美赛论文LaTeX模板.docx

美赛论文LaTeX模板.docx

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美赛论文LaTeX模板

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%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%

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\begin{document}

\begin{CJK*}{GBK}{song}

\CJKtilde

\title{\bf\yihaoAviationBaggageScreening\\{\&}FlightSchedule}

\author{}

\date{}

\maketitle

\section{Introduction}

FollowingtheterroristattacksonSeptember11,2001,thereis

intenseinterestinimprovingthesecurityscreeningprocessfor

airlinepassengersandtheirbaggage.Airlinesandairportsare

consideredhigh-threattargetsforterrorism,soaviationsecurity

iscrucialtothesafetyoftheair-travellingpublic.Bombsand

explosiveshavebeenknowntobeintroducedtoaircraftbyhold

baggageandcargo,carriedonbypassengers,andhiddenwithin

aircraftsupplies.

AtpresentToScreenorNottoScreen,thatisaHobson'schoice.

USCurrentlawsmandate100{\%}screeningofallcheckedbagsatthe429

passengerairportsthroughoutthenationbyexplosivedetectionsystems

（EDS）bytheendoftheDec312003.However,becausethemanufacturersare

notabletoproducetheexpectednumberofEDSrequiredtomeetthefederal

mandate,soitissignificanttodeterminethecorrectnumberofdevices

deployateachairport,andtotakeadvantageofthemeffectively.

TheTransportationSecurityAdministration（TSA）needsacomplicated

analysisonhowtoallocatelimiteddeviceandhowtobestusethem.

OurpapercontainsthemathematicalmodelstodeterminethenumberofEDSs

andflightschedulesforallairportsinMidwestRegion.Wealsodiscussthe

ETDdevicesastheadditionalsecuritymeasuresandthefuturedevelopment

ofthesecuritysystems.

\section{AssumptionandHypothesis}

\begin{itemize}

\itemThepassengerswhowillgetonthesameairplanewillarriveuniformly,namelythedistributionisflat.

\itemThedetectionsystems,bothEDSandETD,operateallthetimeduringpeakhour,exceptdowntime.

\itemTheairlinechecksthepassengersrandomly,accordingtoitsclaim.

\itemThepassengers,whoarejustlandingandleaveout,donothavetobecheckedthroughEDSorETD.

\itemAccordingtotheliterature,theaircraftloadsapproximatelyequalamongthesetsofdepartingflightduringthepeakhour.

\itemThelandingflightdidnotaffectthedepartureoftheplane.

\itemOnceapassengerarrives,hecangotoEDStobechecked,excepthehastowaitinline.

\itemOncepassengersfinishscreening,theycanbroadontheplaneinnotime.

\itemDuringpeakhours,asetofflightsdepartsatthesametimeeverythesameminutes.

\itemAlltherunwaysareusedasmuchaspossibleduringpeakhours.

\itemThemaximumnumberofthebaggageistwo,whichapassengercancarryonplane.[L]

\itemThedetectionmachineexaminesthebagsatthesamespeed.

\itemEDScannotmakemistakesthatitdetectanormalobjectasanexplosive.

\end{itemize}

\section{VariableandDefinition}

\begin{longtable}{p{100pt}p{280pt}}

\caption{Variables}\\%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

\hline\hline

\textbf{Symbol}&\textbf{Description}\\

\hline

$n_{ij}$&Theairplanenumberofthe$i^{\mathrm{th}}$typeinthe$j^{\mathrm{th}}$flightset\\

\hline

${NP}_i\:

（i=1,2,\ldots）$&Thenumberofpassengersoneachairplanesofthesametype.\\

\hline

$\xi_{ij}\:

（i,j=1,2,\cdots）$&Thenumberofbaggageoneachairplaneofthe$j^{\mathrm{th}}$flights\\

\hline

$a$&Themaximalnumberofairplanestype\\

\hline

$B_j^{set}$&Thetotalbaggagenumberofeachsetofflight\\

\hline

${NF}_i$&Numberofairplanesofeachtype\\

\hline

$\bar{\rho}$&Themeanvalueofpassengers'baggagecomingperminuteineveryflightset\\

\hline

$N_{set}$&Thenumberofflightsets\\

\hline

$B_{total}$&Thetotalnumberofcheckedbaggageduringthepeakhour\\

\hline

$H_{peak}$&Thelengthofthepeakhour\\

\hline

$T_{set}$&Thetimelengthduringwhicheachflightset'spassengerswaittobechecked\\

\hline

$\Deltat$&Thetimeintervalbetweentwoconsecutiveflightset\\

\hline

$N_{EDS}$&ThenumberofalltheEDSs\\

\hline

$N_{shadow}$&Thenumberofflightsetswhosepassengerswillbemixedupbeforebeingchecked\\

\hline

$v_{EDS}$&ThenumberofbaggagecheckingbyoneEDSperminute\\

\hline

$\rho_j$&Thenumberofpassengers'baggagecomingperminuteinoneflightset\\

\hline

$N_{runway}$&Thenumberofanairport'srunway\\

\hline\\*[-2.2ex]

${\bar{B}}^{set}$&Themeanvalueofcheckedbaggagenumberofeveryflightset\\

\hline

$M$&Thesecuritycost\\

\hline\hline

\label{tab1}

\end{longtable}

\subsubsection{Definition:

}

\begin{description}

\item[Flightset]Agroupofflightstakeoffatthesametime

\item[Thelengthofpeakhour]Thetimebetweenthefirstsetofflightandthelastset

\end{description}

\section{BasicModel}

Duringapeakhour,manyplanesandmanypassengerswoulddepart

fromairports.Therefore,Itisdifficulttoarrangeforthe

passengerstoenterairports.IftherearenotenoughEDSsfor

passengers'baggagetocheck,itwilltaketoolongtimeforthem

toenter.Thatwouldresultinthedelayofairplanes.Onthe

contrary,iftherearetoomanyEDSs,itwillbeawaste.Itis

ourtasktofindasuitablenumberofEDSsforairport.Inorder

toreachthisobjective,weusethelinearprogrammingmethodto

solveit.

\subsection{Baseanalysis}

Theairplanesareoccupiedatleastpartly.Thepassengers'

baggagewouldbecheckedbyEDSsbeforetheygetontheairplanes.

Wehaveassumedthateverypassengercarrytwobaggages.This

assumptionwouldsimplifytheproblem.Accordingtothedatafrom

theproblemsheet,wecanobtaintheusefulinformationthat

airlinesclaim20{\%}ofthepassengersdonotcheckanyluggage,

20{\%}checkonebag,andtheremainingpassengerschecktwobags.

Therefore,wecangainthetotalnumberofpassengers'baggage

thatshouldbecarriedononeplane:

$\xi_{ij}$.Moreover,wecan

gettheequationthatcalculate$\xi_{ij}$:

\[

\xi_{ij}={NP}_i\times20\%+{NP}_i\times60\%\times2

\]

Wedefinethematrixbelowasairplanebaggagenumbermatrix:

\[

\overset{\rightharpoonup}{\xi}_j=\left[\xi_{1j}\quad\xi_{2j}\quad\cdots\quad\xi_{ij}\quad\cdots\right]

\]

Wedefinethematrixbelowasflightschedulematrix:

\[

\left[\begin{array}{llcl}

n_{11}&n_{12}&\cdots&n_{1N_{set}}\\

n_{21}&n_{22}&