第一篇：2014年美國大學生數學建模競賽賽題翻譯

問題A：除了超車靠右行駛的規則

在一些開車靠右行駛的國家（美國，中國和大多數的其他國家，除了英國，澳大利亞和一些英國的殖民地），多車道高速公路通常采用一個規則，要求司機在大多數高速公路上開車時靠右行駛，除非他們在超車時，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。

建立和分析一個數學模型來分析這個規則在交通暢通和交通擁堵的情況下的表現。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衡。這個規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則），那可能提高更大的交通流量、安全、和其他你認為重要的因素。

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

最后，上述的規則依靠人類的判斷作為規范。如果在相同的公路上汽車運輸完全受智能系統的控制，道路網絡的一部分或者嵌入所有交通工具所用的道路設計，這是你在多大程度上改變你前面的分析的結果？

問題B：大學傳奇教練

《體育畫報》，一個運動愛好者雜志，正在尋找上個世紀男或女的“最好全天候大學教練”。建立數學模型，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教練或教練們（過去或現在）。你用哪一個時間線范圍是否造成不同結果，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動中應用。展示你的模型在每3個不同的運動中的前5名教練。

除了MCM的格式和要求，為體育畫報準備一份1-2頁的文章解釋你的結果，包括體育迷都明白的數學模型的非技術性解釋

第二篇：2014美國數學建模競賽賽題翻譯

問題A：右行左超規則

在美國、中國 和大多數除了英國、澳大利亞和一些前英國殖民地的國家，多車道高速公路常常有這樣一種規則。司機必須盡量在最右的車道行使，只有超車時，司機才可以向左移動一個車道來達成目的。當司機超車完畢后必須回到原車道繼續行使。

建立并分析一個數學模型，使得這個模型能夠分析這個規則在交通高負荷和低負荷情況下的表現。你可以從許多角度來思考這個問題，比如車流量和車輛安全之間的權衡，或者一個過快或過慢的車輛限速帶來的影響等等。這個規則可以使我們獲得更好的交通流？如果不可以，請提出并分析一個替代方案使得交通流得到優化、安全得到保障、或者其他你認為重要的因素得到實現。

在靠左行使才是規則的國家，論證你的解決方案是否可以通過簡單的變換或者通過增加一些新的要求來解決相同的問題。

最后，以上的規則的實行是建立在人們遵守它的基礎上的，然而不是所有人都愿意去遵守。那么現在我們使同一條道（可以只是一段，也可以是全段公路）上的交通車輛都在一個智能系統的嚴格控制下，這個變化對你之前的分析結果有多大的影響？

問題B：體育畫刊是一個為體育愛好者們設計的雜志。這個雜志正在尋找上世紀女性或者男性的“歷來最優秀的大學教練”。建立一個數學模型，從男性或者女性體育教練中選擇最好的大學教練（退役或者在役的都可以）。這些體育教練可以是大學曲棍球、陸上曲棍球、足球、橄欖球、棒球、排球、籃球的教練。你選擇劃分的時間會對你的分析有影響嗎？也就是說，1913年的教練方式和2013年的會有什么不同嗎？清楚的闡述你的評估方式。討論你的模型如何通用于兩性教練和所有可能的運動項目上。用你的模型為三項體育項目分別找到五個最佳教練。

再為體育畫刊提供一篇1－2頁的不涉及技術性問題解釋的通俗易懂的文章來解釋你們的結果，你們必須保證體育愛好者們能夠理解。

第三篇：2001美國數學建模數學競賽試題及翻譯

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在自己的自行車上。兩種基本的車輪類型是分別用金屬輻條和實體圓盤組裝而成（見圖1）。輻條車輪較輕，但試題車輪更符合空氣動力學原理。對于一場公路競賽，實體車輪從來不會用作自行車的前車輪但可以作為后車輪。

