2r8：17.第3个9月,小猪选为肉猪与猪苗的比例为=3r0：1.第4个9月,小猪选为肉猪与猪苗的比例为=4四、符号说明问题1的符号说明W:每头种猪所花的成本(包括饲料、疫苗、医药费、饲养员的工资等).w:从小猪到肉猪所花的成本(包括饲料、疫苗、医药费、饲养员的工资等).M:每头肉猪的平均利润(除去成本的获利)p:每头母猪年平均产仔量.Q:肉猪的利润.S:养猪的总收入.i R :公(母)猪配种比例)2,1(=i .A ：刚开始母猪数量. r :种猪肉猪分配比例.q ：种猪一年总成本.问题2的符号说明x :养猪场在饱和时母猪的头数.a :母猪每天的成本.b ：肉猪每天的成本.c :每头肉猪销售价.n :养猪场存栏数.l :每天肉猪的销量.问题3的符号说明A ：刚开始母猪数量.G :每头肉猪出栏体重.g ：每头猪苗出栏体重.h :猪苗肉每公斤价格.i Q :第i 个9个月的平均成本.)4,3,2,1(=ii S :第i 个9个月的平均生猪价格)4,3,2,1(=i .i K :第i 个9月的利润)4,3,2,1(=i .i r :第i 个9月苗猪的比)4,3,2,1(=i .K :9个月后三年内平均利润.五、模型的建立与求解每年母猪产仔量问题我们根据题意,求出每头母猪每年平均产仔量可以考虑公猪数量,也可以不用考虑,下面我们用两种方法来解释此题.方法一：直接方案模型一假设与预备(考虑公猪数量)由假设,公母猪配种比例=21:R R 1:30,设母猪是A 头,即公母猪)3011(+A ,即种猪肉猪分配比例=r 1:19,猪一年所花的成本平均每头猪3500元,每头肉猪平均获利为400元.模型一的建立依据问题分析与各方面的假设,为了方便计算,对收集到的数据进行相应的处理,分别列出第1—3年的母猪产仔的量以及后几代产出的仔数量的成本和所获的收入方程养猪成本计算 第一年成本则是刚开始的公母猪)3011(+A 吃的饲料与每头母猪生下p 个小猪吃的饲料总和,然而从小猪里我们可以分出种猪和肉猪出来,即:第二年成本则是包括第一年的成本,第二代小猪吃的总饲料与第二代每头母猪生下的p 个第三代的小猪吃的饲料总和,然而第三代小猪里我们同样可以分出种猪和肉猪出来,即:同理,第三年养猪的成本,我们可以根据前面两个公式来算出,第三代小猪与其产生第四代小猪吃的饲料总和,所以我们求得出第三年成本为:养猪收入计算我们算出了各年的成本,同时要算出各年的收入,这样才可以求出盈亏平衡点,所以,列出各三年养猪母猪产仔的量以及后几代产出的仔数量的成本和所获的收入方程:第一年的收入主要来源是卖出刚开始的公母猪生下的小猪中的肉猪价钱,在模型的假设与预备中,我们假设出每头猪盈利500元.所以我们求出第一年收入方程为:第二年的收入除了卖出刚开始的公母猪生下小猪中的肉猪价格,同时还有第二代母猪22C 生下小猪中的肉猪的价钱,即:同理,第三年收入包括第一年和第二年卖肉猪价钱,我们同样根据前面两个公式计算,第三代母猪32C 产出第四代小猪,则求出第三年的收入为:盈亏平衡点计算我们求出各三年收入与成本的计算,对于盈亏平衡点,只需要将总收入与总成本相等,并算出每头母猪每年平均产仔量,即:联立各式可以得出关于p 关系式为：最后我们经过MATLAB 编程软件[1]向上取整算出结果得:18=p .然而一头母猪生一胎猪一般能生12只猪,即一年产出24只小猪[2],我们同时也可以所第二题给出的资料显示母猪每头生产2胎左右,每胎成活9头左右,即一年成活18只左右,所以我们求出的达到或超过盈亏平衡点,即每头母猪每年平均产仔量18=p 头较合理.方案一入手容易.