周易术数学2014美国大学生数学建模竞赛题目(含翻译)

2020年11月19日发(作者：戴彬元)
仅供参考
Teams (Student or Advisor) are now required to submit an electronic copy
(summary sheet and solution) of their solution paper by email too
solutions@ as a Word or PDF attachment. Your email MUST be
received at COMAP by the submission deadline of 8:00 PM EST, February
10, 2014. Note you will not receive an auto response.
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COMAP your control number
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Click here to download a PDF of the complete contest instructions.
Click here to download a copy of the Summary Sheet in Microsoft Word format.
*Be sure to change the control number and problem select before printing
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Teams are free to choose between MCM Problem A, MCM Problem B or ICM
Problem C.
COMAP Mirror Site: For more in:
/undergraduate/contests/mcm/
MCM: The Mathematical Contest in Modeling

ICM: The Interdisciplinary Contest in Modeling

2014 Contest Problems

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.


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