2014年美国大学生数学建模竞赛题目及翻译范文

第一篇：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。

第二篇：2014年 美国大学生数学建模 题目 翻译专题

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 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 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?

在一些国家在右侧驾驶汽车是一种惯例（比如像美国，中国和其他大部分国家，除了英国，澳大利亚，和一部分之前英国殖民的国家）多车道高速公路普遍建立起这样的规则，那就是要求司机在最右边的车道驾驶汽车，除非他们要超越其它车辆，这种情况下他们要移动到左侧车道，超车，然后回到他们原先的车道。

建立和总结一个数学模型去分析这一规则在流畅和拥堵情况下的交通性能，你不妨检查交通流量和安全，过少或过多限速的作用（即，过低或过高的车速限制）和/或不能在问题陈述中被清楚表达的其它因素。这种规则是否能有效的促进交通流量的提升？如果不是，给出建议并分析取而代之的方法（包括当前没有的规则），此方法会促进更多的交通流量，安全性，和/或包括您认为重要的其他因素。

在一些国家，汽车行驶在左边是常态，阐述您的解决方案是否能可行如果仅仅在方向上作出改变，或者是需要额外的要求。

最后，如上所述的规则依赖于人的判断为标准。如果在相同的道路运输车辆的完全是一个智能系统的控制下，系统要么是在部分的道路网络中，要么是嵌入到所有使用高速公路的汽车上。什么样的系统规模会改变你之前的分析。

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 the best 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 that sports fans will understand.体育画报，是一个为体育爱好者打造的杂志，它正在寻找上个世纪中男性或者女性的“全天候最好的大学教练”。建立一个数学模型，从，负责担任例如如下体育活动（高校曲棍球、场地曲棍球、足球、棒球、垒球、篮球、橄榄球）的男性或者女性教练中选择最佳大学教练或教练团体（过去或者现在的），在你的分析中在时间方面是否会造成一些不同，也就是说1913年的训练和2013年的训练有何不同。要求清楚的阐述你评估的指标。讨论你的模型是怎样应用在常见的两个性别都有的运动和全部可能的体育运动中。要求展示用你模型评估出的在3个不同运动中的前5名的教练。

除了MCM的格式和要求，为体育画报准备一份1-2页的文章，解释你的结果并包括能让您的体育爱好者都明白的、能有通俗易懂解释的数学模型。迷都明白的数学模型的非技术性解释。

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：美国数学建模题目2017至2017翻译

美国数学建模题目2017至2017翻译

篇一：2017年建模美赛C题带翻译

Problem C: “Cooperate and navigate”

Traffic capacity is limited in many regions of the United States due to the number of lanes of roads.For example, in the Greater Seattle area drivers experience long delays during peak traffic hoursbecause the volume of traffic exceeds the designed capacity of the road networks.This is particularlypronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interestfor this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highwayswithout increasing number of lanes or roads.The behavior of these cars interacting with the existingtraffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving,cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties.(Seethe provided map and Excel spreadsheet).In particular, how do the effects change as thepercentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there atipping point where performance changes markedly? Under what conditions, if any, should lanes bededicated to these cars? Does your analysis of your model suggest any other policy changes?

Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/oraverage traffic volume, and percentage of vehicles using self-driving, cooperating systems.Yourmodel should address cooperation between self-driving cars as well as the interaction between self-driving and non-self-driving vehicles.Your model should then be applied to the data for the roads ofinterest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to theGovernor’s office, and your solution(not to exceed 20 pages)for a maximum of 23 pages.Note: Theappendix and references do not count toward the 23 page limit.Some useful background information:

On average, 8% of the daily traffic volume occurs during peak travel hours.? The nominal speed limit for all these roads is 60 miles per hour.? Mileposts are numbered from south to north, and west to east.? Lane widths are the standard 12 feet.? Highway 90 is classified as a state route until it intersects Interstate 5.? In case of any conflict between the data provided in this problem and any other source, use thedata provided in this problem.Definitions:

milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”

由于道路的数量，美国许多地区的交通容量有限。例如，在大西雅图地区，由于交通量超过道路网络的设计容量，司机在交通高峰时段经历长时间的延误。这在5号，90号和405号州际公路以及520号国道，特别关注这个问题的道路上尤其明显。

自动驾驶，合作车已被提出作为增加公路的能力而不增加车道或道路的数量的解决方案。在这一点上，这些汽车与现有交通流和彼此交互的行为尚未被很好地理解。

华盛顿州州长要求分析允许在Thurston，Pierce，King和Snohomish县的上述道路上自行驾驶合作汽车的影响。（见提供的地图和Excel电子表格）。特别是，自动驾驶汽车的百分比从10％增加到50％到90％，效果如何变化？平衡是否存在？是否有性能变化明显的临界点？在什么条件下，如果有的话，应该有车道专用于这些车？您对模型的分析是否表明有任何其他政策变化？