题干中小猪全部转换为种猪与肉猪,方案一在直接处理种猪时,过程过于复杂.经过对题目的反复研读,得到更简便的方法,即间接方法.此处的种猪实际上为后备种猪（首次孕育仔猪前的种猪）[3],其地位、孕育方式与产过小猪的种猪不一样.这里我们将种猪与母猪同样看待,这样问题得到很大的简化,我们讨论时达到或超过盈亏平衡点时在是否加上母猪的成本时,曾举棋不定.经对题目的仔细审核,该养猪场利用自己的种猪来繁衍而且规模很大,因此这里的母猪完全有理由靠自身繁育得到,于是此处母猪可以不计入成本.方法二:间接方案模型二的建立(不考虑公猪数量)母猪A 生下小猪pA ,由题设小猪全部转为种猪pA r +11与肉猪pA r r +1,只有肉猪才能获利pAQ r r +1,注意此处Q 为肉猪的利润（9个月）.母猪与公猪共占成本q pA rA )11(++,由此得到方程 q pA r A )11(++=pAQ r r +1 向上取整解得：代入有关数据[4]19=r ,3500=q ,400Q =,得18=p讨论到这里,我们发现在解题过程无论是方法一还是方法二都把开始时母猪数量A 当做参数所抵消掉了,由此可见,每头母猪每年平均的产仔量与母猪的原始数量并没有直接关系.方法二没有考虑公猪数量,方程简单,从而比方法一更加简便.小猪选为种猪的比例和母猪的存栏数问题模型三假设与预备在这里我们可以假设出母猪一天所花的成本为10元,肉猪一天所花的成本为元,每头猪的出栏价为1200元,总的存栏数为10000头(题目已给).生育期母猪每头年产2胎,每胎成活9头.即一年所生18头小猪(题目已给).存栏数与种猪比的计算我们按照题目中的假设,猪仔长成肉猪出栏需要9个月,即274天.然而母猪配种后怀孕约144天产下乳猪,所以肉猪离出栏天数为160(天)=274(天)-114(天),则每天肉猪销量为：每天所有母猪的成本和+每天所有肉猪的成本-每天出售肉猪价格0≤,所以我们可以建立一个优化模型：依据所假设的数据,利用Lingo 软件解此优化模型,养殖规模达到饱和时,母猪与种猪之和为825=x ,由此我们可以列出母猪与种猪的二元一次方程⎩⎨⎧-=-=+825)1(1882518n m A Am A 其中10000=n .解并A 取整得所以我们求得出母猪存栏数525=x ,从小猪中选成种猪比例为%15.3=m ,折合比例为1:30.最佳经营策略,利润,存栏数曲线分析模型四假设与预备我们假设肉猪出栏体重为100公斤;猪苗体重为25公斤;猪苗平均每公斤成本为10元[5];确定最佳经营策略以及年均利润本问题要找最佳经营策略自然从问题2中该养殖场最大规模开始考虑.确定最佳经营策略:当价格低时,作为猪苗的小猪抛售来减少肉猪的养殖规模;当价格高时,将肉猪尽可能抛出,以实现利益最大化,当价格处于中间值时,将肉猪抛出一部分,另一部分可做为猪苗卖出.可以依据题意,列出图中给出的三年价格预测曲线转换时间与生猪价格表如下表1所示：表1：生猪价格表单位：元/公斤日期价格19日期价格1717日期价格17日期价格日期价格14日期价格日期价格15日期价格17日期价格日期价格1516日期价格日期价格13日期价格日期价格母猪是在第二年的6月12日之前的第9个月开始生产,而母猪繁育可看成周期性的[6],母猪从配种到养猪场出栏9个月,三年刚好4个周期,所以我们可以按照母猪生产周期来推算,所以,第一个9月是在第2年的具体如下图3所示：图39个月后3年内生猪价格预测曲线与周期图我们根据以上的假设,第i个9个月母猪生下的猪苗比)4,3,2,1i,可以列出第i个9(=月利润表达式为：利润=母猪存栏数⨯每头母猪9个月产生的肉猪数量⨯每公斤的平均利润+母猪的存栏数⨯每头猪9个月产生的猪苗数量⨯每头猪苗平均重量⨯每公斤猪肉的售价.