第一篇：2014年美國(guó)大學(xué)生數(shù)學(xué)建模競(jìng)賽題目及翻譯范文

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?

問題A：除非超車否則靠右行駛的交通規(guī)則 在一些汽車靠右行駛的國(guó)家（比如美國(guó)，中國(guó)等等），多車道的高速公路常常遵循以下原則：司機(jī)必須在最右側(cè)駕駛，除非他們正在超車，超車時(shí)必須先移到左側(cè)車道在超車后再返回。

建立數(shù)學(xué)模型來分析這條規(guī)則在低負(fù)荷和高負(fù)荷狀態(tài)下的交通路況的表現(xiàn)。你不妨考察一下流量和安全的權(quán)衡問題,車速過高過低的限制，或者這個(gè)問題陳述中可能出現(xiàn)的其他因素。這條規(guī)則在提升車流量的方面是否有效？如果不是，提出能夠提升車流量、安全系數(shù)或其他因素的替代品（包括完全沒有這種規(guī)律）并加以分析。

在一些國(guó)家，汽車靠左形式是常態(tài)，探討你的解決方案是否稍作修改即可適用，或者需要一些額外的需要。

最后，以上規(guī)則依賴于人的判斷，如果相同規(guī)則的交通運(yùn)輸完全在智能系統(tǒng)的控制下，無論是部分網(wǎng)絡(luò)還是嵌入使用的車輛的設(shè)計(jì)，在何種程度上會(huì)修改你前面的結(jié)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.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 thatsports fanswill understand.問題B：大學(xué)傳奇教練

體育畫報(bào)是一個(gè)為運(yùn)動(dòng)愛好者服務(wù)的雜志，正在尋找在整個(gè)上個(gè)世紀(jì)的“史上最好的大學(xué)教練”。建立數(shù)學(xué)模型選擇大學(xué)中在一下體育項(xiàng)目中最好的教練：曲棍球或場(chǎng)地曲棍球，足球，棒球或壘球，籃球，足球。時(shí)間軸在你的分析中是否會(huì)有影響？比如1913年的教練和2013年的教練是否會(huì)有所不同？清晰的對(duì)你的指標(biāo)進(jìn)行評(píng)估，討論一下你的模型應(yīng)用在跨越性別和所有可能對(duì)的體育項(xiàng)目中的效果。展示你的模型中的在三種不同體育項(xiàng)目中的前五名教練。

除了傳統(tǒng)的MCM格式，準(zhǔn)備一個(gè)1到2頁的文章給體育畫報(bào)，解釋你的結(jié)果和包括一個(gè)體育迷都明白的數(shù)學(xué)模型的非技術(shù)性解釋。

第二篇：2014年 美國(guó)大學(xué)生數(shù)學(xué)建模 題目 翻譯專題

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?

在一些國(guó)家在右側(cè)駕駛汽車是一種慣例（比如像美國(guó)，中國(guó)和其他大部分國(guó)家，除了英國(guó)，澳大利亞，和一部分之前英國(guó)殖民的國(guó)家）多車道高速公路普遍建立起這樣的規(guī)則，那就是要求司機(jī)在最右邊的車道駕駛汽車，除非他們要超越其它車輛，這種情況下他們要移動(dòng)到左側(cè)車道，超車，然后回到他們?cè)鹊能嚨馈?/p>

建立和總結(jié)一個(gè)數(shù)學(xué)模型去分析這一規(guī)則在流暢和擁堵情況下的交通性能，你不妨檢查交通流量和安全，過少或過多限速的作用（即，過低或過高的車速限制）和/或不能在問題陳述中被清楚表達(dá)的其它因素。這種規(guī)則是否能有效的促進(jìn)交通流量的提升？如果不是，給出建議并分析取而代之的方法（包括當(dāng)前沒有的規(guī)則），此方法會(huì)促進(jìn)更多的交通流量，安全性，和/或包括您認(rèn)為重要的其他因素。

在一些國(guó)家，汽車行駛在左邊是常態(tài)，闡述您的解決方案是否能可行如果僅僅在方向上作出改變，或者是需要額外的要求。

最后，如上所述的規(guī)則依賴于人的判斷為標(biāo)準(zhǔn)。如果在相同的道路運(yùn)輸車輛的完全是一個(gè)智能系統(tǒng)的控制下，系統(tǒng)要么是在部分的道路網(wǎng)絡(luò)中，要么是嵌入到所有使用高速公路的汽車上。什么樣的系統(tǒng)規(guī)模會(huì)改變你之前的分析。

