篇一：美赛论文模板中文
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本论文的排版主要参考了LaTe*2e插图指南(王磊),LaTe*2e用户手册,media的中文学位
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论文宏包(CDT),happayte*的ORmain1.te*等文件以及ChinaTe*,CTe*论坛上的诸多贴子.
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本论文采用了Mikte*2.2的方式在ChinaTe*.iso系统下得到了实现,其编译方式为
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late*(得到DVI文件)+dvips(得到PS文件)+ps2pdf(可得PDF文件).
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\begin{document}\begin{CJK*}{GBK}{song}\CJKtilde\title{\bf\yihaoAviationBaggageScreening\\{\&}FlightSchedule}\author{}\date{}\maketitle\section{Introduction}FollowingtheterroristattacksonSeptember11,2001,thereisintenseinterestinimprovingthesecurityscreeningprocessforairlinepassengersandtheirbaggage.Airlinesandairportsareconsideredhigh-threattargetsforterrorism,soaviationsecurityiscrucialtothesafetyoftheair-travellingpublic.Bombsande*plosiveshavebeenknowntobeintroducedtoaircraftbyholdbaggageandcargo,carriedonbypassengers,andhiddenwithinaircraftsupplies.AtpresentToScreenorNottoScreen,thatisaHobson"schoice.USCurrentlawsmandate100{\%}screeningofallcheckedbagsatthe429passengerairportsthroughoutthenationbye*plosivedetectionsystems(EDS)bytheendoftheDec312003.However,becausethemanufacturersarenotabletoproducethee*pectednumberofEDSrequiredtomeetthefederalmandate,soitissignificanttodeterminethecorrectnumberofdevicesdeployateachairport,andtotakeadvantageofthemeffectively.TheTransportationSecurityAdministration(TSA)needsaplicatedanalysisonhowtoallocatelimiteddeviceandhowtobestusethem.OurpapercontainsthemathematicalmodelstodeterminethenumberofEDSsandflightschedulesforallairportsinMidwestRegion.WealsodiscusstheETDdevicesastheadditionalsecuritymeasuresandthefuturedevelopmentofthesecuritysystems.\section{AssumptionandHypothesis}\begin{itemize}
\itemThepassengerswhowillgetonthesameairplanewillarriveuniformly,namelythedistributionisflat.
\itemThedetectionsystems,bothEDSandETD,operateallthetimeduringpeakhour,e*ceptdowntime.
\itemTheairlinechecksthepassengersrandomly,accordingtoitsclaim.
\itemThepassengers,whoarejustlandingandleaveout,donothavetobecheckedthroughEDSorETD.
\itemAccordingtotheliterature,theaircraftloadsappro*imatelyequalamongthesetsofdepartingflightduringthepeakhour.
\itemThelandingflightdidnotaffectthedepartureoftheplane.
\itemOnceapassengerarrives,hecangotoEDStobechecked,e*cepthehastowaitinline.
\itemOncepassengersfinishscreening,theycanbroadontheplaneinnotime.
\itemDuringpeakhours,asetofflightsdepartsatthesametimeeverythesameminutes..
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\itemAlltherunwaysareusedasmuchaspossibleduringpeakhours.
\itemThema*imumnumberofthebaggageistwo,whichapassengercancarryonplane.[Luggagepoint.]
\itemThedetectionmachinee*aminesthebagsatthesamespeed.
\itemEDScannotmakemistakesthatitdetectanormalobjectasane*plosive.\end{itemize}\section{VariableandDefinition}\begin{longtable}{p{100pt}p{280pt}}
\caption{Variables}\\
%第一页表头的标题
\endfirsthead
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\caption{(continued)}\\
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\endhead
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\hline\hline
\te*tbf{Symbol}&\te*tbf{Description}\\
\hline
$n_{ij}$&Theairplanenumberofthe$i^{\mathrm{th}}$typeinthe$j^{\mathrm{th}}$flightset\\
\hline
${NP}_i\:(i=1,2,\ldots)$&Thenumberofpassengersoneachairplanesofthesametype.\\
\hline
$\*i_{ij}\:(i,j=1,2,\cdots)$&Thenumberofbaggageoneachairplaneofthe$j^{\mathrm{th}}$flights\\
\hline
$a$&Thema*imalnumberofairplanestype\\
\hline
$B_j^{set}$&Thetotalbaggagenumberofeachsetofflight\\
\hline
${NF}_i$&Numberofairplanesofeachtype\\
\hline
$\bar{\rho}$&Themeanvalueofpassengers"baggageingperminuteineveryflightset\\
\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
$N_{shadow}$&Thenumberofflightsetswhosepassengerswillbemi*edupbeforebeing.
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checked\\
\hline
$v_{EDS}$&ThenumberofbaggagecheckingbyoneEDSperminute\\
\hline
$\rho_j$&Thenumberofpassengers"baggageingperminuteinoneflightset\\
\hline
$N_{runway}$&Thenumberofanairport"srunway\\
\hline\\*[-2.2e*]
${\bar{B}}^{set}$&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,manyplanesandmanypassengerswoulddepartfromairports.Therefore,Itisdifficulttoarrangeforthepassengerstoenterairports.IftherearenotenoughEDSsforpassengers"baggagetocheck,itwilltaketoolongtimeforthemtoenter.Thatwouldresultinthedelayofairplanes.Onthecontrary,iftherearetoomanyEDSs,itwillbeawaste.ItisourtasktofindasuitablenumberofEDSsforairport.Inordertoreachthisobjective,weusethelinearprogrammingmethodtosolveit.\subsection{Baseanalysis}Theairplanesareoccupiedatleastpartly.Thepassengers"baggagewouldbecheckedbyEDSsbeforetheygetontheairplanes.Wehaveassumedthateverypassengercarrytwobaggages.Thisassumptionwouldsimplifytheproblem.Accordingtothedatafromtheproblemsheet,wecanobtaintheusefulinformationthatairlinesclaim20{\%}ofthepassengersdonotcheckanyluggage,20{\%}checkonebag,andtheremainingpassengerschecktwobags.Therefore,wecangainthetotalnumberofpassengers"baggagethatshouldbecarriedononeplane:$\*i_{ij}$.Moreover,wecangettheequationthatcalculate$\*i_{ij}$:\[
\*i_{ij}={NP}_i\times20\%+{NP}_i\times60\%\times2\]Wedefinethematri*belowasairplanebaggagenumbermatri*:.
