2014美赛建模AB题-英文版
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2014-02-08
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2014 MCM
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?
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.
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