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.體育畫報(bào)，是一個(gè)為體育愛好者打造的雜志，它正在尋找上個(gè)世紀(jì)中男性或者女性的“全天候最好的大學(xué)教練”。建立一個(gè)數(shù)學(xué)模型，從，負(fù)責(zé)擔(dān)任例如如下體育活動(dòng)（高校曲棍球、場(chǎng)地曲棍球、足球、棒球、壘球、籃球、橄欖球）的男性或者女性教練中選擇最佳大學(xué)教練或教練團(tuán)體（過去或者現(xiàn)在的），在你的分析中在時(shí)間方面是否會(huì)造成一些不同，也就是說1913年的訓(xùn)練和2013年的訓(xùn)練有何不同。要求清楚的闡述你評(píng)估的指標(biāo)。討論你的模型是怎樣應(yīng)用在常見的兩個(gè)性別都有的運(yùn)動(dòng)和全部可能的體育運(yùn)動(dòng)中。要求展示用你模型評(píng)估出的在3個(gè)不同運(yùn)動(dòng)中的前5名的教練。

除了MCM的格式和要求，為體育畫報(bào)準(zhǔn)備一份1-2頁的文章，解釋你的結(jié)果并包括能讓您的體育愛好者都明白的、能有通俗易懂解釋的數(shù)學(xué)模型。迷都明白的數(shù)學(xué)模型的非技術(shù)性解釋。

第三篇：2001美國(guó)數(shù)學(xué)建模數(shù)學(xué)競(jìng)賽試題及翻譯

Cyclists have different types of wheels they can use on their bicycles.The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk(see Figure 1)The spoked wheels are lighter, but the solid wheels are more aerodynamic.A solid wheel is never used on the front for a road race but can be used on the rear of the bike.Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used.The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations.The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below.For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.? Task 1.Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel.The table should include the wind speeds for different road grades starting from zero percent to ten percent in one percent increments.(Road grade is defined to be the ratio of the total rise of a hill divided by the length of the road.If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.)A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportional to the road grade.A rider will lose about 8 kph for a five percent grade over 100 meters.Task 2.Provide an example of how the table could be used for a specific time trial course.? Task 3.Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.選擇自行車車輪

有不同類型的車輪可以讓自行車手們?cè)谧约旱淖孕熊嚿?。兩種基本的車輪類型是分別用金屬輻條和實(shí)體圓盤組裝而成（見圖1）。輻條車輪較輕，但試題車輪更符合空氣動(dòng)力學(xué)原理。對(duì)于一場(chǎng)公路競(jìng)賽，實(shí)體車輪從來不會(huì)用作自行車的前車輪但可以作為后車輪。

職業(yè)自行車手們審視競(jìng)賽路線，并且請(qǐng)一位識(shí)文斷字的人推斷應(yīng)該使用哪種車輪。選擇決定是根據(jù)沿途山丘的數(shù)量和陡度，天氣，風(fēng)速，競(jìng)賽本身以及其他考慮作出的，你所喜愛的參賽隊(duì)的教練希望準(zhǔn)備妥當(dāng)一個(gè)較好的系統(tǒng)，并且對(duì)于給定的競(jìng)賽路線已經(jīng)向你的參賽隊(duì)索取有助于確定宜用哪種車輪的信息。

這位教練需要明確的信息來幫助做出決定，而且已經(jīng)要求你的參賽隊(duì)完成下面列出的各項(xiàng)任務(wù)，對(duì)于每項(xiàng)任務(wù)都假定同樣的輻條車輪總是裝在前面，而裝在后面的車輪是可以選擇的。任務(wù)1.提供一個(gè)給出風(fēng)速的表格。在這種速度下試題后輪所需要的體能少于輻條后輪。這個(gè)表格應(yīng)當(dāng)包括相應(yīng)于從百分之零到百分之十的不同公路陡度的風(fēng)速。（公路陡度定義為一座山丘的總升高初一公路長(zhǎng)度。如果把山丘看作一個(gè)三角形，它的陡度是指山腳處傾角的正弦。）一位騎手以初始速度45kph從山腳出發(fā)，他的減速度與公路陡度成正比。對(duì)于百分之五的陡度，騎上100米車速要下降8kph左右。