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\[
\overset{\rightharpoonup}{\*i}_j=\left[\*i_{1j}\quad\*i_{2j}\quad\cdots\quad\*i_{ij}\quad\cdots\right]\]Wedefinethematri*belowasflightschedulematri*:\[
\left[\begin{array}{llcl}
n_{11}&n_{12}&\cdots&n_{1N_{set}}\\
n_{21}&n_{22}&\cdots&n_{2N_{set}}\\
\multicolumn{4}{c}\dotfill\\
n_{a1}&n_{a2}&\cdots&n_{aN_{set}}
\end{array}\right]\]Inthismatri*,$n_{ij}$istheairplanenumberofthe$i^{\mathrm{th}}$typeinthe$j^{\mathrm{th}}$flightsetwhichwilltakeoff.Apparently,thisvalueisaninteger.Wedefinethematri*belowasflightsetbaggagenumbermatri*:\[
\left[B_1^{set}\quadB_2^{set}\quad\cdots\quadB_j^{set}\quad\cdots\quadB_a^{set}\right]\]Itisclearthattheymeettherelationbelow:\begin{equation}\begin{array}{cl}
&\left[\*i_{1j}\quad\*i_{2j}\quad\cdots\quad\*i_{ij}\quad\cdots\right]\cdot
\left[\begin{array}{llcl}
n_{11}&n_{12}&\cdots&n_{1N_{set}}\\
n_{21}&n_{22}&\cdots&n_{2N_{set}}\\
\multicolumn{4}{c}\dotfill\\
n_{a1}&n_{a2}&\cdots&n_{aN_{set}}
\end{array}\right]\\
=&\left[B_1^{set}\quadB_2^{set}\quad\cdots\quadB_j^{set}\quad\cdots\quadB_a^{set}\right]\end{array}\label{Flight:baggage}\end{equation}Then,weknow:\[
B_j^{set}=\sum\limits_{i=1}^a\*i_{ij}\timesn_{ij}\]Therearesomeconstraintstotheequation(\ref{Flight:baggage}).First,foreachsetofflight,thetotalnumberofairplanesshouldbelessthanthenumberofrunways.Second,thetotal.
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airplanenumberofthesametypelistedintheequation(\ref{Flight:baggage})fromeverysetofflightshouldbeequaltotheactualairplanenumberofthesametypeduringthepeakhour.Wecane*pressthemlikethese:\[
\sum\limits_{i=1}^an_{ij}\leN_{runway}\quad\quad\sum\limits_{j=1}^bn_{ij}={NF}_i\]Weshouldresolvethenumberofflightsets.Accordingtoourassumptions,duringthepeakhour,theairlinesshouldmakethebestuseoftherunways.Thengetthenumberofflightsetsappro*imatelybasedonthenumberofalltheairplanesduringthepeakhourandthatoftherunways.Weuseanequationbelowtoe*pressthisrelation:\begin{equation}
N_{set}=\left\lceil\frac{\sum\limits_{j=1}^{N_{set}}\sum\limits_{i=1}^an_{ij}}{N_{runway}}\right\rceil
\label{sets:number}\end{equation}Thecheckedbaggagenumbersofeachflightsetareequaltoeachotheraccordingtoourassumption.Wemakeitbasedonliterature.Itcanalsosimplifyourmodel.Wedefine$\bar{B}^{set}$asthemeanvalueofcheckedbaggagenumberofeveryflightset.Moreover,Wedefine$\bar{\rho}$asthemeanvalueofcheckedbaggagenumberofeveryflightsetperminute:\[
\bar{B}^{set}=\frac{B_{total}}{N_{set}}\]\[
\bar{\rho}=\frac{\bar{B}^{set}}{T_{set}}=\frac{B_{total}}{T_{set}N_{set}}=\frac{B_{total}\Deltat}{T_{set}H_{peak}}\]Thecourseofpassengers"arrivalandenteringairportisimportantforustodecidethenumberofEDSsandtomaketheflightsschedule.Therefore,weshouldanalyzethisprocesscarefully.Passengerswillarrivebetweenforty-fiveminutesandtwohourspriortothedeparturetime,andthepassengerswhowillgetonthesameairplanewillarriveuniformly.Thenwecangettheflowdensityofallcheckedbaggageatanytimeduringpassengers"entering.Thisvalueisthesumofnumbersofpassengers"checkedbaggageingperminute.Tocalculatethisvalue,firstly,weshouldobtainflowdensityofeachflightset"scheckedbaggage.Wedefine$\rho_j$,namelythenumberofcheckedbaggageperminuteofoneflightset:\[.
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\rho_j=\frac{B_j^{set}}{T_{set}}\]Secondly,wedrawgraphictohelpustounderstand.Weuserectangletoe*pressthetimelengthforallthepassengersofoneflightsettoeandcheckbags.Inthegraphic,theblackpartistheperiodforthemtoe.Duringthewhitepart,nopassengersforthisflightsete.Accordingtotheproblemsheet,theformeris75minute,andthelatteris45minute.Thelengthofrectangleis120minute.$T_{set}$istheperiodduringwhichallpassengersofoneflightsetwaittobechecked.Sincewehaveassumedthateachtimeintervalbetweentwoconsecutiveflightsetissamevalue,wedefine$\Deltat$asit.Observethesectionthatvaluewewanttosolveis$\sum\limits_j\rho_j$.Moreover,wecangetanotherimportantequationfromthegraphicbelow:\begin{equation}
N_{set}=\frac{H_{peak}}{\Deltat}
\label{PeakHour}\end{equation}\begin{figure}[hbtp]
\centering
\includegraphics[width=298.2pt,totalheight=141.6pt]{fig01.eps}
\caption{}
\label{fig1}\end{figure}EachEDShascertaincapacity.IfthenumberofEDSsis$N_{EDS}$andoneEDScancheckcertainnumberofbaggageperminute(Thatischeckingvelocity,markedby$v_{EDS}$),thetotalcheckingcapacityis$N_{EDS}\cdot\frac{v_{EDS}}{60}$.$v_{EDS}$isbetween160and210.Nowwecaneasilydecideinwhatconditionthepassengerscanbecheckedwithoutdelay:\[
\sum\limits_j\rho_j\lev_{EDS}\]Thepassengershavetoqueuebeforebeingchecked:$\sum\limits_j\rho_j>v_{EDS}$Wellthen,howcanwedecidehowmany$\rho_j$"Itdependsonhowmanyflightsetswhosepassengerswillbemi*edupbeforebeingchecked.Wenoteitas$N_{shadow}$.ReturntotheFigure\ref{fig1},wecanknow:\[
N_{shadow}=\left\lfloor\frac{T_{set}}{\Deltat}\right\rfloor\].
