2015年全国数模B题数据

2015年全国数模B题数据
2015年全国数模B题数据

overview

{"status":1,"errMsg":"","realDate":"2015-09-09","result":{"peakTimeofAMOfCity":8,"largestOrde rAreaOfCity":[116.8567512126168,40.38111820528473],"lowestSatisfyAreaAMOfCity":[116.471 917914003,39.88724095665837],"peakTimeofPMOfCity":18,"lowestSatisfyAreaPMOfCity":[116.3 697741583042,39.90525007900387],"nightLifeAreaOfCity":[116.46906429796483,39.943040506 29388],"overtimeWorkAreaOfCity":[116.46648296025816,39.92450921375481],"richestAreaOfCi ty":[116.4650167301319,39.91436778727339],"shortestWaitAreaOfCity":[116.4722248436204,3 9.90132456030148]}}

Point

{"status":1,"errMsg":"","realDate":"","result":{"scope":"city","cityID":"110100","date":"2015/09/ 03","realDate":"20150903","data":[[["",121.4793,31.2099,646],["",121.5175,31.1963,253],["",12 1.6173,38.9162,152],["",114.3296,30.5451,138],["",121.5521,38.9632,117],["",116.4756,39.9006 ,111],["",116.4655,39.9679,94],["",116.4663,39.9151,94],["",116.3162,39.9074,92],["",116.4771, 39.8994,91],["",116.3571,39.9509,90],["",116.4604,39.9616,88],["",116.3652,39.9493,86],["",11 8.1888,39.6266,84],["",116.4916,39.9899,82],["",116.473,39.9275,81],["",116.3845,39.9895,81],[ "",116.4741,39.9365,81],["",116.4692,39.9209,80],["",116.4724,39.9813,80],["",114.482,38.0123 ,80],["",116.4972,39.9935,78],["",116.4717,39.884,78],["",122.998,41.1178,77],["",116.4853,39.9 868,76],["",116.4684,39.8994,76],["",116.3817,39.9776,75],["",116.3562,39.9951,74],["",116.28 52,39.9087,73],["",116.4772,39.9857,73],["",116.3581,39.9714,72],["",116.4884,39.9757,70],["", 116.3794,39.95,70],["",116.3191,39.8967,70],["",116.4741,39.9447,70],["",116.447,39.8976,69],[ "",116.4953,39.9189,69],["",116.4744,39.9563,69],["",116.3279,39.902,68],["",116.3236,39.9516 ,68],["",116.489,39.9077,68],["",116.4255,39.972,68],["",116.3225,39.8931,67],["",116.4663,39.8 724,66],["",116.3391,40.0589,66],["",116.3673,39.9024,66],["",116.4763,39.9626,65],["",116.34 65,39.9091,65],["",116.3504,39.8983,65],["",116.4684,39.9722,64],["",116.375,39.9897,64],["",1 16.364,39.9364,64],["",116.3183,39.9217,63],["",116.4846,39.9109,63],["",130.2785,47.3086,63] ,["",116.4953,39.9258,63],["",116.4207,39.9772,62],["",116.3175,39.9663,62],["",116.4317,39.95 34,62],["",116.4908,40.003,62],["",116.3132,39.933,62],["",116.362,39.9308,62],["",116.4698,39. 931,62],["",116.4693,39.8852,62],["",116.3515,39.8973,62],["",116.4331,39.9954,61],["",129.61 25,44.5982,61],["",116.2896,39.9378,61],["",116.3567,39.921,61],["",116.5147,40.0069,60],["",1 16.4124,39.9546,60],["",116.3546,39.8547,60],["",116.4469,39.9735,60],["",116.4385,39.9462,5 9],["",116.4972,39.9248,59],["",116.3498,39.843,59],["",116.3805,39.8832,59],["",116.4328,39.9 716,59],["",116.3315,40.0632,59],["",116.5089,39.9995,59],["",116.3244,39.9656,58],["",116.34 85,40.0448,58],["",130.2755,47.3456,58],["",116.3714,39.9508,58],["",116.3139,39.94,58],["",11 6.3701,39.9483,58],["",116.3252,40.0811,57],["",116.319,39.9825,57],["",116.3486,40.0322,57],[ "",116.3645,40.0263,57],["",116.3158,40.0822,57],["",116.3668,39.9075,57],["",116.3775,40.012 1,57],["",116.4633,39.8719,57],["",116.3134,39.9811,57],["",116.3941,39.99,57],["",116.5221,40. 0208,56],["",116.2817,39.8788,56],["",116.3122,39.961,56],["",116.3613,39.9311,56],["",116.52 15,40.0184,56],["",116.3676,39.9769,56],["",116.3452,39.9075,56],["",118.3011,35.111,56],["",1 16.325,40.0671,56],["",116.4364,39.9127,56],["",116.6196,40.0647,56],["",116.2862,39.9208,56] ,["",116.3345,40.0482,55],["",116.3043,39.994,55],["",125.9743,41.748,55],["",130.265,47.302,5 5],["",116.5086,39.994,55],["",116.335,40.0449,55],["",116.3128,39.9329,55],["",125.9608,41.74 17,54],["",116.4187,39.9892,54],["",116.379,39.8675,54],["",116.4079,39.9902,54],["",116.3964, 39.9495,54],["",116.4698,39.8688,53],["",116.4029,39.9526,53],["",116.4744,39.9402,53],["",11

