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2015年全美数学建模A和B题
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【HIMCM 2014美国中学生数学建模竞赛试题】含翻译
【HIMCM 2014美国中学生数学建模竞赛试题】 ProblemA: 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). Thedistance a passenger has to walk to exit the train area is quite long. Eachtrain car has only two exits, one near each end so that the cars can carry asmany people as possible. Each train car has a center aisle and there are twoseats on one side and three seats on the other for each row of seats.To exit atypical station of interest, passengers must exit the car, and then make theirway to a stairway to get to the next level to exit the station. Usually thesetrains are crowded so there is a “fan” of passengers from the train trying toget up the stairway. The stairway could accommodate two columns of peopleexiting to the top of the stairs.Most commuter train platforms have two tracksadjacent to the platform. In the worst case, if two fully occupied trains arrivedat the same time, it might take a long time for all the passengers to get up tothe main level of the station.Build a mathematical model to estimate the amountof time for a passenger to reach the street level of the station to exit thecomplex. Assume there are n cars to a train, each car has length d. The lengthof the platform is p, and the number of stairs in each staircase is q. Use yourmodel to specifically optimize (minimize) the time traveled to reach streetlevel 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。大多数火车很长(也许10个或更多的汽车长)。乘客走到出口的距离也很长，有整个火车区域。每个火车车厢只有两个出口,一个靠近终端, 因此可以携带尽可能多的人。每个火车车厢有一个中心过道和过道两边的座椅，一边每排有两个座椅，另一边每排有三个座椅。走出这样一个典型车站,乘客必须先出火车车厢,然后走入楼梯再到下一个级别的出站口。通常情况下这些列车都非常拥挤,有大量的火车上的乘客试图挤向楼梯，而楼梯可以容纳两列人退出。大多数通勤列车站台有两个相邻的轨道平台。在最坏的情况下,如果两个满载的列车同时到达,所有的乘客可能需要很长时间才能到达主站台。建立一个数学模型来估计旅客退出这种复杂的状况到达出站口路上的时间。假设一列火车有n个汽车那么长,每个汽车的长度为d。站台的长度是p，每个楼梯间的楼梯数量是q。使用您的模型具体来优化(减少)前往主站台的时间，有如下要求: Requirement 1. One fully occupied train*s passengers to exit the train,and ascend the stairs to reach the street access level of the station.要求1.一个满载乘客的火车，所有乘客都要出火车。所有乘客都要出楼梯抵达出主站台的路上。 Requirement 2. Two fully occupied trains* passengers (all passengersexit onto a common platform) to exit the trains, and ascend the stairs to reachthe street access level of the station.要求2.两个满载列车的乘客都要出车厢(所有乘客出到一个公用站台), 所有乘客都要出楼梯抵达出主站台的路上。 Requirement 3. If you could redesign the location of the stairwaysalong the platform, where should these stairways be placed to minimize the timefor one or two trains* passengers to exit the station?要求3.如果你能重新设计楼梯沿着站台的位置，那么这些楼梯应放置在哪,以缩短一列或两列火车的乘客出站所用的时间? Requirement 4. How does the time to street level vary with the number sof stairways that one builds?要求4.乘客到达出主站台的路上所用的时间跟构建楼梯的台阶数有怎样的关系? Requirement 5. How does the time vary if the stairways can accommodatek people, k an integer greater than one?要求5.如果楼梯可以容纳K个人，那么时间会如何变化？（k是大于1的整数） Inaddition to the HiMCM format, prepare a short non-technical article to thedirector of transportation explaining why they should adopt your model toimprove exiting a station.除了要遵循HiMCM规范，准备一个简短的非技术物品向运输主管解释为什么他们应该采取你的模型来提高出站效率。 