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\begin{figure}%[htbp]
\centering
\includegraphics[width=240pt,totalheight=131.4pt]{fig02.eps}
\caption{}
\label{fig2}\end{figure}FromFigure\ref{fig1}andFigure\ref{fig2},wecangettheresultasfollows:\begin{enumerate}
\itemIf$N_{shadow}\leN_{set}$,namely$H_{peak}>T_{set}$,then$\sum\limits_{j=1}^{N_{shadow}}\rho_j\leN_{EDS}\frac{v_{EDS}}{60}$
\renewmand{\theequation}{\arabic{equation}a}
Thatis:
\begin{equation}
N_{EDS}\ge\frac{60}{v_{EDS}}\sum\limits_{j=1}^{N_{shadow}}\rho_j\appro*\frac{60}{v_{EDS}}N_{shadow}\bar{\rho}=\frac{60B_{total}\Deltat}{v_{EDS}T_{set}H_{peak}}N_{shadow}
\label{EDS:number:a}
\end{equation}
\itemIf$N_{shadow}>N_{set}$,namely$H_{peak}\leT_{set}$,then$\sum\limits_{j=1}^{N_{set}}\rho_j\leN_{EDS}\frac{v_{EDS}}{60}$
\setcounter{equation}{3}\renewmand{\theequation}{\arabic{equation}b}
Thatis:
\begin{equation}
N_{EDS}\ge\frac{60}{v_{EDS}}\sum\limits_{j=1}^{N_{set}}\rho_j\appro*\frac{60}{v_{EDS}}N_{set}\bar{\rho}=\frac{60B_{total}\Deltat}{v_{EDS}T_{set}H_{peak}}N_{set}
\label{EDS:number:b}
\end{equation}\end{enumerate}\subsection{ThenumberofEDSs}ThenwebegintoresolvethenumberofEDSsassistedbythelinearprogrammingmethod.EDSisoperationalabout92{\%}ofthetime.Thatistosay,wheneveritisduringapeakhour,therearesomeEDSsstoppingworking.ThentheworkingefficiencyofalltheEDSsislessthanthelevelwehavee*pected.Therefore,theairlinehastoaddmoreEDSstodothework,whichcanbedonewithlessEDSswithoutdowntime.Weusebinomialdistributiontosolvethisproblem.$N$isthenumberofactualEDSswithdowntimeand$k$isthenumberofEDSswithoutdowntime.Ifprobabilityis$P$,wecangettheequationbelow:\[
\left(\begin{array}{c}N\\k\end{array}\right)\cdot98\%^k\cdot(1-98\%)^{N-k}=P.
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\]Wecanobtain$N$whenwegive$P$acertainvalue.Inthispaper,$P$is95{\%}.The$N_{EDS}$istheactualnumberweobtainthroughtheequationabove.Nowwehaveassumedthatpassengerscanbecheckedunlessbedelayedbythepeoplebeforehimoncehearrivesatairport.Apparently,ifthetimelengthbetweentwosetsofflightisshort,thedensityofpassengerswillbegreat.Itwillbringgreatstresstosecuritycheckandmayevenmakesomepassengersmisstheirflight.Toresolvethisquestion,theairlinehastoinstallmoreEDSstomeetthedemand.However,thismeasurewillcostmuchmoremoney.Consequently,wehavetosetasuitabletimeintervalbetweentwosetofflight.Basedonthebaseanalysisabove.Wecanusetheequation(\ref{sets:number})todecidethenumberofflightsets$N_{set}$assumingweknowthenumberofrunwaysofacertainairport.Thenbasedontheequation(\ref{PeakHour}),wecandecidethepeakhourlength$H_{peak}$whenweassumeatimeintervalbetweentwoconsecutiveflightsets.Thenweuse\te*tcircled{1}and\te*tcircled{2}todecidewhichtochoosebetweenequation(\ref{EDS:number:a})andequation(\ref{EDS:number:b}).Inconsequence,wecanobtaintheminimumofEDSsnumber.Ifwechoosedifferentnumbersofrunwaysandthetimeintervalsbetweentwoflightsets,wecangetdifferentEDSsnumbers.Inthispaperthatfollowed,wegainatableofsomevalueof$N_{runway}$and$\Deltat$withthecorrespondingEDSsnumbers.Moreover,wedrawsomefiguretoreflecttheirrelation.Foracertainairport,itsnumberofrunwayisknown.Givencertaintimeinterval($\Deltat$),wecangetthelengthofthepeakhour($H_{peak}$).Whenthe$N_{runway}$isfewenough,perhaps$H_{peak}$istoolongtobeadopted.However,foracertainairline,theycandecidethetimeintervaloftheirownpeakhour.Inthisgiventimeinterval,theycouldfindtheminimumof$N_{runway}$throughtheFigure\ref{fig3}.Wedrawasketchmaptodescribeoursteps.\begin{figure}[hbtp]
\centering
\includegraphics[width=352.8pt,totalheight=214.2pt]{fig03.eps}
\caption{}
\label{fig3}\end{figure}\subsection{TheFlightSchedule}Accordingtothebaseanalysis,wecanknowthattheflightschedulematri*and$\Deltat$isoneformofflighttimetable.In``ThenumberofEDSs"",wecangetsuitable$\Deltat$.Thenwe.
