2014年美国大学生数学建模竞赛赛题翻译

第一篇：2014年美国大学生数学建模竞赛赛题翻译

问题A：除了超车靠右行驶的规则

在一些开车靠右行驶的国家（美国，中国和大多数的其他国家，除了英国，澳大利亚和一些英国的殖民地），多车道高速公路通常采用一个规则，要求司机在大多数高速公路上开车时靠右行驶，除非他们在超车时，这种情况下，他们要移到左边的车道，超车然后回到他们从前的车道。

建立和分析一个数学模型来分析这个规则在交通畅通和交通拥堵的情况下的表现。希望你能检查交通流量和安全、过高或过低车速的限制（那就是，车速太高或太低）或者其它的本题中可能没有提出的因素之间的权衡。这个规则在更好的提高交通流量的安全性上是否有效？如果没有，建议和分析另一种办法（包括可能这种类型的规则），那可能提高更大的交通流量、安全、和其他你认为重要的因素。

在一些靠左行驶的国家里，讨论你的方法能否在简单改变方向的或者需要附加要求的情况下应用。

最后，上述的规则依靠人类的判断作为规范。如果在相同的公路上汽车运输完全受智能系统的控制，道路网络的一部分或者嵌入所有交通工具所用的道路设计，这是你在多大程度上改变你前面的分析的结果？

问题B：大学传奇教练

《体育画报》，一个运动爱好者杂志，正在寻找上个世纪男或女的“最好全天候大学教练”。建立数学模型，从男性或女性教练中，从诸如高校曲棍球或曲棍球，足球，棒球或垒球，篮球，足球或选择其中最好的大学教练或教练们（过去或现在）。你用哪一个时间线范围是否造成不同结果，也就是说，教练在1913年是否不同于教练在2013年？清楚地说明您的度量for评估。讨论你的模型如何可以在一般的跨越男女和所有可能的运动中应用。展示你的模型在每3个不同的运动中的前5名教练。

除了MCM的格式和要求，为体育画报准备一份1-2页的文章解释你的结果，包括体育迷都明白的数学模型的非技术性解释

第二篇：2014美国数学建模竞赛赛题翻译

问题A：右行左超规则

在美国、中国 和大多数除了英国、澳大利亚和一些前英国殖民地的国家，多车道高速公路常常有这样一种规则。司机必须尽量在最右的车道行使，只有超车时，司机才可以向左移动一个车道来达成目的。当司机超车完毕后必须回到原车道继续行使。

建立并分析一个数学模型，使得这个模型能够分析这个规则在交通高负荷和低负荷情况下的表现。你可以从许多角度来思考这个问题，比如车流量和车辆安全之间的权衡，或者一个过快或过慢的车辆限速带来的影响等等。这个规则可以使我们获得更好的交通流？如果不可以，请提出并分析一个替代方案使得交通流得到优化、安全得到保障、或者其他你认为重要的因素得到实现。

在靠左行使才是规则的国家，论证你的解决方案是否可以通过简单的变换或者通过增加一些新的要求来解决相同的问题。

最后，以上的规则的实行是建立在人们遵守它的基础上的，然而不是所有人都愿意去遵守。那么现在我们使同一条道（可以只是一段，也可以是全段公路）上的交通车辆都在一个智能系统的严格控制下，这个变化对你之前的分析结果有多大的影响？

问题B：体育画刊是一个为体育爱好者们设计的杂志。这个杂志正在寻找上世纪女性或者男性的“历来最优秀的大学教练”。建立一个数学模型，从男性或者女性体育教练中选择最好的大学教练（退役或者在役的都可以）。这些体育教练可以是大学曲棍球、陆上曲棍球、足球、橄榄球、棒球、排球、篮球的教练。你选择划分的时间会对你的分析有影响吗？也就是说，1913年的教练方式和2013年的会有什么不同吗？清楚的阐述你的评估方式。讨论你的模型如何通用于两性教练和所有可能的运动项目上。用你的模型为三项体育项目分别找到五个最佳教练。