任務(wù)2.提供一個(gè)例證，說明這個(gè)表格怎樣用于一條時(shí)間實(shí)驗(yàn)路線。

任務(wù)3.請(qǐng)判明這個(gè)表格是不是一件決定車輪配置的適當(dāng)工具，并且關(guān)于如何作出這個(gè)決定提出其他建議。

2001 MCM B: Escaping a Hurricane's Wrath(An Ill Wind...)

Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in 1999 led to a monumental traffic jam.Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state.What is normally an easy two-hour drive took up to 18 hours to complete.Many cars simply ran out of gas along the way.Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.The principal proposal put forth to deal with this problem is the reversal of traffic on I-26, so that both sides, including the coastal-bound lanes, have traffic headed inland from Charleston to Columbia.Plans to carry this out have been prepared(and posted on the Web)by the South Carolina Emergency Preparedness Division.Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.A simplified map of South Carolina is shown.Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip.(More accurate data, if sought, are widely available.)The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three.Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees(including some coming from farther north by other routes), so some traffic continues outbound on I-26 towards Spartanburg;on I-77 north to Charlotte;and on I-20 east to Atlanta.In 1999, traffic leaving Columbia going northwest was moving only very slowly.Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999.Here are the questions that need to be addressed: 1.Under what conditions does the plan for turning the two coastal-bound lanes of I-26 into two lanes of Columbia-bound traffic, essentially turning the entire I-26 into one-way traffic, significantly improve evacuation traffic flow? 2.In 1999, the simultaneous evacuation of the state's entire coastal region was ordered.Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation, perhaps county-by-county over some time period consistent with the pattern of how hurricanes affect the coast? 3.Several smaller highways besides I-26 extend inland from the coast.Under what conditions would it improve evacuation flow to turn around traffic on these? 4.What effect would it have on evacuation flow to establish more temporary shelters in Columbia, to reduce the traffic leaving Columbia? 5.In 1999, many families leaving the coast brought along their boats, campers, and motor homes.Many drove all of their cars.Under what conditions should there be restrictions on vehicle types or numbers of vehicles brought in order to guarantee timely evacuation? 6.It has been suggested that in 1999 some of the coastal residents of Georgia and Florida, who were fleeing the earlier predicted landfalls of Hurricane Floyd to the south, came up I-95 and compounded the traffic problems.How big an impact can they have on the evacuation traffic flow? Clearly identify what measures of performance are used to compare strategies.Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.Clearly identify what measures of performance are used to compare strategies.Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.逃避颶風(fēng)

1999年，在Floyd颶風(fēng)預(yù)報(bào)登錄之前，車?yán)锬峡_來納州沿海地區(qū)的行動(dòng)導(dǎo)致一場(chǎng)永垂青史的交通擁塞。車水馬龍停滯在州際公路I-26上，那是內(nèi)陸上從Charleston通往該州中心Columbia相對(duì)安全處所的主要干線。正常時(shí)輕松的兩個(gè)小時(shí)驅(qū)車路要用18個(gè)小時(shí)才能開到頭。許多車竟然沿途把汽油消耗凈盡。幸運(yùn)的是，F(xiàn)loyd颶風(fēng)掉頭長(zhǎng)驅(qū)北上，這次放過了南卡羅來納州，但是，公眾的喧嚷正在迫使該州官員們尋找各種辦法，以求避免這場(chǎng)交通惡夢(mèng)再度出現(xiàn)。傾力解決這個(gè)問題的主要提議是I-26公路上的車輛轉(zhuǎn)向疏散，因此，包括通往海岸的多條次級(jí)公路在內(nèi)，從兩個(gè)側(cè)面疏導(dǎo)車流在內(nèi)陸從Charleston開往Columbia。把提議付諸實(shí)施的計(jì)劃已經(jīng)由South Carolina Emergency Preparedness Division準(zhǔn)備好（而且貼在互聯(lián)網(wǎng)上）。從Myrtle Beach和Hilton Head通往內(nèi)地的主干道上車輛轉(zhuǎn)向疏散的方案也在規(guī)劃中。

這里有一張南卡羅來納州的簡(jiǎn)化地圖。Charleston有近500000人，Myrtle Beach有200000人左右，而另外一個(gè)250000人分散在沿岸其余地區(qū)。（如果查找，更精確的數(shù)據(jù)隨處可用。）