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shouldresolvetheflightschedulematri*.Becausewehaveassumedthatthecheckedbaggagenumbersofeachflightsetareequaltoeachother.Itcanbedescribedasfollows:\[
\left\{
\begin{array}{l}
\rho_j\appro*\bar{\rho}\\
B_j^{set}\appro*\bar{B}^{set}
\end{array}
\right.
\begin{array}{*{20}c}
\hfill&{j=1,2,\cdots,N_{set}}\hfill
\end{array}\]Theflightschedulematri*subjecttothisgroup:\[
\left\{
\begin{array}{ll}
\sum\limits_{j=1}^{N_{set}}n_{ij}={NF}_i&i=1,2,\cdots\\
\sum\limits_{i=1}^an_{ij}\leN_{runway}&j=1,2,\cdots,N_{set}\\
n_{ij}\ge0,&\mathrm{and}\:n_{ij}\:\mathrm{is}\:\mathrm{a}\:\mathrm{Integer}
\end{array}
\right.\]Inordertomakethebestuseofrunway,weshouldmake$\sum\limits_{i=1}^an_{ij}$asgreataswecanunlessite*ceed$N_{runway}$.Thenwecanseethathowtoresolvetheflightschedulematri*isaproblemofdivideamongagroupofintegers.Thisgroupisallthenumbersofeachflightpassengers"baggageinoneflightset.WeprogramforthisproblemusingMATLABandwegetatleastonesolutionintheend.However,thematri*elementswehaveobtainedarenotinteger,wehavetoadjustthemtobeintegersmanually.\subsection{ResultsandInterpretationforAirportAandB}Thenumberofpassengersinacertainflight(${NP}_i$),thetimelengthofsecuritychecking($T_{set}$),thecheckingvelocityofEDS($v_{EDS}$),andthenumberofbaggagecarriedbyonepassengerarerandom.\subsubsection{DataAssumption:}\begin{itemize}
\item$T_{set}$is110minutes,whichisreasonableforairline.
\itemTosimplifytheproblem,weassumethateverypassengercarry2baggage.Ifsomeofthe
passengerscarryonebaggage,thesolutionbasedon2baggagesperpassengermeetsthe
requirement..
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\itemThenumberofrunwaysinairportAandairportBis5.\end{itemize}\subsubsection{AirportA:}Oncethenumberofrunwayandthenumberoftheflightsaredecided,theflightschedulematri*isdecided,too.Weproducethismatri*usingMATLAB.Thismatri*paniedby$\Deltat$istheflightscheduleforairportA.$\Deltat$willbecalculatedin(\ref{Flight:baggage}),(\ref{sets:number})and(\ref{PeakHour}).Wecalculate$N_{EDS}$andmaketheflighttimetableinthreeconditions.Thethreeconditionsandthesolutionarelistedasfollowed:\paragraph{Everyflightarefullyoccupied}ThecheckingspeedofEDSis160bags/hour.\begin{table}[htbp]
\centering
\caption{}
\begin{tabular}{*{11}c}
\myhline{0.4mm}
$\mathbf{\Deltat(\min)}$&\te*tbf{2}&\te*tbf{4}&\te*tbf{6}&\te*tbf{8}&\te*tbf{10}&\te*tbf{12}&\te*tbf{14}&\te*tbf{16}&\te*tbf{18}&\te*tbf{20}\\
\myhline{0.4mm}
$N_{EDS}(\ge)$&31&31&31&31&31&29&24&22&20&17\\
\hline
$H_{peak}(\min)$&20&40&60&80&100&120&140&160&180&200\\
\myhline{0.4mm}
\end{tabular}
\label{tab2}\end{table}Weassumethatthesuitablevalueof$H_{peak}$is120minutes.Thenthesuitablevalueof$\Deltat$isabout12minutes,and$N_{EDS}$is29judgedfromFigure\ref{fig4}.Certainly,wecanwork$\Deltat$and$N_{EDS}$outthroughequation.\begin{figure}[htbp]
\centering
\includegraphics[width=294.6pt,totalheight=253.2pt]{fig04.eps}
\caption{}
\label{fig4}\end{figure}\paragraph{Everyflightisoccupiedbytheminimalnumberofpassengersonstatisticsinthelongrun.}ThecheckingspeedofEDSis210bags/hour.\begin{table}[htbp].
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\centering
\caption{}
\begin{tabular}{*{11}c}
\myhline{0.4mm}
$\mathbf{\Deltat(\min)}$&\te*tbf{2}&\te*tbf{4}&\te*tbf{6}&\te*tbf{8}&\te*tbf{10}&\te*tbf{12}&\te*tbf{14}&\te*tbf{16}&\te*tbf{18}&\te*tbf{20}\\
\myhline{0.4mm}
$N_{EDS}(\ge)$&15&15&15&15&15&14&13&12&10&7\\
\hline
$H_{peak}(\min)$&20&40&60&80&100&120&140&160&180&200\\
\myhline{0.4mm}
\end{tabular}
\label{tab3}\end{table}Weassumethatthesuitablevalueof$H_{peak}$is120minutes.Thenthesuitablevalueof$\Deltat$isabout12minutes,and$N_{EDS}$is14judgingfromFigure\ref{fig5}.Certainly,wecanwork$\Deltat$and$N_{EDS}$outthroughequation.\begin{figure}[htbp]
\centering
\includegraphics[width=294.6pt,totalheight=253.2pt]{fig05.eps}
\caption{}
\label{fig5}\end{figure}\paragraph{${NP}_i$and$v_{EDS}$arerandomvalueproducedbyMATLAB.}\begin{table}[htbp]
\centering
\caption{}
\begin{tabular}{*{11}c}
\myhline{0.4mm}
$\mathbf{\Deltat(\min)}$&\te*tbf{2}&\te*tbf{4}&\te*tbf{6}&\te*tbf{8}&\te*tbf{10}&\te*tbf{12}&\te*tbf{14}&\te*tbf{16}&\te*tbf{18}&\te*tbf{20}\\
\myhline{0.4mm}
$N_{EDS}(\ge)$&15&22&21&21&15&17&21&16&13&14\\
\hline
$H_{peak}(\min)$&20&40&60&80&100&120&140&160&180&200\\
\myhline{0.4mm}
\end{tabular}
\label{tab4}\end{table}Weassumethatthesuitablevalueof$H_{peak}$is120minutes.Thenthesuitablevalueof$\Deltat$isabout12minutes,and.