即：所以求得这三年来平均利润为：母猪,肉猪存栏数曲线分析我们可以依照第二问算出来的结果可知,然而母猪存栏数是恒定的,母猪产下的肉猪到了第1个9个月将其全部抛出,母猪到了第二轮再生.9个月后再全部抛出,在9—18个月中,猪肉价格下降,故卖出的肉猪较少,18—27个月中猪肉价回升,卖出的肉猪头相对增加,在27个月之后,母猪生下的小猪全部转化为猪苗,从而没有肉猪卖出.具体数据如下图4所示：图4母猪与肉猪的存栏数曲线图然而,实践就是实践,变化无穷,我们无法将所有可能发生的事都能分析到,我们今天所做出的理论,也许并不太适用于现在的生猪养殖场的经营管理此类复杂问题,但我们可以根据以下理论推理推出一个大致的方向[7].六、模型的评价与推广模型的优点：1.简单明了,程序简单.2.充分利用假设条件,并做了恰当简化,与实际紧密相连.3.原创性很强,文章中大部分模型都是自行推导建立的.模型的缺点：1.未充分结合专业知识,仅从数学角度分析.2.在问题3中,比较主观.模型的推广：本文充分利用了假设数据,进行了简单合理的推理,使用了较简单的数学知识,有益于模型进一步推广,其公式以及图表形式呈现,直观易懂.可以推广到其它的畜牧业养殖中.七、参考文献[1]360问答热心网友2014年9月12日.[2]百度百科热心网友2014年9月13日.[3]360问答热心网友2014年9月14日.[4]赵东方,数学模型与计算[M],北京：科学出版社,2007年.[5]新浪网站热心网友2014年9月15日.[6]洪毅等,数学模型[M],北京：高等教育出版社,2004年.[7]吴建国等,数学建模案例精编[M],北京：中国水利水电出版社,2005年.八、附录存栏数与种猪比的计算编程优化问题,生猪养猪场饱和时,在不赔本的情况下,肉猪每天的销售总价与种猪和肉猪每天的成本花销之差最小.min=(10000-x)/160*1200-10**(10000-x);(10000-x)/160*1200-10**(10000-x)>=0;@gin(x);solve('3500*((1+*x*30/31)^2+2+*x*30/31)*(31/30+*x)*x*400-(1+*x*30/31)*x**400-(1+*x *30/31)^2**x*400=0')ans=[[[母猪,肉猪存栏数曲线分析x=[36];x=[36];x=[6];x=[6];x=[6];y=[00];plot(x,y)holdonz=[5525525];plot(x,z)gtext('母猪存栏数曲线图');gtext('肉猪存栏数曲线图');title('母猪与肉猪的存栏数曲线图')xlabel('月份x');ylabel('猪的存栏数y')。
2014年美国大学生数学建模竞赛ICM(C题)一等奖
2 Assumptions
All the data given and found is valid and believable We don’t take the people with Erdos number>1 or Erdos number=0 (being Erdos himself) into account. The timeline of cooperation can be neglected. Neglecting the isolated node does not influence the accurate result.