再为体育画刊提供一篇1－2页的不涉及技术性问题解释的通俗易懂的文章来解释你们的结果，你们必须保证体育爱好者们能够理解。

第三篇：2001美国数学建模数学竞赛试题及翻译

Cyclists have different types of wheels they can use on their bicycles.The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk(see Figure 1)The spoked wheels are lighter, but the solid wheels are more aerodynamic.A solid wheel is never used on the front for a road race but can be used on the rear of the bike.Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used.The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations.The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below.For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear. Task 1.Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel.The table should include the wind speeds for different road grades starting from zero percent to ten percent in one percent increments.(Road grade is defined to be the ratio of the total rise of a hill divided by the length of the road.If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.)A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportional to the road grade.A rider will lose about 8 kph for a five percent grade over 100 meters.Task 2.Provide an example of how the table could be used for a specific time trial course. Task 3.Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.选择自行车车轮

有不同类型的车轮可以让自行车手们在自己的自行车上。两种基本的车轮类型是分别用金属辐条和实体圆盘组装而成（见图1）。辐条车轮较轻，但试题车轮更符合空气动力学原理。对于一场公路竞赛，实体车轮从来不会用作自行车的前车轮但可以作为后车轮。

职业自行车手们审视竞赛路线，并且请一位识文断字的人推断应该使用哪种车轮。选择决定是根据沿途山丘的数量和陡度，天气，风速，竞赛本身以及其他考虑作出的，你所喜爱的参赛队的教练希望准备妥当一个较好的系统，并且对于给定的竞赛路线已经向你的参赛队索取有助于确定宜用哪种车轮的信息。

这位教练需要明确的信息来帮助做出决定，而且已经要求你的参赛队完成下面列出的各项任务，对于每项任务都假定同样的辐条车轮总是装在前面，而装在后面的车轮是可以选择的。任务1.提供一个给出风速的表格。在这种速度下试题后轮所需要的体能少于辐条后轮。这个表格应当包括相应于从百分之零到百分之十的不同公路陡度的风速。（公路陡度定义为一座山丘的总升高初一公路长度。如果把山丘看作一个三角形，它的陡度是指山脚处倾角的正弦。）一位骑手以初始速度45kph从山脚出发，他的减速度与公路陡度成正比。对于百分之五的陡度，骑上100米车速要下降8kph左右。

任务2.提供一个例证，说明这个表格怎样用于一条时间实验路线。

任务3.请判明这个表格是不是一件决定车轮配置的适当工具，并且关于如何作出这个决定提出其他建议。

2001 MCM B: Escaping a Hurricane's Wrath(An Ill Wind...)

Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in 1999 led to a monumental traffic jam.Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state.What is normally an easy two-hour drive took up to 18 hours to complete.Many cars simply ran out of gas along the way.Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.The principal proposal put forth to deal with this problem is the reversal of traffic on I-26, so that both sides, including the coastal-bound lanes, have traffic headed inland from Charleston to Columbia.Plans to carry this out have been prepared(and posted on the Web)by the South Carolina Emergency Preparedness Division.Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.A simplified map of South Carolina is shown.Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip.(More accurate data, if sought, are widely available.)The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three.Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees(including some coming from farther north by other routes), so some traffic continues outbound on I-26 towards Spartanburg;on I-77 north to Charlotte;and on I-20 east to Atlanta.In 1999, traffic leaving Columbia going northwest was moving only very slowly.Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999.Here are the questions that need to be addressed: 1.Under what conditions does the plan for turning the two coastal-bound lanes of I-26 into two lanes of Columbia-bound traffic, essentially turning the entire I-26 into one-way traffic, significantly improve evacuation traffic flow? 2.In 1999, the simultaneous evacuation of the state's entire coastal region was ordered.Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation, perhaps county-by-county over some time period consistent with the pattern of how hurricanes affect the coast? 3.Several smaller highways besides I-26 extend inland from the coast.Under what conditions would it improve evacuation flow to turn around traffic on these? 4.What effect would it have on evacuation flow to establish more temporary shelters in Columbia, to reduce the traffic leaving Columbia? 5.In 1999, many families leaving the coast brought along their boats, campers, and motor homes.Many drove all of their cars.Under what conditions should there be restrictions on vehicle types or numbers of vehicles brought in order to guarantee timely evacuation? 6.It has been suggested that in 1999 some of the coastal residents of Georgia and Florida, who were fleeing the earlier predicted landfalls of Hurricane Floyd to the south, came up I-95 and compounded the traffic problems.How big an impact can they have on the evacuation traffic flow? Clearly identify what measures of performance are used to compare strategies.Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.Clearly identify what measures of performance are used to compare strategies.Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.逃避飓风