州與州之間有兩條車輛往來的次級(jí)公路，自然大都市地區(qū)除外，那里有三條。Columbia，又一個(gè)500000人左右的大都市地區(qū)，沒有充足的旅店空間為撤退者提供食宿（包括咽其他路線來自北邊的一些人），所以，若干車輛繼續(xù)撤離，沿著I-26公路開往Spartanburg市；沿著I-77公路北上Charleston；而且沿著I-20公路東進(jìn)Atlanta市。在1999年，從Columbia開往西北方向的車輛行進(jìn)得非常慢。對(duì)于這個(gè)問題建立一個(gè)模型，調(diào)查研究哪種策略可以降低在1999年觀察到的擁擠。這里有一些問題需要加以考慮：

在什么條件下，把I-26的兩條開往海岸的次級(jí)公路變成開往Columbia的兩條次級(jí)公路，特別是把整個(gè)I-26變成單行道會(huì)使撤離交通狀況得到重大改善？

在1999年，南卡羅來納州的整個(gè)沿海地區(qū)奉命同時(shí)撤離。如果采取另一種策略，逐個(gè)郡按某個(gè)時(shí)間段錯(cuò)開撤離，同時(shí)颶風(fēng)對(duì)沿岸影響的模式相協(xié)調(diào)，撤離交通狀況會(huì)改善嗎？

在I-26公路旁邊有若干較小的高速公路從海岸延伸到內(nèi)陸。在什么條件下，把車輛流轉(zhuǎn)向這些道路會(huì)改善撤離交通？

在Columbia建立更多臨時(shí)收容所來減少離開Columbia的車輛，這會(huì)對(duì)撤離交通有什么影響？

在1999年，離開海岸的許多家庭一路上攜帶他們的船只，露宿設(shè)備和汽車住宅。許多家庭駕駛他們的所有汽車。在什么條件下，應(yīng)當(dāng)對(duì)攜帶的車輛類型或數(shù)目加以限制以求保證適時(shí)撤離？

在1999年，人們還會(huì)記得，若干George州和Florida州的沿岸居民逃避較早預(yù)報(bào)的Floyd颶風(fēng)南部登錄，沿著I-95公路北上家中了南卡羅來納州交通問題。他們對(duì)于撤離交通的沖擊會(huì)有多大？

要求清楚地指明，為了比較各種策略，使用什么方法對(duì)實(shí)施狀況予以評(píng)測(cè)。

要求：預(yù)備一篇簡(jiǎn)短的報(bào)刊文章，不超過兩頁，向公眾解釋你的研究成果和結(jié)論。

第四篇：美國(guó)數(shù)學(xué)建模題目2017至2017翻譯

美國(guó)數(shù)學(xué)建模題目2017至2017翻譯

篇一：2017年建模美賽C題帶翻譯

Problem C: “Cooperate and navigate”

Traffic capacity is limited in many regions of the United States due to the number of lanes of roads.For example, in the Greater Seattle area drivers experience long delays during peak traffic hoursbecause the volume of traffic exceeds the designed capacity of the road networks.This is particularlypronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interestfor this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highwayswithout increasing number of lanes or roads.The behavior of these cars interacting with the existingtraffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving,cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties.(Seethe provided map and Excel spreadsheet).In particular, how do the effects change as thepercentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there atipping point where performance changes markedly? Under what conditions, if any, should lanes bededicated to these cars? Does your analysis of your model suggest any other policy changes?

Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/oraverage traffic volume, and percentage of vehicles using self-driving, cooperating systems.Yourmodel should address cooperation between self-driving cars as well as the interaction between self-driving and non-self-driving vehicles.Your model should then be applied to the data for the roads ofinterest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to theGovernor’s office, and your solution(not to exceed 20 pages)for a maximum of 23 pages.Note: Theappendix and references do not count toward the 23 page limit.Some useful background information:

On average, 8% of the daily traffic volume occurs during peak travel hours.? The nominal speed limit for all these roads is 60 miles per hour.? Mileposts are numbered from south to north, and west to east.? Lane widths are the standard 12 feet.? Highway 90 is classified as a state route until it intersects Interstate 5.? In case of any conflict between the data provided in this problem and any other source, use thedata provided in this problem.Definitions:

milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.問題C：“合作和導(dǎo)航”

由于道路的數(shù)量，美國(guó)許多地區(qū)的交通容量有限。例如，在大西雅圖地區(qū)，由于交通量超過道路網(wǎng)絡(luò)的設(shè)計(jì)容量，司機(jī)在交通高峰時(shí)段經(jīng)歷長(zhǎng)時(shí)間的延誤。這在5號(hào)，90號(hào)和405號(hào)州際公路以及520號(hào)國(guó)道，特別關(guān)注這個(gè)問題的道路上尤其明顯。

