数学名著译丛2014年美国大学生数学建模竞赛题目及翻译

2020年11月19日发(作者：尤珍)
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.