您的答案应包括对车道数量，峰值和/或平均交通量的交通流量的影响的模型，以及使用自动驾驶，合作系统的车辆的百分比。你的模型应该解决自驾车之间的合作以及自驾车和非自驾车之间的相互作用。然后，您的模型应用于附带的Excel电子表格中提供的感兴趣道路的数据。

您的MCM提交应包括1页摘要表，1至2页总督办公室信，以及您的解决方案（不超过20页），最多23页。注意：附录和参考文献不计入23页的限制。一些有用的背景信息：

平均而言，每天交通量的8％发生在高峰旅行时间。

?所有这些道路的名义速度限制为每小时60英里。

?里程数从南到北，从西到东。

?车道宽度为标准12英尺。

?高速公路90被分类为状态路线，直到它与州际5相交。

?如果此问题中提供的数据与任何其他源出现冲突，请使用此问题中提供的数据。定义：

milepost：道路上的标记，用于测量距离路线或天体边界的距离（以英里为单位）。平均每日交通量：在road.interstate上行驶的平均每天的汽车数量：有限访问高速公路，国家系统的一部分。

国家路线：可能受限或不受限制的国家公路。

路由ID：高速公路的编号。

增加方向：N-S道路北行，E-W道路东行。

下降方向：N-S道南行，E-W道西行。

篇二：2017美赛D题中文翻译

D题中文翻译：

问题D：在机场安全检查站优化乘客吞吐量

继2001年9月11日美国发生恐怖袭击事件后，全世界的机场安全状况得到显着改善。机场有安全检查站，在那里，乘客及其行李被检查爆炸物和其他危险物品。这些安全措施的目的是防止乘客劫持或摧毁飞机，并在旅行期间保持所有乘客的安全。然而，航空公司有既得利益，通过最小化他们在安全检查站排队等候并等待他们的航班的时间，为乘客保持积极的飞行体验。因此，在希望之间存在最大化安全性同时最小化对乘客的不便的张力。

在2016年，美国运输安全局（TSA）受到了对极长线路，特别是在芝加哥的奥黑尔国际机场的尖锐批评。在此公众关注之后，TSA投资对其检查点设备和程序进行了若干修改，并增加了在高度拥堵的机场中的人员配置。虽然这些修改在减少等待时间方面有一定的成功，但TSA在实施新措施和增加人员配置方面花费了多少成本尚不清楚。除了在O'Hare的问题，还有在其他机场，包括通常有短的等待时间的机场不明原因和不可预测的长线的事件。检查点线路的这种高差异对于乘客来说可能是极其昂贵的，因为他们决定在不必要地早到达或可能丢失他们的预定航班之间。许多新闻文章，包括[1,2,3,4,5]，描述了与机场安全检查站相关的一些问题。

您的内部控制管理（ICM）团队已经与TSA签订合同，审查机场安全检查站和人员配置，以确定可能干扰乘客吞吐量的瓶颈。他们特别感兴趣的创意解决方案，既增加检查点吞吐量，减少等待时间的方差，同时保持相同的安全和安全标准。

美国机场安全检查点的当前流程如图1所示。

?区域A：

o乘客随机到达检查站，并等待队列，直到安全人员可以检查他们的身份证明和登机文件。

?区域B：

o然后乘客移动到打开的筛选线的后续队列;根据机场的预期活动水平，或多或少的线路可能开放。

o一旦乘客到达这个队列的前面，他们准备所有的物品用于X射线检查。乘客必须用液体去除鞋子，皮带，夹克，金属物体，电子产品和容器，将它们放置在单独的X射线箱中;笔记本电脑和一些医疗设备也需要从其袋中取出并放置在单独的容器中。

o他们的所有物品，包括包含上述物品的箱子，由传送带通过X光机移动，其中一些物品被标记，供安全人员（D区）进行额外的搜索或筛选。

o同时乘客通过毫米波扫描仪或金属探测器进行处理。

o未能通过此步骤的乘客接受安全官员（D区）的轻击检查。

?C区：

o乘客然后前进到X射线扫描仪另一侧的传送带，收集他们的物品并离开检查站区域。

图1：TSA安全筛选过程的图示。

大约45％的乘客报名参加一个称为预检查信任旅行者的计划。这些乘客支付85美元，接受背景调查，并享受五年的独立筛选程序。尽管事实上更多的乘客使用预检查过程，但是每三条常规车道通常有一个预检查车道打开。预检查乘客和他们的行李经过相同的筛选过程，经过一些修改，以加快筛选。预检查乘客还必须移除扫描用的金属和电子物品以及任何液体，但不需要去除鞋子，皮带或灯罩;他们也不需要从他们的包里删除他们的电脑。

