美赛论文LaTeX模板.doc

% 本论文的排版主要参考了LaTeX2e插图指南(王磊), LaTeX2e用户手册, media的中文学位 % 论文宏包(CDT), happaytex的ORmain1.tex等文件以及ChinaTeX, CTeX论坛上的诸多贴子. % 本论文采用了Miktex2.2的方式在ChinaTeX.iso系统下得到了实现,其编译方式为 % latex(得到DVI文件)+dvips(得到PS文件)+ps2pdf(可得PDF文件). %documentclass12ptarticle%需要的一些宏包usepackageCJK % 中文输入环境宏包usepackagetitlesec,titletoc % 配合命令在后面, 章节标题设置usepackageindentfirst % 使首段首行缩进usepackagegraphicx % 插图宏包usepackagecaption2 % 可以更改插图, 表格的标题样式usepackagesubfigure % 产生并列的子图或子表, 命令subfigure, subtableusepackagelongtable % 如果表格太长, 超过了一页时, 就可以试试 longtable 宏包所定义的 longtable 环境usepackageslashbox % 在表格中绘制斜线usepackagefancyhdr % 更改页眉的宏包, 并可在页眉插入图片usepackagetimes % Times Roman + Helvetica + Courierusepackageamsmath % 数学符号宏包AMS-LaTeX, 如下面的overset需要此宏包%页面的设置specialpapersize=21cm,29.7cm setlengthtextwidth15cmsetlengthtextheight23cm setlengthevensidemargin0.46cmsetlengthoddsidemargin0.46cm setlengthtopmargin-1.84cmsetlengthheadheight2.9cm setlengthheadsep0.4cm%字号设置newcommandchuhaofontsize42ptbaselineskipselectfontnewcommandxiaochuhaofontsize36ptbaselineskipselectfontnewcommandyihaofontsize26ptbaselineskipselectfontnewcommandxiyihaofontsize24ptbaselineskipselectfontnewcommanderhaofontsize22ptbaselineskipselectfontnewcommandxiaoerhaofontsize18ptbaselineskipselectfontnewcommandsanhaofontsize16ptbaselineskipselectfontnewcommandxiaosanhaofontsize15ptbaselineskipselectfontnewcommandsihaofontsize14ptbaselineskipselectfontnewcommandxiaosihaofontsize12ptbaselineskipselectfontnewcommandwuhaofontsize10.5ptbaselineskipselectfontnewcommandxiaowuhaofontsize9ptbaselineskipselectfontnewcommandliuhaofontsize7.5ptbaselineskipselectfontnewcommandxiaoliuhaofontsize6.5ptbaselineskipselectfontnewcommandqihaofontsize5.5ptbaselineskipselectfontnewcommandbahaofontsize5ptbaselineskipselectfont%页眉的设置, 要用到fancyhdr宏包pagestylefancy fancyhead fancyfootfancyheadLfootnotesize Team # 189fancyheadRfootnotesize Page thepage of 42fancypagestyleplain%fancyheadLfootnotesize Team # 189fancyheadRfootnotesize Page thepage of 42setcountersecnumdepth4%更改theparagraph的编号样式makeatletterrenewcommandtheparagrapharabiccparagraphmakeatother%章节格式的设置titleformatsectionerhaobf0emtitleformatsubsectionxiaoerhaobf0emtitleformatsubsubsectionsanhaobf0emtitleformatparagraphhangvspace*0.5exsihaobfhspace*1emtheparagraph)0.5emvspace*-0.5ex%更改插图的标题renewcommandfigurenamewuhaobfsf Figurerenewcommandcaptionlabeldelim %更改表格的标题renewcommandtablenamewuhaobfsf Table%更改图形或表格与其标题的间距setlengthabovecaptionskip10ptsetlengthbelowcaptionskip10pt%定义产生不浮动图形和表格的标题的命令figcaption和tabcaptionmakeatletternewcommandfigcaptiondefcaptypefigurecaptionnewcommandtabcaptiondefcaptypetablecaptionmakeatother%自定义的可以调整粗细的水平线命令, 用于绘制表格, 调用格式myhline0.5mm.makeatletterdefmyhline#1% noalignifnum0=fihrule height #1 futurelet reservedaxhlinemakeatother%第一层列表序号为带圈的阿拉伯数字renewcommandlabelenumitextcircledarabicenumi%更改脚注设置renewcommandthefootnotefnsymbolfootnotebegindocumentbeginCJK*GBKsongCJKtildetitlebfyihao Aviation Baggage Screening& Flight ScheduleauthordatemaketitlesectionIntroductionFollowing the terrorist attacks on September 11, 2001, there isintense interest in improving the security screening process forairline passengers and their baggage. Airlines and airports areconsidered high-threat targets for terrorism, so aviation securityis crucial to the safety of the air-travelling public. Bombs andexplosives have been known to be introduced to aircraft by holdbaggage and cargo, carried on by passengers, and hidden withinaircraft supplies.At present To Screen or Not to Screen, that is a Hobsons choice.US Current laws mandate 100% screening of all checked bags at the 429passenger airports throughout the nation by explosive detection systems(EDS) by the end of the Dec 31 2003. However, because the manufacturers arenot able to produce the expected number of EDS required to meet the federalmandate, so