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$N_{EDS}$is17judgingfromFigure\ref{fig6}.Certainly,wecanwork$\Deltat$and$N_{EDS}$outthroughequation.\begin{figure}[htbp]
\centering
\includegraphics[width=294.6pt,totalheight=249.6pt]{fig06.eps}
\caption{}
\label{fig6}\end{figure}\subsubsection{Interpretation:}Byanalyzingtheresultsabove,wecanconcludethatwhen$N_{EDS}$is29,and$\Deltat$is12,theflightschedulewillmeetrequirementatanytime.Theflightscheduleis:\\[\inte*tsep]\begin{minipage}{\te*twidth}
\centering
\tabcaption{}
\begin{tabular}{c|*{8}c|c|c}
\myhline{0.4mm}
\backslashbo*{\te*tbf{Set}}{\te*tbf{Type}}&\te*tbf{1}&\te*tbf{2}&\te*tbf{3}&\te*tbf{4}&\te*tbf{5}&\te*tbf{6}&\te*tbf{7}&\te*tbf{8}&\te*tbf{NumbersofBags}&\te*tbf{NumbersofFlights}\\
\myhline{0.4mm}
1&2&0&0&0&2&1&0&0&766&5\\
\hline
2&2&0&2&0&2&0&0&0&732&4\\
\hline
3&0&1&1&1&2&0&0&0&762&4\\
\hline
4&0&1&0&0&2&1&0&0&735&4\\
\hline
5&0&1&0&0&2&1&0&0&735&5\\
\hline
6&2&0&0&0&1&0&0&1&785&5\\
\hline
7&2&0&0&0&2&0&1&0&795&5\\
\hline
8&0&1&0&0&2&1&0&0&735&4\\
\hline
9&2&0&0&0&2&1&0&0&766&5\\
\hline
10&0&0&0&2&2&0&0&0&758&5\\
\hline
Total&10&4&3&3&19&5&1&1&7569&46\\.
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\myhline{0.4mm}
\end{tabular}
\label{tab5}\end{minipage}\\[\inte*tsep]Wehaveproducedrandomvaluefor${NP}_i$and$v_{EDS}$.Onthiscondition,thenumberofEDSsis17,whichislessthan29thatwedecidefortheairportA.Thatistosayoursolutioncanmeettherealrequirement.\subsubsection{AirportB:}\paragraph{Thepassengerloadis100{\%}}ThecheckingspeedofEDSis160bags/hour.\begin{table}[htbp]
\centering
\caption{}
\begin{tabular}{*{11}c}
\myhline{0.4mm}
$\mathbf{\Deltat(\min)}$&\te*tbf{2}&\te*tbf{4}&\te*tbf{6}&\te*tbf{8}&\te*tbf{10}&\te*tbf{12}&\te*tbf{14}&\te*tbf{16}&\te*tbf{18}&\te*tbf{20}\\
\myhline{0.4mm}
$N_{EDS}(\ge)$&33&33&33&33&33&30&27&23&21&19\\
\hline
$H_{peak}(\min)$&20&40&60&80&100&120&140&160&180&200\\
\myhline{0.4mm}
\end{tabular}
\label{tab6}\end{table}Weassumethatthesuitablevalueof$H_{peak}$is120minutes.Thenthesuitablevalueof$\Deltat$isabout12minutes,and$N_{EDS}$is30judgingfromFigure\ref{fig7}.Certainly,wecanwork$\Deltat$and$N_{EDS}$outthroughequation.\begin{figure}[htbp]
\centering
\includegraphics[width=294.6pt,totalheight=249pt]{fig07.eps}
\caption{}
\label{fig7}\end{figure}\paragraph{Here,weonlyproducedrandomvalueof${NP}_i$and$v_{EDS}$.$\Deltat$willbecalculatedbelow.}\begin{minipage}{\te*twidth}
\centering
\tabcaption{}.
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\begin{tabular}{*{11}c}
\myhline{0.4mm}
$\mathbf{\Deltat(\min)}$&\te*tbf{2}&\te*tbf{4}&\te*tbf{6}&\te*tbf{8}&\te*tbf{10}&\te*tbf{12}&\te*tbf{14}&\te*tbf{16}&\te*tbf{18}&\te*tbf{20}\\
\myhline{0.4mm}
$N_{EDS}(\ge)$&23&22&24&21&22&23&20&19&15&15\\
\hline
$H_{peak}(\min)$&20&40&60&80&100&120&140&160&180&200\\
\myhline{0.4mm}
\end{tabular}
\label{tab7}\end{minipage}\\[\inte*tsep]Weassumethatthesuitablevalueof$H_{peak}$is120minutes.Thenthesuitablevalueof$\Deltat$isabout12minutes,and$N_{EDS}$is23judgingfromFigure\ref{fig8}.Certainly,wecanwork$\Deltat$and$N_{EDS}$outthroughequation.\begin{figure}[htbp]
\centering
\includegraphics[width=294.6pt,totalheight=250.8pt]{fig08.eps}
\caption{}
\label{fig8}\end{figure}\subsubsection{Interpretation:}Byanalyzingtheresultsabove,wecanconcludethatwhen$N_{EDS}$is30,and$\Deltat$is12,theflightschedulewillmeetrequirementatanytime.Theflightscheduleis:\\[\inte*tsep]\begin{minipage}{\te*twidth}
\centering
\tabcaption{}
\begin{tabular}{c|*{8}c|c|c}
\myhline{0.4mm}
\backslashbo*{\te*tbf{Set}}{\te*tbf{Type}}&\te*tbf{1}&\te*tbf{2}&\te*tbf{3}&\te*tbf{4}&\te*tbf{5}&\te*tbf{6}&\te*tbf{7}&\te*tbf{8}&\te*tbf{NumbersofBags}&\te*tbf{NumbersofFlights}\\
\myhline{0.4mm}
1&1&1&1&0&1&1&0&0&766&5\\
\hline
2&1&1&1&0&1&1&0&0&732&5\\
\hline
3&1&1&1&0&1&1&0&0&762&5\\.