Team # 25072Байду номын сангаас
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1 Introduction
Network science is an interdisciplinary academic field which studies complex networks [1]. One of the techniques to determine influence of academic research is to build a citation or co-author networks and analyze its properties. Erdos is the most famous academic co-authors on account of his over 500 co-author and over 1400 papers published. So it is of great significance to analyze the co-author data within Erdos1. How to build the co-author network and develop influence measures to determine the most influential one? It requires us some skills for data extraction in order to remove the invalid data and limit the size of the network that we are going to research. Also, ability to analyze the properties of the network is needed so as to figure out the feature of the network. On one hand our goal is to establish a mathematics model to determine the most significant author. There is no need to consider Erdos since he will link to all nodes in Erdos1. On the other hand we are required to develop another different model to determine the most important works. Moreover, we will implement our algorithm on a completely different set of network influence data –for instance, influential songwriters, music bands, performers, movie actors, directors, movies, TV shows, columnists, journalists, newspapers, magazines, novelists, novels, bloggers, tweeters and so on. Finally, we will discuss the science, understanding and utility of modeling influence and impact within networks and draw some conclusion. What’s more, we can also try to apply our model to the network of university, department, nation and society to demonstrate our models have good practicability and adaptability.
C题数学建模论文终结版
承诺书我们仔细阅读了五一数学建模联赛的竞赛规则。
我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与本队以外的任何人（包括指导教师）研究、讨论与赛题有关的问题。
我们知道，抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其它公开的资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。
我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。
如有违反竞赛规则的行为，我们愿意承担由此引起的一切后果。
我们授权五一数学建模联赛赛组委会，可将我们的论文以任何形式进行公开展示（包括进行网上公示，在书籍、期刊和其他媒体进行正式或非正式发表等）。
我们参赛选择的题号为（从A/B/C中选择一项填写）： C我们的参赛报名号为：1950参赛组别（研究生或本科或专科）：本科生所属学校（请填写完整的全名）山东科技大学参赛队员(打印并签名) ：1. 宫晨2. 李帅3. 徐温博日期：2014 年 5 月 3 日获奖证书邮寄地址：山东省青岛市黄岛区前湾港路579号山东科技大学信息科学与工程学院物联网工程2013级1班宫晨（收）邮政编码266510编号专用页竞赛评阅编号（由竞赛评委会评阅前进行编号）：裁剪线裁剪线裁剪线竞赛评阅编号（由竞赛评委会评阅前进行编号）：参赛队伍的参赛号码：（请各参赛队提前填写好）：题 目 “延迟退休”问题摘 要目前我国已经进入人口老龄化快速发展期，“延迟退休”已成为人们关注的热点话题，如何尽快作出“延迟退休”科学可行的制度设计，是人们关心的问题。
对问题一，我们查阅文献资料，获得四个指标的计算公式，分别为：出生时的平均预期寿命：∑-===1101ωi i x x x L l l T e ；人口老龄化程度指标计算公式：%10%100≥⨯=Z X S 或%7%100≥⨯=ZYS ；劳动力供求状况指标计算公式： )1(r Sq W S N Q +==；国民受教育情况指标计算公式：e ×I ＋d ×L ＋c ×M ＋b ×H ＋a ×U =C然后分别研究这四个指标对延迟退休的影响，得出了我国确实有必要延迟退休年龄的结论。
2014年数学建模优秀论文
对黑匣子落水点的分析和预测摘要本文通过对飞机以及黑匣子受力情况进行分析，构建正交分解模型，得出飞机的坠落轨迹和黑匣子的落水点，及黑匣子在水中的移动情况。
问题一要求在考虑空气气流影响的前提下，建立数学模型，描述飞机坠落轨迹并推测黑匣子的落水点。
本文对飞机失去动力后的全过程建立动力学方程：22d r m mg f dt=-+ 然后对动力学方程进行正交分解，在水平和竖直方向上分别进行分析，根据伯努利方程求得升力的计算公式，得出飞机在刚刚失去动力时，升力大于重力，所以飞机会先上升一段距离，随着水平速度的减小，升力也逐渐减小，然后飞机再下降，通过模拟计算可以得出当飞机坠落至失事点下10000m 时，飞机坠入海面，其飞行速度为515.994m s ，飞机向东北方向飞行了28697m 。
问题二要求建立数学模型，描述黑匣子在水中沉降过程轨迹，并指出它沉在海底的位置所在的区域范围。
由于不用考虑洋流，黑匣子所受到的力中仅有水的阻力是变化的，其重力和浮力始终保持恒定，根据黑匣子的移动速度，得出相应的阻力和加速度。
在不同的速度范围内，使用不同的阻力公式，计算出相应的移动距离并作出轨迹图。
发现在水平方向仅漂出161.095m ，速度几乎为零，因此黑匣子在I 区域内。
关键词 正交分解模拟计算 微分方程伯努利方程一、问题背景和重述1.1问题背景黑匣子是飞机专用的电子记录设备之一，里面装有飞行数据记录器和舱声录音器，它能记录各种飞行参数，供事故分析和飞机维修参考使用。