it is significant to determine the correct number of devicesdeploy at each airport, and to take advantage of them effectively.The Transportation Security Administration (TSA) needs a complicatedanalysis on how to allocate limited device and how to best use them.Our paper contains the mathematical models to determine the number of EDSsand flight schedules for all airports in Midwest Region. We also discuss theETD devices as the additional security measures and the future developmentof the security systems.sectionAssumption and Hypothesisbeginitemize item The passengers who will get on the same airplane will arrive uniformly, namely the distribution is flat. item The detection systems, both EDS and ETD, operate all the time during peak hour, except downtime. item The airline checks the passengers randomly, according to its claim. item The passengers, who are just landing and leave out, do not have to be checked through EDS or ETD. item According to the literature, the aircraft loads approximately equal among the sets of departing flight during the peak hour. item The landing flight did not affect the departure of the plane. item Once a passenger arrives, he can go to EDS to be checked, except he has to wait in line. item Once passengers finish screening, they can broad on the plane in no time. item During peak hours, a set of flights departs at the same time every the same minutes. item All the runways are used as much as possible during peak hours. item The maximum number of the baggage is two, which a passenger can carry on plane. L item The detection machine examines the bags at the same speed. item EDS cannot make mistakes that it detect a normal object as an explosive.enditemizesectionVariable and Definitionbeginlongtablep100ptp280pt captionVariables %第一页表头的标题 endfirsthead %第一页的标题结束 caption(continued) %第二页的标题 endhead %第二页的标题结束 hlinehline textbfSymbol&textbfDescription hline $n_ij$&The airplane number of the $imathrmth$ type in the $jmathrmth$ flight set hline $NP_i:(i=1,2,ldots)$&The number of passengers on each airplanes of the same type. hline $xi_ij:(i,j = 1,2,cdots)$&The number of baggage on each airplane of the $jmathrmth$ flights hline $a$&The maximal number of airplanes type hline $B_jset$&The total baggage number of each set of flight hline $NF_i$&Number of airplanes of each type hline $barrho$&The mean value of passengers baggage coming per minute in every flight set hline $N_set$&The number of flight sets hline $B_total$&The total number of checked baggage during the peak hour hline $H_peak$&The length of the peak hour hline $T_set$&The time length during which each flight sets passengers wait to be checked hline $Delta t$&The time interval between two consecutive flight set hline $N_EDS$&The number of all the EDSs hline $N_shadow$&The number of flight sets whose passengers will be mixed up before being checked hline $v_EDS$&The number of baggage checking by one EDS per minute hline $rho_j$&The number of passengers baggage coming per minute in one flight set hline $N_runway$&The number of an airports runway hline*-2.2ex $barBset$&The mean value of checked baggage number of every flight set hline $M$&The security cost hlinehline labeltab1endlongtablesubsubsectionDefinition:begindescription itemFlight set A group of flights take off at the same time itemThe length of peak hour The time between the first set of flight and the last setenddescriptionsectionBasic ModelDuring a peak hour, many planes and many passengers would departfrom airports. Therefore, It is difficult to arrange for thepassengers to enter airports. If there are not enough EDSs forpassengers baggage to check, it will take too long time for themto enter. That would result in the delay of airplanes. On thecontrary, if there are too many EDSs, it will be a waste. It