6.3186,39.9271,53],["",116.4453,39.8646,53],["",116.3469,40.0521,53],["",116.6264,40.0545,53] ,["",116.3219,39.9473,53],["",116.5082,39.9161,53],["",116.2868,39.8734,52],["",116.346,39.987 2,52],["",116.4987,39.9437,52],["",116.361,40.0359,52],["",116.3759,39.8788,52],["",116.3509,3 9.8317,51],["",116.355,39.8779,51],["",116.4115,39.974,51],["",116.3662,39.9219,51],["",116.42 58,39.8603,51],["",116.4494,39.9942,51],["",116.2873,39.951,51],["",116.3248,39.898,50],["",11 6.3149,39.9064,50],["",124.3869,43.1758,50],["",116.5208,40.0282,50],["",116.3816,39.9775,50] ,["",116.4443,39.9746,49],["",116.3669,40.0162,49],["",116.3585,40.0251,49],["",116.5833,40.03 95,49],["",116.355,39.8925,49],["",116.3907,39.9819,49],["",116.3194,39.9974,49],["",116.3119, 39.8986,49],["",116.3545,39.8813,49],["",116.3725,39.9726,49],["",116.4407,39.9414,49],["",11 6.5394,40.0286,48],["",116.5024,40.006,48],["",116.3364,39.9939,48],["",116.402,39.8636,48],[" ",116.4424,39.9584,48],["",116.5595,40.0312,48],["",116.4357,39.9902,48],["",116.3581,39.871 5,47],["",114.5022,38.0535,47],["",116.2856,39.8875,47],["",116.4697,39.9144,47],["",116.397,3 9.8639,47],["",116.4438,39.9059,47],["",116.2709,39.902,47],["",116.3236,40.0734,47],["",116.3 829,39.9996,47],["",116.3961,39.8797,47],["",116.4184,40.0481,47],["",11