1999年，在Floyd飓风预报登录之前，车里南卡罗来纳州沿海地区的行动导致一场永垂青史的交通拥塞。车水马龙停滞在州际公路I-26上，那是内陆上从Charleston通往该州中心Columbia相对安全处所的主要干线。正常时轻松的两个小时驱车路要用18个小时才能开到头。许多车竟然沿途把汽油消耗净尽。幸运的是，Floyd飓风掉头长驱北上，这次放过了南卡罗来纳州，但是，公众的喧嚷正在迫使该州官员们寻找各种办法，以求避免这场交通恶梦再度出现。倾力解决这个问题的主要提议是I-26公路上的车辆转向疏散，因此，包括通往海岸的多条次级公路在内，从两个侧面疏导车流在内陆从Charleston开往Columbia。把提议付诸实施的计划已经由South Carolina Emergency Preparedness Division准备好（而且贴在互联网上）。从Myrtle Beach和Hilton Head通往内地的主干道上车辆转向疏散的方案也在规划中。

这里有一张南卡罗来纳州的简化地图。Charleston有近500000人，Myrtle Beach有200000人左右，而另外一个250000人分散在沿岸其余地区。（如果查找，更精确的数据随处可用。）

州与州之间有两条车辆往来的次级公路，自然大都市地区除外，那里有三条。Columbia，又一个500000人左右的大都市地区，没有充足的旅店空间为撤退者提供食宿（包括咽其他路线来自北边的一些人），所以，若干车辆继续撤离，沿着I-26公路开往Spartanburg市；沿着I-77公路北上Charleston；而且沿着I-20公路东进Atlanta市。在1999年，从Columbia开往西北方向的车辆行进得非常慢。对于这个问题建立一个模型，调查研究哪种策略可以降低在1999年观察到的拥挤。这里有一些问题需要加以考虑：

在什么条件下，把I-26的两条开往海岸的次级公路变成开往Columbia的两条次级公路，特别是把整个I-26变成单行道会使撤离交通状况得到重大改善？

在1999年，南卡罗来纳州的整个沿海地区奉命同时撤离。如果采取另一种策略，逐个郡按某个时间段错开撤离，同时飓风对沿岸影响的模式相协调，撤离交通状况会改善吗？

在I-26公路旁边有若干较小的高速公路从海岸延伸到内陆。在什么条件下，把车辆流转向这些道路会改善撤离交通？

在Columbia建立更多临时收容所来减少离开Columbia的车辆，这会对撤离交通有什么影响？

在1999年，离开海岸的许多家庭一路上携带他们的船只，露宿设备和汽车住宅。许多家庭驾驶他们的所有汽车。在什么条件下，应当对携带的车辆类型或数目加以限制以求保证适时撤离？

在1999年，人们还会记得，若干George州和Florida州的沿岸居民逃避较早预报的Floyd飓风南部登录，沿着I-95公路北上家中了南卡罗来纳州交通问题。他们对于撤离交通的冲击会有多大？

要求清楚地指明，为了比较各种策略，使用什么方法对实施状况予以评测。

要求：预备一篇简短的报刊文章，不超过两页，向公众解释你的研究成果和结论。

第四篇：2014年美国大学生数学建模竞赛题目及翻译范文

PROBLEM A: The Keep-Right-Except-To-Pass Rule

In 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 employa 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 rule effective 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：除非超车否则靠右行驶的交通规则 在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。

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。你不妨考察一下流量和安全的权衡问题,车速过高过低的限制，或者这个问题陈述中可能出现的其他因素。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？

PROBLEM B: College Coaching Legends

Sports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or female for the previous century.Build a mathematical model to choose thebest college coach or coaches(past or present)from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer.Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for assessment.Discuss how your model can be applied in general across both genders and all possible sports.Present your model’s top 5 coaches in each of 3 different sports.In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model thatsports fanswill understand.问题B：大学传奇教练