自動(dòng)駕駛，合作車已被提出作為增加公路的能力而不增加車道或道路的數(shù)量的解決方案。在這一點(diǎn)上，這些汽車與現(xiàn)有交通流和彼此交互的行為尚未被很好地理解。

華盛頓州州長(zhǎng)要求分析允許在Thurston，Pierce，King和Snohomish縣的上述道路上自行駕駛合作汽車的影響。（見提供的地圖和Excel電子表格）。特別是，自動(dòng)駕駛汽車的百分比從10％增加到50％到90％，效果如何變化？平衡是否存在？是否有性能變化明顯的臨界點(diǎn)？在什么條件下，如果有的話，應(yīng)該有車道專用于這些車？您對(duì)模型的分析是否表明有任何其他政策變化？

您的答案應(yīng)包括對(duì)車道數(shù)量，峰值和/或平均交通量的交通流量的影響的模型，以及使用自動(dòng)駕駛，合作系統(tǒng)的車輛的百分比。你的模型應(yīng)該解決自駕車之間的合作以及自駕車和非自駕車之間的相互作用。然后，您的模型應(yīng)用于附帶的Excel電子表格中提供的感興趣道路的數(shù)據(jù)。

您的MCM提交應(yīng)包括1頁摘要表，1至2頁總督辦公室信，以及您的解決方案（不超過20頁），最多23頁。注意：附錄和參考文獻(xiàn)不計(jì)入23頁的限制。一些有用的背景信息：

平均而言，每天交通量的8％發(fā)生在高峰旅行時(shí)間。

?所有這些道路的名義速度限制為每小時(shí)60英里。

?里程數(shù)從南到北，從西到東。

?車道寬度為標(biāo)準(zhǔn)12英尺。

?高速公路90被分類為狀態(tài)路線，直到它與州際5相交。

?如果此問題中提供的數(shù)據(jù)與任何其他源出現(xiàn)沖突，請(qǐng)使用此問題中提供的數(shù)據(jù)。定義：

milepost：道路上的標(biāo)記，用于測(cè)量距離路線或天體邊界的距離（以英里為單位）。平均每日交通量：在road.interstate上行駛的平均每天的汽車數(shù)量：有限訪問高速公路，國(guó)家系統(tǒng)的一部分。

國(guó)家路線：可能受限或不受限制的國(guó)家公路。

路由ID：高速公路的編號(hào)。

增加方向：N-S道路北行，E-W道路東行。

下降方向：N-S道南行，E-W道西行。

篇二：2017美賽D題中文翻譯

D題中文翻譯：

問題D：在機(jī)場(chǎng)安全檢查站優(yōu)化乘客吞吐量

繼2001年9月11日美國(guó)發(fā)生恐怖襲擊事件后，全世界的機(jī)場(chǎng)安全狀況得到顯著改善。機(jī)場(chǎng)有安全檢查站，在那里，乘客及其行李被檢查爆炸物和其他危險(xiǎn)物品。這些安全措施的目的是防止乘客劫持或摧毀飛機(jī)，并在旅行期間保持所有乘客的安全。然而，航空公司有既得利益，通過最小化他們?cè)诎踩珯z查站排隊(duì)等候并等待他們的航班的時(shí)間，為乘客保持積極的飛行體驗(yàn)。因此，在希望之間存在最大化安全性同時(shí)最小化對(duì)乘客的不便的張力。

在2016年，美國(guó)運(yùn)輸安全局（TSA）受到了對(duì)極長(zhǎng)線路，特別是在芝加哥的奧黑爾國(guó)際機(jī)場(chǎng)的尖銳批評(píng)。在此公眾關(guān)注之后，TSA投資對(duì)其檢查點(diǎn)設(shè)備和程序進(jìn)行了若干修改，并增加了在高度擁堵的機(jī)場(chǎng)中的人員配置。雖然這些修改在減少等待時(shí)間方面有一定的成功，但TSA在實(shí)施新措施和增加人員配置方面花費(fèi)了多少成本尚不清楚。除了在O'Hare的問題，還有在其他機(jī)場(chǎng)，包括通常有短的等待時(shí)間的機(jī)場(chǎng)不明原因和不可預(yù)測(cè)的長(zhǎng)線的事件。檢查點(diǎn)線路的這種高差異對(duì)于乘客來說可能是極其昂貴的，因?yàn)樗麄儧Q定在不必要地早到達(dá)或可能丟失他們的預(yù)定航班之間。許多新聞文章，包括[1,2,3,4,5]，描述了與機(jī)場(chǎng)安全檢查站相關(guān)的一些問題。