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2015全国大学生数学建模竞赛B题

“互联网+”时代的出租车资源配置 摘要 随着“互联网+”时代的到来,针对当今社会“打车难”的问题,多家公司建立了打车软件服务平台,并推出了多种补贴方案,这无论是对乘客和司机自身需求还是对出租车行业发展都具有一定的现实意义。本文依靠ISM解释结构、AHP-模糊综合评价、价格需求理论、线性规划等模型依次较好的解决了三个问题。 对于问题一求解不同时空出租车资源“供求匹配”程度的问题,本文先将ISM模型里的层级隶属关系进行改进,将影响出租车供求匹配的12个子因素分为时间、空间、经济、其它共四类组合,然后使用经过改进的AHP-模糊综合评价方法建立模型,提出了出租车空载率这一指标作为评价因子的方案,来分析冬季某节假日市南岗区出租车资源“供求匹配”程度。通过代入由1-9标度法确定的各因素相互影响的系数,得出各个影响因素的权重大小,利用无量纲化处理各影响因素,得出最终评判因子为0.3062,根据“供求匹配”标准,得出市南岗区出租车资源“供求匹配”程度处于供需合理状态的结论。同理,也得到了市不同区县、不同时间的供求匹配程度,最后作出市出租车“供求匹配”程度图。 对于问题二我们运用价格需求理论建立模型,以补贴前后打车人数比值与空驶率变化分别对滴滴和快的两个公司的不同补贴方案进行求解,依次得到补贴后对应的打车人数及空驶率的变化,再和无补贴时的状态对比,最后得出结论:当各公司补贴金额大于5元时,打车容易,即补贴方案能够缓解“打车难”的状况;当补贴小于5元时,不能缓解“打车难”的状况。 对于问题三,在问题二的模型下,建立了一个寻找最优补贴金额的优化模型,利用lingo软件[1]进行求解算出最佳补贴金额为8元,然后将这个值带入问题二的模型进行验证,经论证合理后将补贴金额按照4种分配方案分配给司机乘客。关键词:ISM解释结构模型;AHP-模糊综合评价;价格需求理论;线性规划

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X=[0 400 800 1200 1600 2000 2400 2800]; Y=[0 400 800 1200 1600 2000 2400]; [x,y]=meshgrid(X,Y); z=[1180 1320 1450 1420 1400 1300 700 900;... 1230 1390 1500 1500 1400 900 1100 1060;... 1270 1500 1200 1100 1350 1450 1200 1150;... 1370 1500 1200 1100 1550 1600 1550 1380;... 1460 1500 1550 1600 1550 1600 1600 1600;... 1450 1480 1500 1550 1510 1430 1300 1200;... 1430 1450 1470 1320 1280 1200 1080 940]; figure(1); meshz(x,y,z) title('源数据点') xi=[0:40:2800]; yi=[0:40:2400]; zc=interp2(x,y,z,xi,yi','spline'); figure(2); surfc(xi,yi,zc); title('地貌图'); figure(3); contour(xi,yi,zc); 【2】结果:

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编号专用页 赛区评阅编号(由赛区组委会评阅前进行编号): 全国统一编号(由赛区组委会送交全国前编号):全国评阅编号(由全国组委会评阅前进行编号):

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数学建模一周作业题目

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预测T=10 时野兔的数量。 (三)停车场的设计问题 在New England的一个镇上,有一位于街角处面积100 200平方英尺的停车场,场主请你代为设计停车车位的安排方式,即设计在场地上划线的方案。 容易理解,如果将汽车按照与停车线构成直角的方向,一辆紧挨一辆地排列成行,则可以在停车场内塞进最大数量的汽车,但是对于那些缺乏经验的司机来说,按照这种方式停靠车辆是有困难的,它可能造成昂贵的保险费用支出。为了减少因停车造成意外损失的可能性,场主可能不得不雇佣一些技术熟练的司机专门停车;另一方面,如果从通道进入停车位有一个足够大的转弯半径,那么,看来大多数的司机都可以毫无困难地一次停车到位。当然通道越宽,场内所容纳的车辆数目也越少,这将使得场主减少收入。 请你通过建模的计算结果,来给出一个合理的设计方案。 (四)奖学金的评定(A) 背景 A Better Class (ABC)学院的一些院级管理人员被学生成绩的评定问题所困 ),这使得扰。平均来说,ABC的教员们一向打分较松(现在所给的平均分是A — 无法对好的和中等的学生加以区分。然而,某项十分丰厚的奖学金仅限于资助占总数10%的最优秀学生,因此,需要对学生排定名次。 教务长的想法是在每一课程中将每个学生与其他学生加以比较,运用由此得到的信息构造一个排名顺序。例如,某个学生在一门课程中成绩为A,而在同一课程中所有学生都得A,那么就此课而言这个学生仅仅属于“中等”。反之,如果一个学生得到了课程中唯一的A,那么,他显然处在“中等至上”水平。综合从几门不同课程所得到的信息,使得可以把所有学院的学生按照以10%划分等级顺序(最优秀的10%,其次的10%,等等)排序。 问题 , B+ ,…)这样的方式给出的,教务(1)假设学生成绩是按照(A+,A, A — 长的想法能否实现?

