2018第七届数学中国数学建模国际赛赛题.rar
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Problem A(MCM)
Aerial Refueling Flight Plan
Residents on a small island in the central Pacific Ocean are trapped by natural
disasters. Rescuers need to dispatch a light aircraft to transport a small amount
of emergency medicine to the island and transport a seriously wounded person
to the medical base for assistance. The island has an unattended airstrip that
can be used, but no aircraft or fuel reserves. The aircraft departs from the base
that is 615 nautical miles away from the island. The aircraft has a maximum
range of 680 nautical miles under normal load conditions. In order to return,
we must carry out aerial refueling.
This type of aircraft has the ability to receive oil in the air. After a simple
modification, the same type of aircraft can perform the task of partner air
refueling, that is, to distribute its own fuel to partners. The maximum fuel
capacity of the type of aircraft is 155kg. After the installation of aerial refueling
equipment, the maximum oil load is increased to 170kg, but other loads cannot
be carried. The base has a fleet of aircraft and sufficient equipment, which can
be converted into tankers in a short time.
Questions:
1. Please design a viable air refueling program to enable rescuers to complete
the task.
2. Air refueling is a high-risk operation and there is a possibility of failure.
Transport and refueling aircraft also have a probability of failure. Please
consider the probability of failure in each part of the work. When we need
to ensure the total success rate, please give the corresponding optimal
solution.
Problem B(MCM)
The Match Arrangement of FIFA World Cup
There are 32 teams participating in the final stage of the FIFA World Cup.
But starting in 2026, the number of teams will increase to 48. Due to limited
time, one team can’t play too many games. Therefore, FIFA proposes to change
the format. Each group will be changed from 4 teams to 3 teams, the first two
teams are eligible to enter the second round. In order to keep the excitement of
the game, we do not want to have too many games whose result does not affect
the team’s qualifying. For the fairness of the competition, we do not want to
have too many games that the collusion is beneficial to both sides. We also hope
that the final result of the competition should not contain the factor of luck too
much. Please analyze this issue, and give the best competition arrangement
system. The final result needs to include answers to the following questions:
1. The number of teams in each group and who can enter the second round.
2. The method for arranging the order of the matches in advance.
3. The impact of the final match results on FIFA Coca-Cola ranking.
Problem C(ICM)
The Impact of Bike Sharing on Urban Transportation
Shared bicycles have changed the urban traffic conditions in many cities, and
many large cities have introduced shared bicycles to solve traffic problems. We
need to quantitatively assess the impact of shared bicycles on urban traffic, as
well as the associated economic, social and environmental impacts. The key to
this problem is to establish a reasonable model to predict people’s traffic behavior
if there is no shared bicycles in a city. For example, comparing all travels
using shared bicycles with driving cars is not credible. As an attachment to the
paper, we need to submit a formal report to the transportation department on
the changes that the shared bicycle caused to the city. You can use data from
the citibike in New York, or collect data from other cities.
The data of the citibike and traffic in New York includes but not limited to
the following links:
https://www.citibikenyc.com/system-data/operating-reports
www.nyc.gov/html/dot/downloads/pdf/mobility-report-2016-print.pdf
www.nyc.gov/html/dot/downloads/pdf/mobility-report-2016-print.pdf
https://opendata.cityofnewyork.us
https://github.com/fivethirtyeight/uber-tlc-foil-response
http://web.mta.info/developers/turnstile.html
Problem D(ICM)
Speed Kills Love
In the age of online dating there are more romantic options than there are fish
in the, well, you know. On the appropriately named site Plenty of Fish, for
instance, you can pore over profiles of hundreds or thousands of potential mates
before deciding which ones to contact. Such unfettered choice means a better
shot at true love—or so many daters believe. The more options you have, the
assumption goes, the more likely you are to find the one who truly suits you.
Yet many daters are finding that less romantic choice yields top-notch results
without all the angst. EHarmony is one of the largest dating sites in the United
Stateswhich has its customers fill out a detailed compatibility survey, then sends
them a restricted number of matches, typically anywhere from a few to a dozen
or so at a time. The success rate of marriage is relatively high. Studies find
speed daters often choose partners on the basis of appearance. When presented
with fewer choices, daters are likely to spend time reflecting on a person’s deeper
qualities.
Barry Schwartz, Dorwin Cartwright Professor of Social Theory and Social
Action at Swarthmore College, has spent years arguing that limiting our options
consistently leads to better outcomes. He thinks too much choice overwhelms us
and makes us unhappy—a phenomenon he calls the paradox of choice. Endless
choices, Schwartz says, are more stultifying than gratifying. In one canonical
experiment dubbed “the jam study,” grocery-store shoppers scanning 24 different
gourmet jams were less likely to make a purchase than shoppers who
looked at only six jams. The shoppers choosing from a wider selection were
also unhappier with the jam they’d bought. The problem, Schwartz explains,
is that when you have more options, you tend to put more pressure on yourself
to make the perfect choice—and you feel more let down when it doesn’t turn
out to be perfect, after all. “Even when you choose well, you end up disappointed,”
Schwartz says. “You’re convinced that even though you did well, you
should have done better.” Based on work by psychologists Daniel Kahneman
and Amos Tversky, who have shown bad feelings about losses are stronger than
good feelings we have about gains, Schwartz argues that as you’re presented
with countless choices, your pleasure at the prospect of more options is canceled
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out by the anticipated loss of making a wrong choice.
