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2014美赛建模mcm及翻译


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?

问题一:除了超车的靠右行驶规则 在右行驾驶国家(即,美国,中国和大多数其他国家,除了英国,澳大利亚,和一些前英国 殖民地) , 多车道高速公路通常使用一个规则, 要求司机开车在最右边的车道, 除非超车 (超 车:移动一个车道的左侧,通过,并回到他们原来的车道)。 建立并分析了一个数学模型来分析这一规则在轻、 重交通的性能。 你可能要检查的交通流量 和安全性之间的权衡,作用下或在车速限制(即,太低或太高速度的限制),和/或其他可 能不会明显影响这一问题的声明。 这条规则促进交通流更有效?如果不是, 建议和分析的替 代品(包括可能提出目前没有的新规则)可能促进更大的交通流量,安全性,和/或其你认 为重要的因素。 在驾驶汽车在左边的规范国家, 认为是否您的解决方案可以通过一个简单的改变, 或额外的 要求,来适应需求。 最后, 规则如上依赖于人对于规则的服从性。 如果在同一车道形式的车辆完全被智能化系统 控制。可能是嵌入道路系统,也可能通过嵌入机动车系统来实现。如果可实现,对你之前的 分析有多大程度的影响?

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.
问题 B:大学的传奇教练 体育画报,一个体育爱好者的杂志,是寻找“最好的大学教练”,上个世纪的男性或女性。建 立了一个数学模型来选择最佳的大学教练或教练们(过去或现在),在大学曲棍球或足球, 曲棍球,棒球或垒球,篮球,足球的男女性教练之间。选取不同的时间线视角会对你的分析 造成影响么?比如,在 1913 与 2013 执教有不同么?讨论你的模型,跨性别跨运动种类。 在每 3 个不同的体育项目中给出你模型的 top 5 教练们。


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