【正文】 fear Loss of billions of dollars in revenue by airlines to date Build a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline pany in order to find an optimal overbooking strategy, ., the number of people by which an airline should overbook a particular flight
。究竟他們對疏散交通流有多少影響？清楚地鑒別用什么性能的量度標(biāo)準(zhǔn)用于比較各種策略？ 2022 Contest Problems Problem A Wind and Waterspray An ornamental fountain in a large open plaza surrounded by buildings squirts water high into the air. On gusty days, the wind blows spray from the fountain onto passersby. The waterflow from the fountain is controlled by a mechanism linked to an anemometer (which measures wind speed and direction) located on top of an adjacent building. The objective of this control is to provide passersby with an acceptable balance between an attractive spectacle and a soaking: The harder the wind blows, the lower the water volume and height to which the water is squirted, hence the less spray falls outside the pool area. Your task is to devise an algorithm which uses data provided by the anemometer to adjust the waterflow from the fountain as the wind conditions change. Problem B Airline Overbooking You39。大多數(shù)人是駕駛他們的汽車的。下面的幾個問題是要處理到的： I26號公路中兩條通向海岸的線路逆轉(zhuǎn)，變成通向哥倫比亞方向，本質(zhì)上就是把整條I26號公路變成單向公路，上述的這個計(jì)劃什么條 件下能非常有效地改善疏散交通流？ 1999年，整個州的沿岸區(qū)域同時下達(dá)指令要進(jìn)行疏散。在 1999年，從哥倫比亞往西北方向的交通變得非常緩慢。（更精確的數(shù)據(jù)，如果查詢的話，也可以容易得到）這些州際公路每個方向有兩條交通線路，除了在大城市區(qū)域，那里有三條。從 Myrtle海灘以及 Hilton Head出發(fā)通往內(nèi)陸的主要公路的交通逆轉(zhuǎn)也作了類似計(jì)劃。 解決這個問題的主要解決提議是將 I26公路的交通逆轉(zhuǎn)，令兩邊包括沿岸通 道都改為通往內(nèi)陸 從查爾斯頓到哥倫比亞。 不幸中的萬幸是，這次 佛洛伊德 颶風(fēng)轉(zhuǎn)向北方并減弱了。 通常是輕松的兩小時車程結(jié)果變成了 18小時才能完成。 問題 B: 逃命吧！ 颶風(fēng)的憤怒 （一種 III級的風(fēng)）來了！ 1999年 在預(yù)報(bào)過的颶風(fēng) 佛洛伊德 登陸之前，美國南卡羅萊納州海岸的疏散 工作導(dǎo)致了一場極端的交通擠塞。 表格應(yīng)該 包括一個對應(yīng)不同道路等級（從 0%到 10%，增量為 1%）的風(fēng)速（道路等級定義為斜坡高度與長度之比，如果斜坡視為一個三角，則等級就是山腳處的斜角正弦）。 圖 1：左邊的是實(shí)心輪子，右邊的是裝有條幅的輪子 教練需要細(xì)節(jié)信息去幫助做決定，并已經(jīng)要求你的隊(duì)伍去完成下面列出的任務(wù)。所 作的決定是基于小山波的數(shù)目和險峻程度、天氣、風(fēng)速、競爭對手和其他考慮因素。在公路自行車比賽中，一個實(shí)心的輪子從來不會被用于做前輪，而可以做后輪。其中兩種基本類型是使用了輻條的車輪和使用實(shí)心盤的車輪（見圖 1）。 and on I20 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: what conditions does the plan for turning the two coastalbound lanes of I26 into two lanes of Columbiabound traffic, essentially turning the entire I26 into oneway traffic, significantly improve evacuation traffic flow? 1999, the simultaneous evacuation of the state39。s Wrath (An Ill Wind...) Evacuating the coast of South Carolina ahead of the predicted landfallof Hurricane Floyd in 1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I26, 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 twohour drive took up to 18 hours to plete. Many cars simply ran out of gas along the , 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 reversalof traffic on I26, so that both sides, including the coastalbound 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 acmodate the evacuees (including some ing from farther north by other routes), so some traffic continues outbound on I26 towards Spartanburg。s deciles. Is this possible? Data Sets Teams should design data sets to test and demonstrate their algorithms. Teams should characterize data sets that limit the effectiveness of their algorithms. Mathematical Contest in Modeling 1999 Problems Problem A Deep Impact For some time, the National Aeronautics and Space Administration (NASA) has been considering the consequences of a large asteroid impact on the earth. As part of this effort, your team has been asked to consider the effects of such an impact were the asteroid to land in Antarctica. There are concerns that an impact there could have considerably different consequences than one striking elsewhere on the pla. You are to assume that an asteroid is on the order of 1000 m in diameter, and that it strikes the Antarctic continent directly at the South Pole. Your team has been asked to provide an assessment of the impact of such an asteroid. In particular, NASA would like an estimate of the amount and location of likely human casualties from this impact, an estimate of the damage done to the food production regions in the oceans of the southern hemisphere, and an estimate of possible coastal flooding caused by largescale melting of the Antarctic polar ice sheet. Problem B Unlawful Assembly Many