isour task to find a suitable number of EDSs for airport. In orderto reach this objective, we use the linear programming method tosolve it.subsectionBase analysisThe airplanes are occupied at least partly. The passengersbaggage would be checked by EDSs before they get on the airplanes.We have assumed that every passenger carry two baggages. Thisassumption would simplify the problem. According to the data fromthe problem sheet, we can obtain the useful information thatairlines claim 20% of the passengers do not check any luggage,20% check one bag, and the remaining passengers check two bags.Therefore, we can gain the total number of passengers baggagethat should be carried on one plane: $xi_ij$. Moreover, we canget the equation that calculate $xi_ij$: xi_ij=NP_itimes 20%+NP_itimes 60%times 2We define the matrix below as airplane baggage number matrix: oversetrightharpoonupxi_j=leftxi_1jquadxi_2jquadcdotsquadxi_ijquadcdotsrightWe define the matrix below as flight schedule matrix: leftbeginarrayllcl n_11&n_12&cdots&n_1N_set n_21&n_22&cdots&n_2N_set multicolumn4cdotfill n_a1&n_a2&cdots&n_aN_set endarrayrightIn this matrix, $n_ij$ is the airplane number of the$imathrmth$ type in the $jmathrmth$ flight set whichwill take off. Apparently, this value is an integer.We define the matrix below as flight set baggage number matrix: leftB_1setquad B_2setquadcdotsquad B_jsetquadcdotsquad B_asetrightIt is clear that they meet the relation below:beginequationbeginarraycl &leftxi_1jquadxi_2jquadcdotsquadxi_ijquadcdotsrightcdot leftbeginarrayllcl n_11&n_12&cdots&n_1N_set n_21&n_22&cdots&n_2N_set multicolumn4cdotfill n_a1&n_a2&cdots&n_aN_set endarrayright =&leftB_1setquad B_2setquadcdotsquad B_jsetquadcdotsquad B_asetrightendarraylabelFlight:baggageendequationThen, we know: B_jset=sumlimits_i=1axi_ijtimes n_ijThere are some constraints to the equation (refFlight:baggage).First, for each set of flight, the total number of airplanesshould be less than the number of runways. Second, the totalairplane number of the same type listed in the equation(refFlight:baggage) from every set of flight should be equal tothe actual airplane number of the same type during the peak hour.We can express them like these: sumlimits_i=1a n_ijle N_runwayquadquadsumlimits_j=1b n_ij=NF_iWe should resolve the number of flight sets. According to our assumptions,during the peak hour, the airlines should make the best use of the runways.Then get the number of flight sets approximately based on the number of allthe airplanes during the peak hour and that of the runways. We use anequation below to express this relation:beginequation N_set=leftlceilfracsumlimits_j=1N_setsumlimits_i=1a n_ijN_runwayrightrceil labelsets:numberendequationThe checked baggage numbers of each flight set are equal to eachother according to our assumption. We make it based on literature.It can also simplify our model. We define $barBset$ as themean value of checked baggage number of every flight set.Moreover, We define $barrho$ as the mean value of checkedbaggage number of every flight set per minute: barBset=fracB_totalN_set barrho=fracbarBsetT_set=fracB_totalT_setN_set=fracB_totalDelta tT_setH_peakThe course of passengers arrival and entering airport isimportant for us to decide the number of EDSs and to make theflights schedule. Therefore, we should analyze this processcarefully. Passengers will arrive between forty-five minutes andtwo hours prior to the departure time, and the passengers who willget on the same airplane will arrive uniformly. Then we can getthe flow density of all checked baggage at any time duringpassengers entering. This value is the sum of numbers ofpassengers checked baggage coming per minute. To calculate thisvalue, firstly, we should obtain flow density of each flight setschecked baggage. We define $rho_j $, namely the number of checkedbaggage per minute of one flight set: rho_j=fracB_jsetT_setSecondly, we draw graphic to help us to understand. We userectangle to express the time length for all the passengers of oneflight set to come and check bags. In the graphic, the black partis the period for them to come. During the white part, nopassengers for this flight set come. According to the problemsheet, the former is 75 minute, and the latter is 45 minute. Thelength of rectangle is 120 minute. $T_set$ is the period duringwhich all passengers of one flight set wait to be checked. Sincewe have assumed that each time interval between two consecutiveflight set is same value, we define $Delta t$ as it. Observe thesection that value we want to solve is $sumlimits_jrho_j$.Moreover, we can get another important equation from the graphicbelow:beginequation N_set=fracH_peakDelta t labelPeakHourendequationbeginfigurehbtp centering includegraphicswidth=298.2pt,totalheight=141.6ptfig01.eps caption labelfig1endfigureEach EDS has certain capacity. If the number of EDSs is $N_EDS$and one EDS can check certain number of baggage per minute (Thatis checking velocity, marked by $v_EDS$), the total checkingcapacity is $N_EDScdotfracv_EDS60$. $v_EDS$ is between160 and 210.Now we can easily decide in what condition the passengers can be checkedwithout delay: sumlimits_jrho_jle v_EDSThe passengers have to queue before being checked:$sumlimits_jrho_jv_EDS$Well then, how can we decide how many $rho_j$? It depends on howmany flight sets whose passengers will be mixed up before beingchecked. We note it as $N_shadow $. Return to the Figurereffig1, we can know: N_shadow=leftlfloorfracT_setDelta trightrfloorbeginfigure%htbp centering includegraphicswidth=240pt,totalheight=131.4ptfig02.eps caption labelfig2endfigureFrom Figure reffig1 and Figure reffig2, we can get theresult as follows:beginenumerate item If $N_shadowle N_set$, namely $H_peakT_set$, then $sumlimits_j=1N_shadowrho _jle N_EDSfracv_EDS60$ renewcommandtheequationarabicequationa That is: beginequation N_EDSgefrac60v_EDSsumlimits_j=1N_shadowrho_japproxfrac60v_EDSN_shadowbarrho=frac60B_totalDelta tv_EDST_setH_peakN_shadow labelEDS:number:a endequation item If $N_shadowN_set$, namely $H_peakle T_set$, then $sumlimits_j=1N_setrho_jle N_EDSfracv_EDS60$ setcounterequation3renewcommandtheequationarabicequationb That is: beginequation N_EDSgefrac60v_EDSsumlimits_j=1N_setrho_japproxfrac60v_EDSN_setbarrho=frac60B_totalDelta tv_EDST_setH_peakN_set labelEDS:number:b endequationendenumeratesubsectionThe number of EDSsThen we begin to resolve the number of EDSs assisted by the linearprogramming method.EDS is operational about 92% of the time. That is to say, whenever it isduring a peak hour, there are some EDSs stopping working. Then the workingefficiency of all the EDSs is less than the level we have expected.Therefore, the airline has to add more EDSs to do the work, which can bedone with less EDSs without downtime.We use binomial distribution to solve this problem. $N$ is the number ofactual EDSs with downtime and $k$ is the number of EDSs without downtime. Ifprobability is $P$, we can get the equation below: left(beginarraycNkendarrayright)cdot98%kcdot(1-98%)N-k=PWe can obtain $N$ when we give $P$ a certain value. In this paper,$P$ is 95%. The $N_EDS$ is the actual number we obtainthrough the equation above.Now we have assumed that passengers can be checked unless be delayed by thepeople before him once he arrives at airport. Apparently, if the time lengthbetween two sets of flight is short, the density of passengers will begreat. It will bring great stress to security check and may even make somepassengers miss their flight. To resolve this question, the airline has toinstall more EDSs to meet the demand. However, this meas