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\hline
4&1&1&1&0&1&1&0&0&735&5\\
\hline
5&1&1&0&1&1&1&0&0&735&5\\
\hline
6&0&0&1&1&0&1&0&1&785&4\\
\hline
7&0&0&1&1&1&1&1&0&795&5\\
\hline
8&0&0&1&1&1&1&1&0&735&5\\
\hline
9&1&1&1&0&1&1&0&0&766&5\\
\hline
10&1&1&0&1&1&1&0&0&758&5\\
\hline
Total&8&6&7&5&9&10&2&1&8110&48\\
\myhline{0.4mm}
\end{tabular}
\label{tab8}\end{minipage}\\[\inte*tsep]Wehaveproducedrandomvaluefor${NP}_i$and$v_{EDS}$.Onthiscondition,thenumberofEDSsis17,whichislessthan29thatwedecidefortheairportA.Thatistosayoursolutioncanmeettherealrequirement.\subsubsection{Note:}The$H_{peak}$aboveisdecidedbytheairline.Wehaveassumedit120todescribeonepossibleresult.Perhapsitisnotthesuitablevalue,however,theairlinewouldselectsuitablevalue.\subsection{Simulation}Intheory,wecouldresolvethenumberofEDSsandtheflightschedulebythequeuingtheory.Wefindthatthismethodistoople*.Moreover,somevalueneededbythesolutioncan"tbeobtainedeasily.Therefore,weadoptthelinearprogrammingandintegerprogrammingmethodtoresolvethe$N_{EDS}$andtheflightschedule.However,ifwesimulatetheprocessoftheairline"srun,queuingtheoryismuchmoreconvenientanditmeetstherealitybetter.\subsubsection{Assumption}\begin{itemize}
\itemWeassumethatoncethepassengergoesintoacertainqueue,hewon"tchangeintoanotherqueue.
\itemThenumbersofpassengerswaitingtobecheckedineveryqueueequaleachother.
\itemThedistributionofsecuritychecktimethatapassengerspendstowaitisflat..
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\end{itemize}\subsubsection{Flowchart}\begin{description}
\item[Figure\ref{fig9}]Theprogramusedtoproducerandomnumber
\item[Figure\ref{fig10}]Theprogramusedtosimulate\footnote{现在才发现这个流程图有错误，正确的流程图应按照~\te*tbf{Appendi*\ref{MATLABProgram}}~中的~simulation.m~来绘制。}\end{description}\begin{minipage}{\te*twidth}
\centering
\includegraphics[width=174.6pt,totalheight=297.6pt]{fig09.eps}
\figcaption{\wuhao\bf\sfTheprogramusedtoproducerandomnumber}
\label{fig9}\end{minipage}\\[\inte*tsep]\paragraph*{Theparametersintheprogramtosimulate:}ST(k):servicetimeofpassengerk.CAT(k):arrivaltimeofpassengerk.IDT(k):idletimethatEDSorETDwaitforpassengerk.QL(I):thelengthofwaitedqueue.WT(I):waittimeofpassengerk.CDT(I):lefttimeofpassengerk.CLOCK:simulationtime.NATisatemporaryvariantforarrivaltime.NDTisatemporaryvariantforlefttime.N:thenumberoftotalpassengers.\\[\inte*tsep]\begin{minipage}{\te*twidth}
\centering
\includegraphics[width=356.4pt,totalheight=419.4pt]{fig10.eps}
\figcaption{\wuhao\bf\sfTheprogramusedtosimulate}
\label{fig10}\end{minipage}\\[\inte*tsep]\subsubsection{TheResultofSimulation}\paragraph*{Initialparameters:AtAirportA}FlightType=8;\qquadThecheck-timeofeachset:110minutes;TheintervalofFlightsets=6minutes,\qquad$H_{peak}$=60minutes.Simulationresults:Totalpassengers=4007,\qquadCheckedbags=5771Ifweusetheintegerprogrammingmethod,thenumberofEDSshouldbe22.\paragraph*{WhenthenumberofEDSis20,}lengthofthequeue=40;mean{\_}wait{\_}time=41.285minBoththelengthofqueueandthemeanwaittimeistoolong.Itmeansthe.
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numberofEDShereisnotreasonable.\paragraph*{WhenthenumberofEDSis30,}lengthofthequeue=14;mean{\_}wait{\_}time=37minBoththelengthofqueueandthemeanwaittimeisacceptable.ItmeansthenumberofEDShereisreasonable.\vskip1e*Moredetailedsimulationresultsarelistedinthe\te*tbf{Appendi*\ref{SimulationResult}}.\vskip1e*Ifwehavemoretime,wewillsimulatewithmoreotherkindsofdistributionstogetbetterresults.\subsection{RemendationtoMr.Sheldon}Itisclaimedthatmanufacturesarenotabletoproducethee*pectednumberofEDSsrequiredtomeetthefederalmandateof100{\%}screeningofcheckedluggage.Moreover,itsinstallcostandpurchasecostisveryhigh.Whenanairlineinstallsthisfacility,itsweightandvolumemaketheinstalldifficult.Therefore,atpresent,airlineshavetoinstallfewerEDSstoreducecost.Foracertainairport,weknowthatwhenthetimeintervaloftwoconsecutiveflightsincrease,namelyincreasingthetimeintervalofthepeakhour,thenumberofEDSsdecreasesclearly.Therefore,weremendairlineadopttheflightschedulewithalongpeakhourifithasnotenoughEDSstouse.Accordingtotheanalysisinthebaseanalysis,wesuggestairlineprolongthetimelengthduringwhichoneflightset"spassengerswaittobechecked,thatis$T_{set}$.Moreover,ifairlinesrestrictthenumberofpassengers"baggage,italsodecreasesthenumberofEDSs.Thismeasuretoreducecostwilldecreasetheservicequalityoftheairline.However,itwon"treducethesecurityrateapparently.\subsection{AdaptedforAlltheAirports}Nowwehaveacplishedthisproblemforacertainairlineintheory.Wecanget$N_{EDS}$andtheflighttimetable.Becausethismodelhaven"tmaderestricttothenumberofpassengersandflights,andsomerestrictinassumptionsisaccordwiththefact,wecanregardituniversal.Therefore,ourmodelcanbeadaptedtodeterminethenumberofEDSsandairlineschedulingforall193airportsintheMidwestRegion.However,wecanfindtwoissuesinthismodel.Firstly,ifthenumberofrunwayisnotenough,theproblemofdivideamongintegermaybehavenoanswersorunsuitableanswers.Therefore,ourmodelcanonlybeusedbytheairlineslargeenough.Nonetheless,ifthenumberofrunwayisnotenough,itmeansitisasmallairport.Infact,apeakhourthatisdistinctonlyemergeinlargeairports,therefore,thesmallairportisoutofourtask..