您的內(nèi)部控制管理（ICM）團(tuán)隊(duì)已經(jīng)與TSA簽訂合同，審查機(jī)場(chǎng)安全檢查站和人員配置，以確定可能干擾乘客吞吐量的瓶頸。他們特別感興趣的創(chuàng)意解決方案，既增加檢查點(diǎn)吞吐量，減少等待時(shí)間的方差，同時(shí)保持相同的安全和安全標(biāo)準(zhǔn)。

美國(guó)機(jī)場(chǎng)安全檢查點(diǎn)的當(dāng)前流程如圖1所示。

?區(qū)域A：

o乘客隨機(jī)到達(dá)檢查站，并等待隊(duì)列，直到安全人員可以檢查他們的身份證明和登機(jī)文件。

?區(qū)域B：

o然后乘客移動(dòng)到打開的篩選線的后續(xù)隊(duì)列;根據(jù)機(jī)場(chǎng)的預(yù)期活動(dòng)水平，或多或少的線路可能開放。

o一旦乘客到達(dá)這個(gè)隊(duì)列的前面，他們準(zhǔn)備所有的物品用于X射線檢查。乘客必須用液體去除鞋子，皮帶，夾克，金屬物體，電子產(chǎn)品和容器，將它們放置在單獨(dú)的X射線箱中;筆記本電腦和一些醫(yī)療設(shè)備也需要從其袋中取出并放置在單獨(dú)的容器中。

o他們的所有物品，包括包含上述物品的箱子，由傳送帶通過X光機(jī)移動(dòng)，其中一些物品被標(biāo)記，供安全人員（D區(qū)）進(jìn)行額外的搜索或篩選。

o同時(shí)乘客通過毫米波掃描儀或金屬探測(cè)器進(jìn)行處理。

o未能通過此步驟的乘客接受安全官員（D區(qū)）的輕擊檢查。

?C區(qū)：

o乘客然后前進(jìn)到X射線掃描儀另一側(cè)的傳送帶，收集他們的物品并離開檢查站區(qū)域。

圖1：TSA安全篩選過程的圖示。

大約45％的乘客報(bào)名參加一個(gè)稱為預(yù)檢查信任旅行者的計(jì)劃。這些乘客支付85美元，接受背景調(diào)查，并享受五年的獨(dú)立篩選程序。盡管事實(shí)上更多的乘客使用預(yù)檢查過程，但是每三條常規(guī)車道通常有一個(gè)預(yù)檢查車道打開。預(yù)檢查乘客和他們的行李經(jīng)過相同的篩選過程，經(jīng)過一些修改，以加快篩選。預(yù)檢查乘客還必須移除掃描用的金屬和電子物品以及任何液體，但不需要去除鞋子，皮帶或燈罩;他們也不需要從他們的包里刪除他們的電腦。

收集了關(guān)于乘客如何進(jìn)行安全檢查過程的每個(gè)步驟的數(shù)據(jù)。

您的特定任務(wù)是：

一個(gè)。開發(fā)一個(gè)或多個(gè)模型，允許您通過安全檢查點(diǎn)探索乘客流，并識(shí)別瓶頸。清楚地確定當(dāng)前流程中存在哪些問題區(qū)域。

b。對(duì)當(dāng)前流程開發(fā)兩個(gè)或多個(gè)潛在修改，以提高旅客吞吐量并減少等待時(shí)間的差異。對(duì)這些更改進(jìn)行建模，以演示修改如何影響流程。