收集了关于乘客如何进行安全检查过程的每个步骤的数据。

您的特定任务是：

一个。开发一个或多个模型，允许您通过安全检查点探索乘客流，并识别瓶颈。清楚地确定当前流程中存在哪些问题区域。

b。对当前流程开发两个或多个潜在修改，以提高旅客吞吐量并减少等待时间的差异。对这些更改进行建模，以演示修改如何影响流程。

C。众所周知，世界上不同的地方都有自己的文化规范，塑造了地方社会互动的规则。考虑这些文化规范如何影响你的模型。例如，美国人以深为尊重和优先考虑别人的个人空间而闻名，并且在他人面前有一个社会歧视“切割”。同时，瑞士人以集体效率为重点，中国人以优先个人效率而闻名。考虑文化差异如何影响乘客的过程通过检查点作为敏感性分析的方式。您应用于敏感性分析的文化差异可以基于真实的文化差异，或者您可以模拟与任何特定文化（例如，较慢的旅行者）无关的不同旅行者风格。安全系统如何以加快乘客吞吐量并减少差异的方式来适应这些差异？

d。根据您的模型为安全管理器提出政策和程序建议。这些策略可以是全球适用的，或者可以针对特定文化和/或旅行者类型来定制。

除了开发和实施您的模型来解决这个问题，您的团队还应该验证您的模型，评估优势和弱点，并提出改进建议（未来工作）。

您的ICM提交应包含1页的摘要表，您的解决方案不能超过20页，最多21页。注意：附录和参考文献不计入20页的限制。

篇三：2017年建模美赛B题带翻译

Problem B: Merge After Toll

Multi-lane divided limited-access toll highways use “ramp tolls” and “barrier tolls” to collect tolls from motorists.A ramp toll is a collection mechanism at an

entrance or exit ramp to the highway and these do not concern us here.A barrier toll is a row of tollbooths placed across the highway, perpendicular to the

direction of traffic flow.There are usually(always)more tollbooths than there are incoming lanes of traffic(see former 2005 MCM Problem B).So when exiting the tollbooths in a barrier toll, vehicles must “fan in” from the larger number of tollbooth egress lanes to the smaller number of regular travel lanes.A toll plaza is the area of the highway needed to facilitate the barrier toll, consisting of the fan-out area before the barrier toll, the toll barrier itself, and the fan-in area after the toll barrier.For example, a three-lane highway(one direction)may use 8

tollbooths in a barrier toll.After paying toll, the vehicles continue on their journey on a highway having the same number of lanes as had entered the toll plaza(three, in this example).Consider a toll highway having L lanes of travel in each direction and a barrier toll containing B tollbooths(B > L)in each direction.Determine the shape, size, and merging pattern of the area following the toll barrier in which vehicles fan in from

B tollbooth egress lanes down to L lanes of traffic.Important considerations to incorporate in your model include accident prevention, throughput(number of vehicles per hour passing the point where the end of the plaza joins theL outgoing traffic lanes), and cost(land and road construction are expensive).In particular, this problem does not ask for merely a performance analysis of any particular toll plaza design that may already be implemented.The point is to determine if there are better solutions(shape, size, and merging pattern)than any in common use.Determine the performance of your solution in light and heavy traffic.How does your solution change as more autonomous(self-driving)vehicles are added to the traffic mix? How is your solution affected by the proportions of conventional(human-staffed)tollbooths, exact-change(automated)tollbooths, and electronic toll collection booths(such as electronic toll collection via a transponder in the vehicle)?

Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the New Jersey Turnpike Authority, and your solution(not to exceed 20 pages)for a maximum of 23 pages.Note: The appendix and references do not count toward the 23 page limit.多车道有限接入收费公路使用“坡道收费”和“障碍收费”

收取驾驶人士的收费。斜坡收费是一个收集机制

入口或出口匝道到高速公路，这些不关心我们在这里。障碍

收费是一排收费站横跨高速公路，垂直于

交通方向。通常（总是）更多的收费站比

（见2005年前MCM问题B）。所以退出时

收费站在通行费，车辆必须“扇入”从大量

收费站出口车道到较少数量的常规旅行车道。收费广场 是高速公路所需的便利通行费的区域，包括

障碍物前的扇出区域，收费口障本身以及后面的扇入区域 收费屏障。例如，三车道公路（一个方向）可以使用8 收费站。在支付费用后，车辆继续他们的旅程

在具有与进入收费广场相同数量的车道的高速公路上

（在本示例中为三个）。

考虑在每个方向上具有L个行驶车道的收费高速公路和障碍收费（B> L）。确定形状，大小和

合并模式的区域跟随收费障碍车辆扇入

B收费站出口线下至L车道的交通。重要注意事项

包括在您的模型包括事故预防，吞吐量（车辆每小时通过广场的末端加入L的点

出行车道）和成本（土地和道路建设昂贵）。在 特别的，这个问题不要求任何的性能分析

特定的收费广场设计可能已经实施。关键是要

确定是否有更好的解决方案（形状，大小和合并模式）任何常见的使用。

确定您的解决方案在轻和重的流量的性能。如何

您的解决方案随着更多自主（自驾）车辆添加而改变

交通混合？你的解决方案如何影响常规的比例

（人员）收费站，精确更换（自动）收费站和电子

收费亭（例如通过转发器在电子收费站收集

车辆）？

您的MCM提交应包含1页的摘要表，1-2页

给新泽西州收费公路局的信，以及您的解决方案（不超过20 页面），最多23页。注意：附录和参考文献没有

计数到23页的限制。

第五篇：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