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Secondly,manyactualfactorsmayhaverandomvalue,suchasthenumberofpassengersinoneflight,thenumberofbaggagecarriedbyonepassenger,thecheckingvelocityofEDS.However,wecangettheirvaluerangebasedonourassumptionsandtheproblemsheet.Therefore,wecangetthema*imumandminimumoftheEDSsnumberusingourmodel.Wealsocanmaketheflighttimetable.Welisttheseanswersinourpaperthatfollowed.Inaddition,weuseMATLABtoproducetherandomvalueofeachvariableitem.Basedontheserandomvalues,wesimulatethecourseofairlineduringapeakhour.Theresultofsimulationisverygood.\subsection{IsETDworth"}AlthoughEDShaveahighaccuracy98.5{\%}inidentifyinge*plosivedevicesincheckedbags,thesafetystillcannotmeetthesecurityneedofpublic.Afterall,thefailtodetectane*plosivewillresultaterrifyingdisaster.Hence,alltheairportshavetotakeadditionalsecuritymeasurestoimprovethesafetybeforethenewlawsmandate100{\%}screeningofallcheckedbags.ThemeasurerequirethatapartofpassengerswillneedtohavealltheircheckedbagsscreenedthroughbothanEDSandane*plosivetracedetection(ETD)machine.LackingsufficientEDSmachines,tracedetectionequipmentcanofferadegreeofadditionalbombdetectioncapabilitythatwillincreaseoverallsecurity.DirectorofAirportSecurity,Mr.SheldonbelievethatETDisapromisingtechnologyandwillbedeployedasanintegralpartofnationalairportsecuritysystems,althoughithasnotbeencertified.However,willETDmachinereallyplaysuchanimportantroleinthesecuritysystemsinthefuture"Wediscussthisproblemconsideringboththecostandsafetyofthem,andmakesomeadviceinthefollowing.WecollectedtheknowndataaboutEDSandETDfromtheproblemandparedtheminthetable.\begin{table}[htbp]
\begin{center}
\caption{\wuhao\bf\sfparisonofEDS\&ETD}
\label{tab9}
\begin{tabular}{ccc}
\myhline{0.4mm}
&\te*tbf{EDS}&\te*tbf{ETD}\\
\myhline{0.4mm}
OperationalReliability&92{\%}&98{\%}\\
\hline
Accuracy&98.5{\%}&99.7{\%}\\
\hline
Speed&160$\sim$210&40$\sim$50\\
\hline.
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PurchaseCost&1,000,000&45,000\\
\hline
InstallCost&Severalthousand$^{\*iaowuhao\te*tcircled{1}}$&40,000$^{\*iaowuhao\te*tcircled{2}}$\\
\hline
LaborCost&510,000$^{\*iaowuhao\te*tcircled{3}}$&10timesofEDS\\
\hline
Weight&8tons&N.A.\\
\myhline{0.4mm}
\end{tabular}
\end{center}
{\wuhao\qquad\te*tcircled{1}:AirportA:{\$}100,000\qquadAirportB:{\$}80,00\qquad\te*tcircled{2}\te*tcircled{3}:Thesedataisfromtheliterature[ViggoButlerandRobertW.Poole,Jr.(2002)]}\end{table}\subsubsection{ETDnumberandtheflightschedule}Accordingtothedatapresentedinthetable,weassumethatthespeedofEDSisappro*imatelyfourtimesofthatofETDforsimplicity.\[
v_{EDT}=\frac{1}{4}v_{EDS}\]Theenhancedscreeningpolicyrequiresthat20{\%}ofthepassengers"bagswillneedtogothroughtie2-ETDs.Andtheairlineclaimthat80{\%}thepassengersshouldbecheckedbyEDS.SinceETDfollowEDS,EDScheckallthebagscheckedbyETD.WecangettheratioofthebagsgoingthroughoneETDandoneEDS.\[
\frac{\mathrm{Bag}_{ETD}}{\mathrm{Bag}_{EDS}}=\frac{20\%\:\mathrm{of}\:\mathrm{people}}{80\%\:\mathrm{of}\:\mathrm{people}}=\frac{1}{4}\]\[
\mathrm{Bag}_{ETD}=\frac{1}{4}\mathrm{Bag}_{EDS}\]ToensurethatETDdonotaffecttheflowofbaggage,weletthenumberofETDequalthenumberofEDS:\[
N_{ETD}=N_{EDS}\]Inactualoperation,thescreenersselecteveryfourthbagandsendtotheETDtobechecked.SothatETDdoesnotproducedelaytimeandtheflightschedulesneednottobechanged.SincetheoperationalreliabilityofETD98{\%}ishigherthanthatofEDS.
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92{\%},thenumberofETDissufficient.\subsubsection{Analysisoftheenhancepolicy}WeplantodiscussbothETDandEDSonthecostandthesafetytoassesstheenhancepolicy.\paragraph*{TheCost}\te*tbf{TakeairportAase*ample:}\[
\mathrm{Cost}=C_{purchase}+C_{install}+C_{labor}\]\[
\mathrm{Cost}_{EDS}=1000000+100000+510000=1610000\]\[
\mathrm{Cost}_{ETD}=45000+40000+510000\times10=5185000\]ThecostofETDismuchgreaterthanthatofEDS.ThisseemstotellusETDisnotworthtoinstall,theassessmentisnotplete.Wehavetotakeantherfactor-thesafetyintoaccount.\paragraph*{TheSafety}Herewediscussthesafetyundersomecircumstances.\begin{itemize}
\itemOnlyEDS:\end{itemize}Letussupposethereisaterroristinthepassengers,whotakesabombinhisbaggage.IfonlyusingEDS,whatistheprobabilitythattheterroristwillbedetected"Airlinefollowthisruletorandomlyselectpeopleandhavetheirluggagechecked:\begin{table}[htbp]
\centering
\begin{tabular}{ccc}
\myhline{0.4mm}
\te*tbf{20{\%}}&\te*tbf{20{\%}}&\te*tbf{60{\%}}\\
\myhline{0.4mm}
Donotcheckanyluggage&Checkonebag&Checktwobag\\
\myhline{0.4mm}
\end{tabular}\end{table}Iftheterroristcarrybombsinhisbaggage,theprobabilitythatbaggagewillbecheckis\begin{table}[htbp]
\centering
\caption{}
\begin{tabular}{ccc}.