C。眾所周知，世界上不同的地方都有自己的文化規(guī)范，塑造了地方社會(huì)互動(dòng)的規(guī)則?？紤]這些文化規(guī)范如何影響你的模型。例如，美國(guó)人以深為尊重和優(yōu)先考慮別人的個(gè)人空間而聞名，并且在他人面前有一個(gè)社會(huì)歧視“切割”。同時(shí)，瑞士人以集體效率為重點(diǎn)，中國(guó)人以優(yōu)先個(gè)人效率而聞名?？紤]文化差異如何影響乘客的過程通過檢查點(diǎn)作為敏感性分析的方式。您應(yīng)用于敏感性分析的文化差異可以基于真實(shí)的文化差異，或者您可以模擬與任何特定文化（例如，較慢的旅行者）無關(guān)的不同旅行者風(fēng)格。安全系統(tǒng)如何以加快乘客吞吐量并減少差異的方式來適應(yīng)這些差異？

d。根據(jù)您的模型為安全管理器提出政策和程序建議。這些策略可以是全球適用的，或者可以針對(duì)特定文化和/或旅行者類型來定制。

除了開發(fā)和實(shí)施您的模型來解決這個(gè)問題，您的團(tuán)隊(duì)還應(yīng)該驗(yàn)證您的模型，評(píng)估優(yōu)勢(shì)和弱點(diǎn)，并提出改進(jìn)建議（未來工作）。

您的ICM提交應(yīng)包含1頁的摘要表，您的解決方案不能超過20頁，最多21頁。注意：附錄和參考文獻(xiàn)不計(jì)入20頁的限制。

篇三：2017年建模美賽B題帶翻譯

Problem B: Merge After Toll

Multi-lane divided limited-access toll highways use “ramp tolls” and “barrier tolls” to collect tolls from motorists.A ramp toll is a collection mechanism at an

entrance or exit ramp to the highway and these do not concern us here.A barrier toll is a row of tollbooths placed across the highway, perpendicular to the

direction of traffic flow.There are usually(always)more tollbooths than there are incoming lanes of traffic(see former 2005 MCM Problem B).So when exiting the tollbooths in a barrier toll, vehicles must “fan in” from the larger number of tollbooth egress lanes to the smaller number of regular travel lanes.A toll plaza is the area of the highway needed to facilitate the barrier toll, consisting of the fan-out area before the barrier toll, the toll barrier itself, and the fan-in area after the toll barrier.For example, a three-lane highway(one direction)may use 8

tollbooths in a barrier toll.After paying toll, the vehicles continue on their journey on a highway having the same number of lanes as had entered the toll plaza(three, in this example).Consider a toll highway having L lanes of travel in each direction and a barrier toll containing B tollbooths(B > L)in each direction.Determine the shape, size, and merging pattern of the area following the toll barrier in which vehicles fan in from

B tollbooth egress lanes down to L lanes of traffic.Important considerations to incorporate in your model include accident prevention, throughput(number of vehicles per hour passing the point where the end of the plaza joins theL outgoing traffic lanes), and cost(land and road construction are expensive).In particular, this problem does not ask for merely a performance analysis of any particular toll plaza design that may already be implemented.The point is to determine if there are better solutions(shape, size, and merging pattern)than any in common use.Determine the performance of your solution in light and heavy traffic.How does your solution change as more autonomous(self-driving)vehicles are added to the traffic mix? How is your solution affected by the proportions of conventional(human-staffed)tollbooths, exact-change(automated)tollbooths, and electronic toll collection booths(such as electronic toll collection via a transponder in the vehicle)?

Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the New Jersey Turnpike Authority, and your solution(not to exceed 20 pages)for a maximum of 23 pages.Note: The appendix and references do not count toward the 23 page limit.多車道有限接入收費(fèi)公路使用“坡道收費(fèi)”和“障礙收費(fèi)”

收取駕駛?cè)耸康氖召M(fèi)。斜坡收費(fèi)是一個(gè)收集機(jī)制

入口或出口匝道到高速公路，這些不關(guān)心我們?cè)谶@里。障礙

收費(fèi)是一排收費(fèi)站橫跨高速公路，垂直于

交通方向。通常（總是）更多的收費(fèi)站比

（見2005年前MCM問題B）。所以退出時(shí)

收費(fèi)站在通行費(fèi)，車輛必須“扇入”從大量

收費(fèi)站出口車道到較少數(shù)量的常規(guī)旅行車道。收費(fèi)廣場(chǎng) 是高速公路所需的便利通行費(fèi)的區(qū)域，包括

障礙物前的扇出區(qū)域，收費(fèi)口障本身以及后面的扇入?yún)^(qū)域 收費(fèi)屏障。例如，三車道公路（一個(gè)方向）可以使用8 收費(fèi)站。在支付費(fèi)用后，車輛繼續(xù)他們的旅程

