2014 MCM Problems
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.
在一些以行车靠右为规则的国家中（比如美国、中国以及除了大不列颠、澳大利亚和一些前英属殖民国家以外的其他国家），多行道的高速公路经常采用要求驾驶人在除超车以外时都靠右行驶的交通规则。
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.
1、请你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堵塞条件下的表现。
你可能乐意在交通流通和安全性、过低或者过高的限速（即速度限制太高或者太低）、以及其他可能不能从这个问题的陈述中直接发现的因素中找到一个平衡。
这个规则是否有效地促进了交通更好地流通？如果没有，请你提出并分析可能促进交通流通、保证交通安全、改善其他你认为重要的因素的其他规则。
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.
2、在一些以行车靠左为准则的国家中，讨论你的解决方案是否可以在仅仅改变方向时被应用，或者是否需要额外的要求？
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?
3、最后，上面陈述的规则是基于人们对于是否遵守规则的主观判断的。
如果现在在同一条道路上的车辆交通完全在一个智能的系统（系统被内嵌于所有车辆都使用道路的设计中，系统是路网的一部分）的控制之下，那么这会在何种程度上改变你的早期预测的结果？
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
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.
一个运动发烧友的专属杂志Sports Illustrated正在寻找上一个世纪最好的大学教练（无论男女），1、请你们建立一个数学模型来遴选最好的几位college hockey或field hockey, 足球，棒球或垒球，篮球，或者橄榄球教练，无论男女。
2、在你的分析中使用的时间段是否会对结果造成影响？比如：1913年的训练是否和2013年的训练不同？请清楚地表述你们评估度量的标准。
3、并讨论你们的模型如何能被普遍的应用在两性和所有可能的运动项目中。
4、最后，请你用你们的模型给出三个不同运动的前五位顶尖教练。
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.。