第一篇：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。

第二篇：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：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。

第五篇：2009美國數學建模數學競賽試題及翻譯

2009年美國數學建模題

PROBLEM A: Designing a Traffic Circle

Many cities and communities（社區）have traffic circles—from large ones with many lanes（小巷、車道）in the circle(such as at the Triumphal Arch in Paris and the Victory Monument in Bangkok(曼谷))to small ones with one or two lanes in the circle.Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority（優先權）to traffic already in the circle;some position a yield sign in the circle at each incoming road to give priority to incoming traffic;and some position a traffic light on each incoming road(with no right turn allowed on a red light).Other designs may also be possible.The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle.State clearly the objective(s)(客觀的、目標)you use in your model for making the optimal（最理想的）choice as well as the factors that affect this choice.Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle.That is, summarize the conditions under which each type of traffic-control method should be used.When traffic lights are recommended, explain a method for determining how many seconds each light should remain green(which may vary according to the time of day and other factors).Illustrate how your model works with specific examples.問題A ： 設計圓形交通路口

許多城市和社區有環形通道——從那些繁華、交通擁擠的地方（例如巴黎的凱旋門和曼谷的勝利紀念碑）到擁有一兩條車道的小巷。一些圓形交通路口放置了停止或等待信號燈來決定等待中的車輛通行的優先權；一些在路口安置等待信號來控制每條車道的流通量；還有一些在每個路口安置紅綠燈(紅燈時不允許的向右轉)。其他設計也許也是可能的。這個問題的目標是使用模型來確定怎樣最好地控制車輛的進、出、繞行的流通量。清楚陳述模型的目標及做出最優選擇的原因和影響因素。包括一個給交通工程師的不超過兩頁關于如何使用模型來選擇具體圓形交通路口的適當的流量控制的方法的一個技術總結。也就是說，總結交通控制方法的每種類型應該使用的條件。當能夠使用時紅綠燈，確定的路燈亮的時間間隔（根據時刻和其他因素變化)。結合具體例子來說明說明模型的使用。

PROBLEM B: Energy and the Cell Phone

This question involves the “energy” consequences of the cell phone revolution.Cell phone usage is mushrooming, and many people are using cell phones and giving up their landline telephones.What is the

consequence of this in terms of electricity use? Every cell phone comes with a battery and a recharger.這個問題涉及到手機革命的能源問題。手機使用率迅速增加，許多人使用手機并放棄了固定電話。這方面的使用會給供電系統帶來什么后果？每個手機都配備了電池和充電器。

Requirement 1

Consider the current US, a country of about 300 million people.Estimate from available data the number H of households, with m members each,that in the past were serviced by landlines.Now, suppose that all the landlines are replaced by cell phones;that is, each of the members of the household has a cell phone.Model the consequences of this change for electricity utilization in the current US, both during the transition and during the steady state.The analysis should take into account the need for charging the batteries of the cell phones, as well as the fact that cell phones do not last as long as landline phones(for example, the cell phones get lost and break).要求1

目前認為美國是一個人口約為3億人的國家，從現有數據估計家庭用電量為h，每個家庭有M個成員，以前是使用座機電話的。現在，假設所有的座機被手機取代，也就是說每個家庭成員都有手機。分別建立美國在過渡轉換電能和穩定電能轉換的模式下的用電模型，分析應該考慮到對移動電話充電的需要，同時移動電話不能像固定電話那樣持續使用也是一個現實問題（比如說移動電話可能會丟失或者損壞）Requirement 2

Consider a second “Pseudo US”——a country of about 300 million people with about the same economic status as the current US.However, this emerging country has neither landlines nor cell phones.What is the optimal way of providing phone service to this country from an energy perspective? Of course, cell phones have many social consequences and uses that landline phones do not allow.A discussion of the broad and

hidden consequences of having only landlines, only cell phones, or a mixture of the two is welcomed.考慮到第二個“偽美國”——一個約3億人口、具有跟當前美國相同的經濟地位的國家，然而，這個新興國家既沒有固定電話也沒有移動電話，從這個國家的能源角度看，用什么最佳方式為這個國家提供電話服務，當然，手機有很多固定電話所不具有的用處和社會影響。這個討論是關于單獨使用固定電話或者單獨使用移動電話，或者混合使用兩種電話帶來的廣泛或潛在的影響。

Requirement 3

Cell phones periodically need to be recharged.However, many people always keep their recharger plugged in.Additionally, many people charge their phones every night, whether they need to be recharged or not.Model the energy costs of this wasteful practice for a Pseudo US based upon your answer to Requirement 2.Assume that the Pseudo US supplies electricity from oil.Interpret your results in terms of barrels of oil.手機需要定期充電。但是許多人在不考慮手機是否要充電的情況下，總是將充電器一直插在電器插槽上。在前兩個假設成立的基礎上，建立能源浪費的數學模型。另外，假定美國以石油作為電力來源，計算、解釋浪費的石油量。

Requirement 4

Estimates vary on the amount of energy that is used by various recharger types(TV, DVR, computer peripherals, and so forth)when left plugged in

but not charging the device.Use accurate data to model the energy wasted by the current US in terms of barrels of oil per day.在估計不同電器設備（電視、DVR、電腦外圍設備等）所使用的能源數量時，電器特性：沒有充電設備。要求用精確的數據建立關于當前美國每天所浪費的能源數量的模型，以原油（桶/天）計量。Requirement 5

Now consider population and economic growth over the next 50 years.How might a typical Pseudo US grow? For each 10 years for the next 50 years, predict the energy needs for providing phone service based upon your analysis in the first three requirements.Again, assume electricity is provided from oil.Interpret your predictions in term of barrels of oil.現在考慮人口及經濟增長在未來的50年內的情況。如何使這個假設中的美國發展壯大。對于每一個10年的今后50年內進行能源的需求預測，前提是在你前三次的分析基礎上而進行的提供的電話服務。另外還有一個假設是：電力來自石油。解釋你預測到的石油桶數目。