在具有與進(jìn)入收費(fèi)廣場(chǎng)相同數(shù)量的車道的高速公路上

（在本示例中為三個(gè)）。

考慮在每個(gè)方向上具有L個(gè)行駛車道的收費(fèi)高速公路和障礙收費(fèi)（B> L）。確定形狀，大小和

合并模式的區(qū)域跟隨收費(fèi)障礙車輛扇入

B收費(fèi)站出口線下至L車道的交通。重要注意事項(xiàng)

包括在您的模型包括事故預(yù)防，吞吐量（車輛每小時(shí)通過廣場(chǎng)的末端加入L的點(diǎn)

出行車道）和成本（土地和道路建設(shè)昂貴）。在 特別的，這個(gè)問題不要求任何的性能分析

特定的收費(fèi)廣場(chǎng)設(shè)計(jì)可能已經(jīng)實(shí)施。關(guān)鍵是要

確定是否有更好的解決方案（形狀，大小和合并模式）任何常見的使用。

確定您的解決方案在輕和重的流量的性能。如何

您的解決方案隨著更多自主（自駕）車輛添加而改變

交通混合？你的解決方案如何影響常規(guī)的比例

（人員）收費(fèi)站，精確更換（自動(dòng)）收費(fèi)站和電子

收費(fèi)亭（例如通過轉(zhuǎn)發(fā)器在電子收費(fèi)站收集

車輛）？

您的MCM提交應(yīng)包含1頁的摘要表，1-2頁

給新澤西州收費(fèi)公路局的信，以及您的解決方案（不超過20 頁面），最多23頁。注意：附錄和參考文獻(xiàn)沒有

計(jì)數(shù)到23頁的限制。

第五篇：2014年美國(guó)大學(xué)生數(shù)學(xué)建模競(jìng)賽賽題翻譯

問題A：除了超車靠右行駛的規(guī)則

在一些開車靠右行駛的國(guó)家（美國(guó)，中國(guó)和大多數(shù)的其他國(guó)家，除了英國(guó)，澳大利亞和一些英國(guó)的殖民地），多車道高速公路通常采用一個(gè)規(guī)則，要求司機(jī)在大多數(shù)高速公路上開車時(shí)靠右行駛，除非他們?cè)诔嚂r(shí)，這種情況下，他們要移到左邊的車道，超車然后回到他們從前的車道。

建立和分析一個(gè)數(shù)學(xué)模型來分析這個(gè)規(guī)則在交通暢通和交通擁堵的情況下的表現(xiàn)。希望你能檢查交通流量和安全、過高或過低車速的限制（那就是，車速太高或太低）或者其它的本題中可能沒有提出的因素之間的權(quán)衡。這個(gè)規(guī)則在更好的提高交通流量的安全性上是否有效？如果沒有，建議和分析另一種辦法（包括可能這種類型的規(guī)則），那可能提高更大的交通流量、安全、和其他你認(rèn)為重要的因素。

在一些靠左行駛的國(guó)家里，討論你的方法能否在簡(jiǎn)單改變方向的或者需要附加要求的情況下應(yīng)用。

最后，上述的規(guī)則依靠人類的判斷作為規(guī)范。如果在相同的公路上汽車運(yùn)輸完全受智能系統(tǒng)的控制，道路網(wǎng)絡(luò)的一部分或者嵌入所有交通工具所用的道路設(shè)計(jì)，這是你在多大程度上改變你前面的分析的結(jié)果？

問題B：大學(xué)傳奇教練

《體育畫報(bào)》，一個(gè)運(yùn)動(dòng)愛好者雜志，正在尋找上個(gè)世紀(jì)男或女的“最好全天候大學(xué)教練”。建立數(shù)學(xué)模型，從男性或女性教練中，從諸如高校曲棍球或曲棍球，足球，棒球或壘球，籃球，足球或選擇其中最好的大學(xué)教練或教練們（過去或現(xiàn)在）。你用哪一個(gè)時(shí)間線范圍是否造成不同結(jié)果，也就是說，教練在1913年是否不同于教練在2013年？清楚地說明您的度量for評(píng)估。討論你的模型如何可以在一般的跨越男女和所有可能的運(yùn)動(dòng)中應(yīng)用。展示你的模型在每3個(gè)不同的運(yùn)動(dòng)中的前5名教練。

除了MCM的格式和要求，為體育畫報(bào)準(zhǔn)備一份1-2頁的文章解釋你的結(jié)果，包括體育迷都明白的數(shù)學(xué)模型的非技術(shù)性解釋