数学建模B题

数学建模B题 The following text is amended on 12 November 2020.

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2015年数学建模作业题

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适的月份维修。除了磨床外,每月机床在这6个月中的一个月中必须停工维修;6个月中4台磨床只有2台需要维修。扩展工厂计划模型,以使可作上述灵活安排维修时间的决策。停工时间的这种灵活性价值若何? 注意,可假设每月仅有24个工作日。 5、生产计划 某厂有4台磨床,2台立钻,3台水平钻,1台镗床和1台刨床,用来生产7种产品,已知生产单位各种产品所需的有关设备台时以及它们的利润如表所示: 台镗床,4月—1台立钻,5月—1台磨床和1台立钻,6月—1台刨床和1台水平钻,被维修的设备在当月内不能安排生产。又知从1月到6月份市场对上述7种产品最大需求量如表所示: 量均不得超过100件。现在无库存,要求6月末各种产品各贮存50件。若该厂每月工作24天,每天两班,每班8小时,假定不考虑产品在各种设备上的加工顺序,要求: (a)该厂如何安排计划,使总利润最大; (b)在什么价格的条件下,该厂可考虑租用或购买有关的设备。 34、瓶颈机器上的任务排序 在工厂车间中,经常会出现整个车间的生产能力取决于一台机器的情况(例如,仅有一台的某型号机床,生产线上速度最慢的机器等)。这台机器就称为关键机器或瓶颈机器。此时很重要的一点就是尽可能地优化此机器将要处理的任务计划。

2015年全国大学生数学建模比赛A题一等奖论文

太阳影子定位问题 摘要 目前,如何确定视频的拍摄地点和拍摄日期是计算机视觉的热点研究问题,是视频数据分析的重要方面,有重要的研究意义。本文通过建立数学模型,给出了通过分析视频中物体的太阳影子变化,确定视频拍摄的地点和日期的方法。 对于问题一,建立空间三维直角坐标系和球面坐标系对直杆投影和地球进行数学抽象,引入地方时、北京时间、太阳赤纬、杆长、太阳高度角等五个参数,建立了太阳光下物体影子的长度变化综合模型。求解过程中,利用问题所给的数据,得到太阳赤纬等变量,将太阳赤纬等参量代入模型,求得了北京地区的9:00至15:00的影子长度变化曲线,当12:09时,影子长度最短;并分析出影长随这些参数的变化规律,利用控制变量法思想,总结了五个参数与影子长度的关系。最后进行模型检验,将该模型运用于东京、西藏两地,得到了这两座城市的影长变化规律曲线,发现变化规律符合实际两地实际情况。 对于问题二,为了消除不同直角坐标系带来的影响,将实际坐标转换为二次曲线的极坐标,建立了极坐标下基于多层优化搜索算法的空间匹配优化模型。求解时,先将未知点的直角坐标系的点转换为极坐标,然后设计了多层优化搜索算法,通过多次不同精度的搜索,最后得出实际观测点的经纬度为东经E115?北纬N25?。同时对模型进行验证,实地测量了现居住地的某个时间段的值,通过模型二来求解出现居住地的经纬度,分析了误差产生的原因:大气层的折射和拟合误差。 对于问题三,将极坐标转换后的基本模型转换为优化模型,建立了基于遗传算法的时空匹配优化模型。将目标函数作为个体的适应度函数,将经度纬度及日期作为待求解变量,用遗传算法进行求解,得到可能的经度纬度及其日期:北纬20度,东经114度,5月21日;北纬20度,东经114度,7月24日;东经94.5度,北纬33.8度,6月19日。最后,将遗传算法与多层优化搜索算法进行对比分析,得出遗传算法的求解效率和求解精度均优于多层次搜索算法。 对于问题四,首先将视频材料以1min为间隔进行采样得到41帧(静态图片),将这些静止图片先利用matlab进行处理,后进行阀值归一化处理,得到这些帧的灰度值矩阵。在图片上建立参考模型,获得影子端点的参考位置。利用投影系统和模型二,建立了基于图形处理的视频拍摄地点搜索模型。利用模型二中多层搜索算法,求得满足精度的最优地点。最优的地点是:东经119,北纬48.7,在内蒙古的呼伦贝尔市。同时假设日期是未知量,将模型四与模型三相结合,得到了可能的地点和时间,并分析了可能出现误差的原因,最后回答了当视频日期未知,也可以确定其位置和日期。 最后,给出了模型的优缺点和改进方案。 关键词:极坐标化,多层优化搜索算法,遗传算法,图像处理,MATLAB