体育画报是一个为运动爱好者服务的杂志，正在寻找在整个上个世纪的“史上最好的大学教练”。建立数学模型选择大学中在一下体育项目中最好的教练：曲棍球或场地曲棍球，足球，棒球或垒球，篮球，足球。时间轴在你的分析中是否会有影响？比如1913年的教练和2013年的教练是否会有所不同？清晰的对你的指标进行评估，讨论一下你的模型应用在跨越性别和所有可能对的体育项目中的效果。展示你的模型中的在三种不同体育项目中的前五名教练。

除了传统的MCM格式，准备一个1到2页的文章给体育画报，解释你的结果和包括一个体育迷都明白的数学模型的非技术性解释。

第五篇：2005美国数学建模数学竞赛试题及翻译

2005 年美国大学生数学建模竞赛 MCM试题

2005 MCM A: Flood Planning 洪水计划

Lake Murray in central South Carolina is formed by a large earthen dam, which was completed in 1930 for power production Model the flooding downstream in the event there is a catastrophic earthquake that breaches the dam

Two particular questions:

Rawls Creek is a year-round stream that flows into the Saluda River a short distance downriver from the dam How much flooding will occur in Rawls Creek from a dam failure, and how far back will it extend?

Could the flood be so massive downstream that water would reach up to the SC State Capitol Building, which is on a hill overlooking the Congaree River? South Carolina中部的Murray河是由北部的一个巨大水坝形成的，这是在1930年为了发电而修建的。模拟一起洪水淹没下游的事件，这起事件是由于一次灾难性的地震损坏了水坝造成的。两个问题：

1、Rawls Creek是水坝下游流入Saluda河的一条终年流动的河流，在当水坝损坏后，在Rawls Creek将会出现多大的洪流，洪水的波及面将有多大？

2、S.C.国会大厦大楼在一座小山上，在S.C.国会大厦大楼能俯视Congaree河。洪水能如此巨大顺流以至于水将扩展到S.C.国会大厦大楼吗？

2005 MCM B: Tollbooths收费亭

Heavily-traveled toll roads such as the Garden State Parkway, Interstate 95, and so forth, are multi-lane divided highways that are interrupted at intervals by toll plazas Because collecting tolls is usually unpopular, it is desirable to minimize motorist annoyance by limiting the amount of traffic disruption caused by the toll plazas Commonly, a much larger number of tollbooths is provided than the number of travel lanes entering the toll plaza Upon entering the toll plaza, the flow of vehicles fans out to the larger number of tollbooths, and when leaving the toll plaza, the flow of vehicles is required to squeeze back down to a number of travel lanes equal to the number of travel lanes before the toll plaza Consequently, when traffic is heavy, congestion increases upon departure from the toll plaza When traffic is very heavy, congestion also builds at the entry to the toll plaza because of the time required for each vehicle to pay the toll

Make a model to help you determine the optimal number of tollbooths to deploy in a barrier-toll plaza Explicitly consider the scenario where there is exactly one tollbooth per incoming travel lane Under what conditions is this more or less effective than the current practice? Note that the definition of “optimal” is up to you to determine

像 Garden State Parkway, Interstate 95这类的长途收费公路，通常是多行道德，被分成几条高速公路，在这些高速公路上每隔一段会设立一个通行税收费广场。因为征收通行税通常不受欢迎，所以应该尽量减少通过通行税收费广场引起的交通混乱给汽车司机带来的烦恼。通常，收费亭的数量要多于进入收费广场的道路的数量。进入通行税收费广场的时候，流到大量收费亭的车辆呈扇形展开，当离开通行税广场的时候，车流只能按照收费广场前行车道路的数量排队，按次通过！从而，当交通拥挤的时候，拥挤在违背通行税广场增加。当交通非常拥挤的时候，因为每辆车付通行费的时间要求，阻塞也会出现在通行税收费广场的入口处。建立一个模型来确定一个容易造成阻塞的通行税收费广场中应该部署的最优的收费亭数量。需要保证每一个进入收费广场的交通路线都仅有一个收费亭。与当今的实践相比较，在什么条件下，这或多或少有效。注意：最佳的定义由你自己决定。