第一篇：2014年數(shù)學(xué)建模競(jìng)賽試題說(shuō)明

2014年西安電子科技大學(xué)數(shù)模校內(nèi)賽試題說(shuō)明

各位同學(xué)：

近日西北大學(xué)教務(wù)處網(wǎng)站上公布的五校聯(lián)賽的前三個(gè)題目不是本次西安電子科技大學(xué)數(shù)學(xué)建模競(jìng)賽校內(nèi)賽題目。我校校內(nèi)賽題目已在教務(wù)處實(shí)踐教學(xué)網(wǎng)站公布。

特此說(shuō)明！

校競(jìng)賽組委會(huì) 2014年5月1日

第二篇：數(shù)學(xué)建模競(jìng)賽試題

A題：中國(guó)人口老齡化問(wèn)題

目前，中國(guó)已進(jìn)入人口老齡化社會(huì)，而且老齡化趨勢(shì)越來(lái)越明顯。眾所周知，人口老齡化是個(gè)重大問(wèn)題，它涉及到經(jīng)濟(jì)、政治、文化和社會(huì)的各個(gè)領(lǐng)域，關(guān)系到國(guó)計(jì)民生和國(guó)家的長(zhǎng)治久安。為此，國(guó)內(nèi)外許多人口專家都提出了一些應(yīng)對(duì)人口老齡化的方法，如調(diào)整生育政策、延長(zhǎng)退休年齡以及完善社會(huì)化養(yǎng)老體系等。（1）收集有關(guān)數(shù)據(jù)，給出我國(guó)人口老齡化現(xiàn)狀的統(tǒng)計(jì)結(jié)果；

（2）試建立模型，預(yù)測(cè)在目前政策體系下，我國(guó)未來(lái)30年人口老齡化的變化趨勢(shì)；

（3）結(jié)合我國(guó)實(shí)際，給出應(yīng)對(duì)我國(guó)人口老齡化的具體方案，并預(yù)測(cè)該方案的效果。

B題：動(dòng)態(tài)生產(chǎn)問(wèn)題

某化肥廠生產(chǎn)一種復(fù)合肥料，根據(jù)銷售部門(mén)的預(yù)測(cè)，下一市場(chǎng)的月需求量如下表（單位：千噸）:

月份 1 2 3 4 5 6 7 8 9 10 11 12 在生產(chǎn)過(guò)程中，由于停機(jī)后再啟動(dòng)的費(fèi)用很高，故我們假定生產(chǎn)是連續(xù)的。生產(chǎn)出來(lái)的化肥除滿足當(dāng)月供貨外，剩下的可以存儲(chǔ)起來(lái)供以后用。現(xiàn)廠房有一個(gè)容量為5千噸的倉(cāng)庫(kù)可供使用。因?yàn)閭}(cāng)庫(kù)是廠方的，可以不考慮存儲(chǔ)費(fèi)用。生產(chǎn)過(guò)程中可以每月或者若干月調(diào)整一次生產(chǎn)量以滿足市場(chǎng)需求。由于生產(chǎn)工藝原因，如果從某月開(kāi)始增加產(chǎn)量，每噸化肥要增加成本10元，如果減少產(chǎn)量，則每噸要增加成本5元?？紤]到再下一的市場(chǎng)需求，要求年底有2千噸的庫(kù)存。根據(jù)以上條件，編制一個(gè)下一的生產(chǎn)計(jì)劃，要求因產(chǎn)量變化引起的成本增加總額最少，同時(shí)又保證有足夠的庫(kù)存來(lái)滿足各月份的銷售要求。又假如存儲(chǔ)需要費(fèi)用，每噸每月的存儲(chǔ)費(fèi)為6元，對(duì)上面的最優(yōu)生產(chǎn)計(jì)劃有影響嗎？

第三篇：大學(xué)生數(shù)學(xué)建模競(jìng)賽試題A

2014桂電大學(xué)生數(shù)學(xué)建模競(jìng)賽試題

A題 計(jì)劃生育新政對(duì)我國(guó)人口數(shù)量、結(jié)構(gòu)

及其經(jīng)濟(jì)的影響研究

李克強(qiáng)總理代表國(guó)務(wù)院在2014年政府工作報(bào)告中指出：“堅(jiān)持計(jì)劃生育基本國(guó)策不動(dòng)搖，落實(shí)一方是獨(dú)生子女的夫婦可生育兩個(gè)孩子政策?！?/p>

人口的數(shù)量和結(jié)構(gòu)是影響經(jīng)濟(jì)社會(huì)發(fā)展的重要因素。從20世紀(jì)70年代后期以來(lái)，我國(guó)鼓勵(lì)晚婚晚育，提倡一對(duì)夫妻生育一個(gè)孩子。該政策實(shí)施30多年來(lái)，有效地控制了我國(guó)人口的過(guò)快增長(zhǎng)，對(duì)經(jīng)濟(jì)發(fā)展和人民生活的改善做出了積極的貢獻(xiàn)。但另一方面，其負(fù)面影響也開(kāi)始顯現(xiàn)。如小學(xué)招生人數(shù)（1995年以來(lái)）、高校報(bào)名人數(shù)（2009年以來(lái)）逐年下降，勞動(dòng)人口絕對(duì)數(shù)量開(kāi)始步入下降通道，人口撫養(yǎng)比的“拐點(diǎn)”時(shí)刻即將到來(lái)。這些問(wèn)題都會(huì)對(duì)我國(guó)的經(jīng)濟(jì)和社會(huì)健康、可持續(xù)發(fā)展等產(chǎn)生一系列影響。