職業自行車手們審視競賽路線，并且請一位識文斷字的人推斷應該使用哪種車輪。選擇決定是根據沿途山丘的數量和陡度，天氣，風速，競賽本身以及其他考慮作出的，你所喜愛的參賽隊的教練希望準備妥當一個較好的系統，并且對于給定的競賽路線已經向你的參賽隊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，而且已經要求你的參賽隊完成下面列出的各項任務，對于每項任務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1.提供一個給出風速的表格。在這種速度下試題后輪所需要的體能少于輻條后輪。這個表格應當包括相應于從百分之零到百分之十的不同公路陡度的風速。（公路陡度定義為一座山丘的總升高初一公路長度。如果把山丘看作一個三角形，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，他的減速度與公路陡度成正比。對于百分之五的陡度，騎上100米車速要下降8kph左右。

任務2.提供一個例證，說明這個表格怎樣用于一條時間實驗路線。

任務3.請判明這個表格是不是一件決定車輪配置的適當工具，并且關于如何作出這個決定提出其他建議。

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

1999年，在Floyd颶風預報登錄之前，車里南卡羅來納州沿海地區的行動導致一場永垂青史的交通擁塞。車水馬龍停滯在州際公路I-26上，那是內陸上從Charleston通往該州中心Columbia相對安全處所的主要干線。正常時輕松的兩個小時驅車路要用18個小時才能開到頭。許多車竟然沿途把汽油消耗凈盡。幸運的是，Floyd颶風掉頭長驅北上，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，以求避免這場交通惡夢再度出現。傾力解決這個問題的主要提議是I-26公路上的車輛轉向疏散，因此，包括通往海岸的多條次級公路在內，從兩個側面疏導車流在內陸從Charleston開往Columbia。把提議付諸實施的計劃已經由South Carolina Emergency Preparedness Division準備好（而且貼在互聯網上）。從Myrtle Beach和Hilton Head通往內地的主干道上車輛轉向疏散的方案也在規劃中。

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

州與州之間有兩條車輛往來的次級公路，自然大都市地區除外，那里有三條。Columbia，又一個500000人左右的大都市地區，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Atlanta市。在1999年，從Columbia開往西北方向的車輛行進得非常慢。對于這個問題建立一個模型，調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公路變成開往Columbia的兩條次級公路，特別是把整個I-26變成單行道會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沿海地區奉命同時撤離。如果采取另一種策略，逐個郡按某個時間段錯開撤離，同時颶風對沿岸影響的模式相協調，撤離交通狀況會改善嗎？

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

在Columbia建立更多臨時收容所來減少離開Columbia的車輛，這會對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，應當對攜帶的車輛類型或數目加以限制以求保證適時撤離？

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

要求清楚地指明，為了比較各種策略，使用什么方法對實施狀況予以評測。

要求：預備一篇簡短的報刊文章，不超過兩頁，向公眾解釋你的研究成果和結論。

第四篇：2014年美國大學生數學建模競賽題目及翻譯范文

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則 在一些汽車靠右行駛的國家（比如美國，中國等等），多車道的高速公路常常遵循以下原則：司機必須在最右側駕駛，除非他們正在超車，超車時必須先移到左側車道在超車后再返回。

建立數學模型來分析這條規則在低負荷和高負荷狀態下的交通路況的表現。你不妨考察一下流量和安全的權衡問題,車速過高過低的限制，或者這個問題陳述中可能出現的其他因素。這條規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、安全系數或其他因素的替代品（包括完全沒有這種規律）并加以分析。

在一些國家，汽車靠左形式是常態，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，以上規則依賴于人的判斷，如果相同規則的交通運輸完全在智能系統的控制下，無論是部分網絡還是嵌入使用的車輛的設計，在何種程度上會修改你前面的結果？

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：大學傳奇教練

體育畫報是一個為運動愛好者服務的雜志，正在尋找在整個上個世紀的“史上最好的大學教練”。建立數學模型選擇大學中在一下體育項目中最好的教練：曲棍球或場地曲棍球，足球，棒球或壘球，籃球，足球。時間軸在你的分析中是否會有影響？比如1913年的教練和2013年的教練是否會有所不同？清晰的對你的指標進行評估，討論一下你的模型應用在跨越性別和所有可能對的體育項目中的效果。展示你的模型中的在三種不同體育項目中的前五名教練。