数学建模b题标准答案

2011高教社杯全国大学生数学建模竞赛 承诺书 我们仔细阅读了中国大学生数学建模竞赛的竞赛规则. 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,我们将受到严肃处理。 我们参赛选择的题号是(从A/B/C/D中选择一项填写): B 我们的参赛报名号为(如果赛区设置报名号的话): 所属学校(请填写完整的全名):北京大学 参赛队员(打印并签名) :1. 姚胜献 2. 许锦敏 3. 刘迪初 指导教师或指导教师组负责人(打印并签名):刘业辉 日期: 2011 年 9 月 12日赛区评阅编号(由赛区组委会评阅前进行编号):

2011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): 交巡警服务平台的设置与调度 摘要 本文通过建立整数规划模型,解决了分配各平台管辖范围、调度警务资源以及合理设置交巡警服务平台这三个方面的问题;通过建立线性加权评价模型定量评价了某市现有交巡警服务平台设置方案的合理性,并根据各个区对服务平台需求量的不同,提出了重新分配全市警力资源的解决方案。在计算交巡警服务平台到各个路口节点的路程时,使用了图论里的floyd算法。 针对问题一的第一个子问题,首先假设交巡警服务平台对某个路口节点的覆盖度是二元的,引入决策变量,建立了0-1整数规划模型。交巡警出警应体现时间的紧迫性,所以选择平均每个突发事件的出警时间最短作为目标函数,运用基于MATLAB的模拟退火算法进行求解,给出了中心城区A的20个服务平台的管辖范围,求得平均每个案件的出警时间为1.013分钟。 针对问题一的第二个子问题,为了实现对中心城区A的13个交通要道的快速全封锁,以最短的封锁时间为目标,建立了0-1整数规划模型,利用lingo软件编程求解,给出了该区交巡警服务平台警力合理的调度方案,并求得对13个交通要道实现全封锁最短需要8.02分钟。 问题一的第三个子问题是交巡警服务平台的选址问题。考虑到建设新的服务平台需要投入更多的成本和警务资源,还需平衡各个服务平台的工作量。因此,以增加最少的服务平台数和服务平台工作量方差最小为目标,采用集合覆盖理论,建立了双目标0-1整数规划模型,用基于MATLAB的模拟退火算法求解出增加的服务平台数为4个,新增 的服务平台具体位置为A 28,A 40 ,A 48 ,A 88 ,并得到各个服务平台的工作强度方差为2.28。 针对问题二的第一个子问题,通过建立线性加权评价模型定量评价了该市现有交巡警服务平台设置方案的合理性,结果发现全市服务平台覆盖率较低且各个区的工作量不均衡,得出全市服务平台的布局存在明显的不合理的结论。并确定各区域人口密度、各区域公路总长度以及各区域平均每天总的发案率为各区域对交巡警需求的指标,然后根据各个区对服务平台需求量的不同,提出了较为合理的分配全市警力资源的解决方案。 对于问题二的第二个子问题,以围堵范围最小和调动警力最少的原则,通过分析案发后嫌疑犯可能到达的位置,给出了围堵方案。 关键词:交巡警服务平台 0-1整数规划模拟退火法

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