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[建模教程] 2014美赛题目翻译

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	奋斗 2014-4-11 20:50

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2014美赛题目翻译

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

In countries where driving automobiles on the rightis the rule (that is, USA, China and most other countries except for GreatBritain, Australia, and some former British colonies), multi-lane freewaysoften employ a rule that requires drivers to drive in the right-most laneunless they are passing another vehicle, in which case they move one lane tothe left, pass, and return to their former travel lane.

Build and analyze a mathematical model to analyzethe performance of this rule in light and heavy traffic. You may wish toexamine tradeoffs between traffic flow and safety, the role of under- orover-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 problemstatement. Is this rule effective in promoting better traffic flow? If not,suggest and analyze alternatives (to include possibly no rule of this kind atall) that might promote greater traffic flow, safety, and/or other factors thatyou deem important.

In countries where driving automobiles on the leftis the norm, argue whether or not your solution can be carried over with asimple change of orientation, or would additional requirements be needed.

Lastly, the rule as stated above relies upon humanjudgment for compliance. If vehicle transportation on the same roadway wasfully under the control of an intelligent system – either part of the roadnetwork or imbedded in the design of all vehicles using the roadway – to whatextent would this change the results of your earlier analysis?

问题A：超车之外靠右行原则

在一些开车必须靠右行驶的国家（比如：美国，中国，以及其他除了英国，澳大利亚，和一些前英国殖民地的国家），行驶在多车道高速路必须遵循一个规则，那就是要求驾驶员在超车之外的情况下，必须在最靠右的车道行驶，超车时，他们向左变道，超车，然后再回到之前行驶的车道。

构建一个数学模型来分析该规则在车流量很少和很大的时候的执行情况。你最好能考察车流量与安全的之间的相互关系，过低或是过量的速度限制的作用（速度设置过低或是过高），以及/或者其他在该问题陈述中没有明确提到的因素。该原则是否能有效促进更好的车流量？如果无效，请建议和分析其他更有助于提高车流量、安全、以及其他你认为重要的因素的其他方案（可以完全不包括该原则）。

在开车靠左行的国家，讨论一下你的方案在经过对方向的简单修改之后或是添加额外的要求之后是否也适用。

最后，以上原则取决于人们遵循交通规则的判断力。如果道路上的车流完全在智能系统（要么是道路体系的一部分，要么是包含在使用道路的所有车辆的设计之中）的控制之下，该改变在多大程度上会影响你先前分析的结果？

PROBLEM B: College CoachingLegends

Sports Illustrated, a magazine for sportsenthusiasts, is looking for the “best all time college coach” male or femalefor the previous century. Build a mathematical model to choose the best collegecoach or coaches (past or present) from among either male or female coaches insuch sports as college hockey or field hockey, football, baseball or softball,basketball, or soccer. Does it make a difference which time line horizon thatyou use in your analysis, i.e., does coaching in 1913 differ from coaching in2013? Clearly articulate your metrics for assessment. Discuss how your modelcan be applied in general across both genders and all possible sports. Presentyour 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 resultsand includes a non-technical explanation of your mathematical model that sportsfans will understand.

问题B: 大学教练传说

《体育画报》，一本体育爱好者的杂志，正在寻找上世纪 “最好的大学教练”，包括男性和女性。建立一个数学模型以从诸如大学曲棍球，曲棍球，橄榄球，棒球，垒球，篮球，或足球等运动的男性或女性教练中选出最好的一个教练或几个教练（过去的或现在的）。分析中使用的时间分界线是否有影响？即在1913执教和在2013年执教有不同吗？清晰地表达你们模型中的评判标准。讨论你们的模型如何能广泛地应用于两种性别及所有可能的体育运动。分别选出你模型中3种不同运动的前5位教练。

除了MCM格式及要求，准备一篇1-2页的文章给《体育画报》以解释你们的结论并包括一份能让体育迷们看懂的对你们数学模型的非技术性解释。

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