ProblemB: The Next Plague?In 2014, the worldsaw the infectious Ebola virus spreading in western Africa. Throughout humanhistory, epidemics have come and gone with some infecting and/or killingthousands and lasting for years and others taking less of a human toll. Somebelieve these events are just nature’s way of controlling the growth of aspecies while others think they could be a conspiracy or deliberate act tocause harm. This problem will most likely come down to how to expend (or notexpend) scarce resources (doctors, containment facilities, money, research,serums, etc…) to deal with a crisis.问题二:下一场瘟疫?在2014年，世界看到了感染埃博拉病毒在西非蔓延。纵观人类历史，流行病来了又走，有些感染带到来然后杀死成千上万的人并且持续数百年，另外一些流行病导致少量的人员伤亡的。一些人认为，这些事件只是大自然控制物种的生长方式，而其他人则认为，这可能是一个阴谋，或者是故意行为造成伤害。这个问题很可能会归咎到如何花费（或不花费）稀缺资源（医生，防护设施，资金，科研，精华素等），以应对危机。 SectionA:A routine humanitarian mission on an islandin Indonesia reported a small village where almost half of its 300 inhabitantsare showing similar symptoms. In the past week, 15 of the “infected” have died.This village is known to trade with nearby villages and other islands. Yourmodeling team works for a major center of disease control in the capital ofyour country (or if you prefer, for the International World HealthOrganization).A部分：一个常见的人道主义报道：在印度尼西亚的一个岛上的一个小村庄，那里的300名居民中几乎有一半都出现了类似的症状。在过去的一周，15个“传染”着已经死亡。这个村与附近的村庄和其他岛屿进行交易而出名。您的建模团队工作的疾病控制的一个主要中心是在贵国的首都（或者，如果你喜欢，可以说是国际世界卫生组织）。Requirement 1: develop amathematical model that performs the following functions as well as how/when tobest allocates these scarce resources and…- Determines and classifies the type and severity of the spread of the disease- Determines if an epidemic is contained or not - Triggers appropriate measures( when to treat, when to transport victims, whento restrict movement, when to let a disease run its course, etc…) to contain adisease.Note: While you may want to start with the well-known “SIR” family or modelsfor parts of its problem, consider others,modifications to the SIR, multiple models,or creating your own.要求1：建立一个数学模型执行以下功能，包括如何/何时最佳分配这些稀缺资源...- 确定和分类的疾病传播的类型和严重程度- 或者，确定疫情是否受控（爆发）- 引发适当的措施（什么时候治疗，什么时候运送受害者，什么时候限制转移，什么时候让疾病听其自然，等等）去控制某种疾病。注意：此时你可能要开始使用著名的“SIR”模型或该模型的部分，或者考虑别的修正后的SIR模型，多个模型，或者创建自己的模型。 Requirement2: Based on theinformation given, your model, and the assumptions your team has made, whatinitial recommendations does your team have for your country center for diseasecontrol? (Given 3-5 recommendations with
justifications)Additional Situational Information: Amulti-national research team just returned to your country capital afterspending7 days gathering information in theinfected village.要求2：根据所给出的信息、你的模型以及你的团队所做的假设，你的团队需要为你的国家疾病预防控制中心给出哪些初步建议？（3-5给出建议，理由）附加态势信息：多国研究小组花7天聚集在村里被感染后的信息返回给你的国家首都。 Requirement3: You can ask them upto 3 questions to improve your model. What would your ask and why?
Additional Situational Information: The mulit-national research team concludedthat the disease:-Appears to spread through contact with bodily fluids of an infected person-The elderly and children are more likely to die if infected-A nearby island is starting to show similar signs of infection-One of the researchers that returned to your capital appears infected要求3：你可以要求问他们3个问题，以改进你的模型。你需要问什么问题和原因？附加情境信息：多国研究小组得出结论一致认为，本病：-出现传播是通过与受感染者的体液接触-如果感染，老人和儿童更容易感染-附近的岛上开始出现类似感染的迹象-一个研究者返回到贵国首都出现感染Requirement 4:How does theadditional information above change/modify your model?要求4：如何根据以上的附加信息改版/修改模型？Requirement 5:Write a one-pagesynopsis of your findings for your local non-technical news outlet.要求5：写下你的发现，为当地的非技术广播电台(或电视台)提供新闻稿。
大自然的搬运工。。。。
神秘的搬运工系列_(:3」∠)_
你觉得问题4,5我们翻译的对吗？是改变阶梯数还是改变楼梯数？
呵呵 比前年的难多了
有神已获得这个问题的获奖论文吗？
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