為此，根據(jù)要求回答下列問(wèn)題：

1.請(qǐng)你們就我國(guó)（或廣西區(qū)）上世紀(jì)50年代至今人口和經(jīng)濟(jì)的變化做出簡(jiǎn)要分析。

2.建立關(guān)于生育率、死亡率和性別比等多個(gè)因素的人口數(shù)學(xué)模型，分析計(jì)劃生育新政策（單獨(dú)二孩政策）對(duì)我國(guó)（或廣西區(qū)）未來(lái)人口數(shù)量，結(jié)構(gòu)及經(jīng)濟(jì)的影響（注：可到網(wǎng)上收集一些相關(guān)的文獻(xiàn)和數(shù)據(jù)，建立數(shù)學(xué)模型）；并對(duì)模型的結(jié)論發(fā)表自己的獨(dú)立見(jiàn)解。

參考文獻(xiàn)及數(shù)據(jù)來(lái)源：

1.2014年政府工作報(bào)告。

2.姜啟源，謝金星.數(shù)學(xué)模型.北京：高等教育出版社.2003.162-166.3.第六次全國(guó)人口普查數(shù)據(jù)（2010年）4.國(guó)家數(shù)據(jù)

第四篇：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)谧约旱淖孕熊嚿稀煞N基本的車輪類型是分別用金屬輻條和實(shí)體圓盤(pán)組裝而成（見(jiàn)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(lái)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(ài)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(lái)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(shuō)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(lái)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(kāi)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(guò)了南卡羅來(lái)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(wèn)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(kāi)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(lái)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(lái)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(méi)有充足的旅店空間為撤退者提供食宿（包括咽其他路線來(lái)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(kāi)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(kāi)往西北方向的車輛行進(jìn)得非常慢。對(duì)于這個(gè)問(wèn)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(wèn)題需要加以考慮：

在什么條件下，把I-26的兩條開(kāi)往海岸的次級(jí)公路變成開(kāi)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(lái)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(kāi)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(lái)減少離開(kāi)Columbia的車輛，這會(huì)對(duì)撤離交通有什么影響？

在1999年，離開(kāi)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(lái)納州交通問(wèn)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)。

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第五篇：數(shù)學(xué)建模歷年競(jìng)賽試題25

在一年一度的全國(guó)大學(xué)生數(shù)學(xué)建模競(jìng)賽中，設(shè)某校有20名隊(duì)員準(zhǔn)備參加競(jìng)賽，根據(jù)隊(duì)員的能力和水平要選出18名優(yōu)秀隊(duì)員分別組成6個(gè)隊(duì)，每個(gè)隊(duì)3名隊(duì)員去參加比賽，選拔隊(duì)員主要考慮的條件依次為有關(guān)學(xué)科成績(jī)（平均成績(jī)），智力水平（反映思維能力，分析問(wèn)題和解決問(wèn)題的能力等），動(dòng)手能力（計(jì)算機(jī)能力的使用，編程能力和其他方面的時(shí)間操作能力），寫(xiě)作能力，外語(yǔ)能力，協(xié)作能力（團(tuán)隊(duì)合作能力）和其他特長(zhǎng)，每個(gè)隊(duì)員的基本條件量化后如下表

隊(duì)員基本條件量化數(shù)據(jù)表

水平Ⅳ

寫(xiě)作能力

隊(duì)員

Ⅰ 8.68.28.08.68.89.29.27.07.78.39.09.69.58.69.19.38.48.77.89.0

Ⅱ 9.08.88.68.98.49.29.68.08.28.18.29.19.68.38.78.48.48.38.18.8

Ⅲ

動(dòng)手能力

Ⅴ

外語(yǔ)水平

Ⅵ

協(xié)作能力

Ⅶ

其他特長(zhǎng)

學(xué)科成績(jī)智力水平

A B C DE FG HIJK L M NO P QRS T 8.28.18.58.38.58.29.09.88.48.68.08.18.38.28.88.69.49.29.69.58.06.58.59.67.77.97.26.26.56.97.89.98.18.18.48.89.29.17.67.97.97.79.29.79.69.09.18.79.68.59.08.79.09.08.88.68.48.79.07.79.59.19.69.79.29.09.29.79.39.49.59.79.39.09.49.59.09.29.69.***567896

現(xiàn)在的問(wèn)題是：

1.在20名隊(duì)員中選擇18名優(yōu)秀隊(duì)員參加競(jìng)賽； 2.確定一個(gè)最佳的組隊(duì)使競(jìng)賽水平最高；

3.給出由18名隊(duì)員組成6個(gè)隊(duì)的組隊(duì)方案，使整體競(jìng)賽水平最高，并給出每個(gè)隊(duì)的競(jìng)賽技術(shù)水平。