黑匣子记录的参数包括：飞机停止工作或失事坠毁前半小时的语音对话和两小时的飞行高度、速度、航向、爬升率、下降率、加速情况、耗油量、起落架放收、格林尼治时间、飞机系统工作状况和发动机工作参数等[1]作为飞机数据客观、真实、全面的记录者，它能把飞机停止工作或失事坠毁前半小时的有关技术参数和驾驶舱内的声音记录下来，它是飞机失事后查明事故原因的最可靠、最科学、最有效的手段。
2014年数学建模美赛题目原文及翻译
2014年数学建模美赛题目原文及翻译作者：Ternence Zhang转载注明出处：MCM原题PDF：PROBLEM A: The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this ruleeffective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system –either part of the road network or imbedded in the design of all vehicles using the roadway –to what extent would this change the results of your earlier analysis?问题A：车辆右行在一些规定汽车靠右行驶的国家（即美国，中国和其他大多数国家，除了英国，澳大利亚和一些前英国殖民地），多车道的高速公路经常使用这样一条规则：要求司机开车时在最右侧车道行驶，除了在超车的情况下，他们应移动到左侧相邻的车道，超车，然后恢复到原来的行驶车道（即最右车道）。
2014美国大学生数学建模特等奖优秀论文
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Best all time college coach Summary
In order to select the “best all time college coach” in the last century fairly, We take selecting the best male basketball coach as an example, and establish the TOPSIS sort - Comprehensive Evaluation improved model based on entropy and Analytical Hierarchy Process. The model mainly analyzed such indicators as winning rate, coaching time, the time of winning the championship, the number of races and the ability to perceive .Firstly ， Analytical Hierarchy Process and Entropy are integratively utilized to determine the index weights of the selecting indicators Secondly，Standardized matrix and parameter matrix are combined to construct the weighted standardized decision matrix. Finally, we can get the college men's basketball composite score, namely the order of male basketball coaches, which is shown in Table 7. Adolph Rupp and Mark Few are the last century and this century's "best all time college coach" respectively. It is realistic. The rank of college coaches can be clearly determined through this method. Next, ANOVA shows that the scores of last century’s coaches and this century’s coaches have significant difference, which demonstrates that time line horizon exerts influence upon the evaluation and gender factor has no significant influence on coaches’ score. The assessment model, therefore, can be applied to both male and female coaches. Nevertheless, based on this, we have drawn coaches’ coaching ability distributing diagram under ideal situation and non-ideal situation according to the data we have found, through which we get that if time line horizon is chosen reasonably, it will not affect the selecting results. In this problem, the time line horizon of the year 2000 will not influence the selecting results. Furthermore, we put the data of the three types of sports, which have been found by us, into the above Model, and get the top 5 coaches of the three sports, which are illustrated in Table10, Table 11, Table12 and Table13 respectively. These results are compared with the results on the Internet[7], so as to examine the reasonableness of our results. We choose the sports randomly which undoubtedly shows that our model can be applied in general across both genders and all possible sports. At the same time, it also shows the practicality and effectiveness of our model. Finally, we have prepared a 1-2 page article for Sports Illustrated that explains our results and includes a non-technical explanation of our mathematical model that sports fans will understand. Key words: TOPSIS Improved Model; Entropy; Analytical Hierarchy Process; Comprehensive Evaluation Model; ANOVA