除了傳統的MCM格式，準備一個1到2頁的文章給體育畫報，解釋你的結果和包括一個體育迷都明白的數學模型的非技術性解釋。

第五篇：2005美國數學建模數學競賽試題及翻譯

2005 年美國大學生數學建模競賽 MCM試題

2005 MCM A: Flood Planning 洪水計劃

Lake Murray in central South Carolina is formed by a large earthen dam, which was completed in 1930 for power production Model the flooding downstream in the event there is a catastrophic earthquake that breaches the dam

Two particular questions:

Rawls Creek is a year-round stream that flows into the Saluda River a short distance downriver from the dam How much flooding will occur in Rawls Creek from a dam failure, and how far back will it extend?

Could the flood be so massive downstream that water would reach up to the SC State Capitol Building, which is on a hill overlooking the Congaree River? South Carolina中部的Murray河是由北部的一個巨大水壩形成的，這是在1930年為了發電而修建的。模擬一起洪水淹沒下游的事件，這起事件是由于一次災難性的地震損壞了水壩造成的。兩個問題：

1、Rawls Creek是水壩下游流入Saluda河的一條終年流動的河流，在當水壩損壞后，在Rawls Creek將會出現多大的洪流，洪水的波及面將有多大？

2、S.C.國會大廈大樓在一座小山上，在S.C.國會大廈大樓能俯視Congaree河。洪水能如此巨大順流以至于水將擴展到S.C.國會大廈大樓嗎？

2005 MCM B: Tollbooths收費亭

Heavily-traveled toll roads such as the Garden State Parkway, Interstate 95, and so forth, are multi-lane divided highways that are interrupted at intervals by toll plazas Because collecting tolls is usually unpopular, it is desirable to minimize motorist annoyance by limiting the amount of traffic disruption caused by the toll plazas Commonly, a much larger number of tollbooths is provided than the number of travel lanes entering the toll plaza Upon entering the toll plaza, the flow of vehicles fans out to the larger number of tollbooths, and when leaving the toll plaza, the flow of vehicles is required to squeeze back down to a number of travel lanes equal to the number of travel lanes before the toll plaza Consequently, when traffic is heavy, congestion increases upon departure from the toll plaza When traffic is very heavy, congestion also builds at the entry to the toll plaza because of the time required for each vehicle to pay the toll

Make a model to help you determine the optimal number of tollbooths to deploy in a barrier-toll plaza Explicitly consider the scenario where there is exactly one tollbooth per incoming travel lane Under what conditions is this more or less effective than the current practice? Note that the definition of “optimal” is up to you to determine

像 Garden State Parkway, Interstate 95這類的長途收費公路，通常是多行道德，被分成幾條高速公路，在這些高速公路上每隔一段會設立一個通行稅收費廣場。因為征收通行稅通常不受歡迎，所以應該盡量減少通過通行稅收費廣場引起的交通混亂給汽車司機帶來的煩惱。通常，收費亭的數量要多于進入收費廣場的道路的數量。進入通行稅收費廣場的時候，流到大量收費亭的車輛呈扇形展開，當離開通行稅廣場的時候，車流只能按照收費廣場前行車道路的數量排隊，按次通過！從而，當交通擁擠的時候，擁擠在違背通行稅廣場增加。當交通非常擁擠的時候，因為每輛車付通行費的時間要求，阻塞也會出現在通行稅收費廣場的入口處。建立一個模型來確定一個容易造成阻塞的通行稅收費廣場中應該部署的最優的收費亭數量。需要保證每一個進入收費廣場的交通路線都僅有一個收費亭。與當今的實踐相比較，在什么條件下，這或多或少有效。注意：最佳的定義由你自己決定。