If you do persist in choosing someone from a large array, not only will you
come away less satisfied—you’ll probably make a worse choice. When online
daters had more search options in a University of Taiwan study, they spent less
time considering each possibility and found it harder to sort the good prospects
from the bad ones. Stretching your cognitive capacity too thinly, the researchers
explain, tends to hamstring you on irrelevant details and distract you from the
criteria you consider most important. That suggests that in order to assess
the qualities that matter—which, for most people, are things like a partner’s
honesty, his dependability, her sense of humor—you need to go deeper in your
search, not wider.
Does that mean you should opt for the expert-guided, custom-flight approach
proffered by vendors like eHarmony? Quite a few daters appreciate curated
selection enough to be willing to pay extra for it. Suppose you are a partner of
an online dating website. You should finish the following tasks:
1. Create an objective quantitative algorithm or set of algorithms to complete
online dating matches by few options .
2. Use your algorithm(s) to develop your ”Top 20 Recommended Daters”
list. And give a more suitable estimate of an ideally sized choice set when
it comes to dating—one large enough to include variety and depth, yet
small enough that you can fairly weigh each prospect’s potential without
tripping your brain’s overload switch.
3. Give the design of information forms that users need to fill out for your
website. Study the relationship between forms design and success rate of
online dating.
4. Write a one-page non-technical News Release describing your new algorithm,
results, and website.
Your submission should consist of:
• One-page Summary Sheet,
• One-page News Release,
• Your solution of no more than 30 pages, for a maximum of 32 pages with
your summary and news release.
Note: Reference list and any appendices do not count toward the 32-page limit
and should appear after your completed solution.
第七届“认证杯”数学中国数学建模国际赛赛前通知
一、开卷、交卷时间的规定
第七届“认证杯”数学中国数学建模国际赛按照美国大学生数学建模竞赛的程序和规则进行,采用通讯的方式,网上报名。报名截止时间为北京时间2018年11月29日零时,报名截止时间后不能再提交报名或者修改报名信息。29日上午8:00准时开始竞赛,并在网上公布赛题,网上报名及公布赛题网站地址: 国际赛官网: http://mcm.tzmcm.cn/shiti.html 各参赛队若有疑问,可发邮件到: service@tzmcm.cn 相同的竞赛时间是保证竞赛公正性的一个重要方面,各校各队都应准时交卷。原则上迟交的赛卷不参加评审,请各参赛队、教练高度重视。由于撰写、编辑、拷盘论文需要一定的时间,其中还有很多的偶然因素,请各参赛队务必留足相关时间,教练员有责任督促同学,尤其是首次参赛的同学掌握好时间。赛题未全部完成的论文只要准时交卷一样可以参加评审。 竞赛截止时间统一规定为北京时间2018年12月03日上午8:00,截止时间之后所有参赛队不能再修改论文,需要在8:30之前将电子版论文发到指定的邮箱(不需要邮寄纸质论文)。
二、论文上交办法 本次比赛结束时间为北京时间2018年12月03日上午8:00,统一上交电子档论文(不需要提交纸质档论文)。 1.电子档上交方式: 各参赛队需要 在2018年12月03日上午8时前将电子档(最终稿,若多次发送不完全版本或非最终稿将取消评奖资格,有特殊情况请注明详细原因)以邮件方式发送到以下邮箱: solutions@tzmcm.cn邮件主题请注明参赛队号及所选的题目号,如1001队选择A题可注明:1001队 A题 请使用附件的形式加载论文解决方案,如果有数据、程序等其他文件需要和论文一起打包成一个压缩文件再提交,附件的文件名和邮件主题一致。请不要将论文直接放在邮件内容中提交,也不要使用云盘、链接或者超大附件等形式提交论文。否则有可能造成附件接收不到。 如果是集体报名的学校也可以统一打包发送论文,但是一定要把每篇论文的标题写对。 三、论文格式要求 本次比赛定位为美国大学生数学建模竞赛的练习赛,所有论文格式要求与美赛相同,具体要求请按照美赛的格式要求执行。具体请点击查看: 本次比赛提供了论文参考模版,模版中的前三页必须在提交的论文中出现,后面的部分可以根据实际需要进行变更和修改,但是美赛参赛帮助中要求的论文中需要的部分必须要有体现。参考模版中页眉中的参赛队号和页码需要按照你的实际参赛队号进行修改。 注意:电子版的第一页承诺书上需要填上参赛队号、所选择的题目、三个队员的姓名、指导教师姓名(如果无指导教师,填入“无”),名字后面再加上手写签名的图片,或者单独附一张带手写签名的承诺书的图片也可以,word和latex排版均可,鼓励使用latex排版。
四、其它相关内容请登录组委会网站: http://mcm.tzmcm.cn 或数学中国www.madio.net查询,或者关注数学中国官方新浪微博,或者关注数学中国官方微信,帐号是:shuxuezhongguo,或者扫描二维码: file:///C:/Users/madio/AppData/Local/Temp/msohtmlclip1/01/clip_image003.jpg。 数学建模国际赛组委会 2018年11月
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