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\myhline{0.4mm}
\te*tbf{Ifhetake}&\te*tbf{Thenumberofbaghavebomb}&\te*tbf{Probability($p$)}\\
\myhline{0.4mm}
Onebag&1&0.8\\
\hline
\raisebo*{-1.50e*}[0cm][0cm]{Twobags}&1&0.7\\
\cline{2-3}
&2&0.8\\
\myhline{0.4mm}
\end{tabular}
\label{tab10}\end{table}Forthesafety,wetakethelowestprobability,so\[
p_{select\_people}=0.7\]AnEDSis98.5{\%}accurateinidentifyinge*plosivedeviceincheckedbags,thenwegetthewholeprobabilityis\[
P(A)=0.7\times0.985=0.6895\]Definethisprobabilityassafetyrate.SoiftheairportonlyusesEDS,thesafetyrateis0.6895.Thisisnothigh.Butifwechangeourruletoselectcheckedpeopleandscreen100{\%}baggageasthelawsmandate,thesaferatewillbesameastheEDS"saccuracy0.985whichishighenough.Thus,iftheallthe429passengersairportshavetheirneededtheEDSinstalled,theaviationsecuritywillbeguaranteed.\begin{itemize}
\itemEDS+ETD\end{itemize}\begin{picture}(120,30)
\thicklines
\put(30,10){\fbo*{EDS}}\put(60,15){\vector(1,0){20}}\put(80,10){\fbo*{ETD}}\put(110,15){\vector(1,0){20}}\put(130,10){\fbo*{Aircraft}}\end{picture}Nowthemanufacturesarenotabletoproducethee*pectednumberoftheEDS,sotheairlineisnotabletocheck100{\%}ofallthebaggage.Theriskishigh.Thereforetheadditionalsecuritymeasureisneed.ThatistoaddanotherinspectionusingETDfollowtheEDS.TheaccuracyofETDinidentifyinge*plosivematerialsisveryhigh,whichis99.7{\%}.Theadditionalmeasurescreenedallcheckedbagsof20{\%}ofallpassengers.
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throughETDs,sothenumberofbagscheckedbyETDsis25{\%}oftheonescheckedbyEDSs.IfweonlyconsidertheETDselectandinspectthebags,wegot\[
P(B)=0.25\times0.997=0.24925\]ThenifETDisthefollow-upinspectionbehindEDS,thesafetyratewillbe\[
P(A+B)=P(A)+P(B)-P(A)P(B)=0.7669\]AfteraddingETDasthesecondinspection,thesafetyrateisimprovedfrom0.6895to0.7669.However,iftheairlinecarryout100{\%}screeningofallcheckedbaggageandETDsarestillfollowEDSs,thesafetyrateis\[
P(A+B)"=0.9965\]Itisonlychangealittlefrom0.985to0.9965.Soifanairportscreening100{\%},itwillnotneedETD.WecanconcludethatETDisthealternativeapproach,becausetheairportlacke*pectedamountofEDStoe*ecute100{\%}checkedwhichthelawsmandate.ETDisjustaninterimmeasuretoenhancethesecuritybecauseofthescarcityofEDS.\begin{itemize}
\itemThesecuritycost\end{itemize}Wedefine$M$asthecostfortheunitofsecurityrate\[
M=\frac{\mathrm{Cost}}{\mathrm{Security}\:\mathrm{Rate}}\]ThenfortheoptiononlyusingEDS,\[
M_{EDS}=\frac{\mathrm{Cost}_{EDS}}{P(A)}=\frac{1610000}{0.6895}=2335025\]FortheoptionusingETDafterEDS\[
M_{EDS-ETD}=\frac{\mathrm{Cost}_{EDS-ETD}}{P(AB)}=\frac{5185000}{0.7669}=6760985\]\[
M_{EDS-ETD}=2.89M_{EDS}\].
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ThesecuritycostofaddingETDisappro*imatelythreetimesofthecostofonlyusingEDS.Sowebelievethecostofsuchenhancedscreeningpolicyisnotjustifiedinlightofthevaluethatitprovides.TheETDtechnologystillhastobeimprovedinthefuture.\newpage\begin{itemize}
\itemShouldETDreplaceEDS"\end{itemize}IfwerequirethatonlyusingETDdonottogeneratedelaytime,ETDneedstocheckthesamequantityofbagsinthesametimeasEDSdo.Weknow$v_{EDT}=\frac{1}{4}v_{EDS}$,soweneed4ETDstoreplace1EDS.Undertheselectingrulewhichtheairlineclaim,thesecurityrateis\[
P(C)=0.7\times0.997=0.6979\]\[
M_{EDS-ETD}=\frac{4\times\mathrm{Cost}_{ETD}}{P(C)}=\frac{4\times5185000}{0.6979}=29717724\]\[
M_{EDS-ETD}=12.7M_{EDS}\]ETDsecuritycostismuchgreaterthanEDS.SincethenumberofETDis4timesofEDS,ETDconsumesmoreairportspaceandmorescreenertooperation.WeconcludethatETDcannotreplaceEDSdevicesundercurrenttechnologycondition.HerewestartimagineifEDScanbethefollow-upinspection,maybethismeasurewillcostlessthanETD.\begin{itemize}
\itemEDS+EDS\end{itemize}\begin{picture}(120,30)
\thicklines
\put(30,10){\fbo*{EDS}}\put(60,15){\vector(1,0){20}}\put(80,10){\fbo*{EDS}}\put(110,15){\vector(1,0){20}}\put(130,10){\fbo*{Aircraft}}\end{picture}Inthisscene,thecheckedbagsgothroughthetwoEDSssequentially.Thesecurityrateis\[.
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P(D)=0.25\times0.985=0.24625\]\[
P(A+D)=0.7659;\quadM_{EDS-EDS}=\frac{\mathrm{Cost}_{EDS-EDS}}{P(A+D)}=\frac{1610000\times2}{0.7659}=4204204\]paredwith``EDS+ETD"":$P(A+B)=0.7669;\:M_{EDS-ETD}=6760985$.\[
P(A+D)-P(A+B)=0.001;\quadM_{EDS-EDS}=0.62M_{EDS-ETD}\]ItisclearthatusingtheEDSasthesecondinspectionmeasurewillsavemuchmoneyonthedetectionsystemandwillnotdecreasethesecuritynoticeably.Thedecreasedamountcanbeneglect.Inaword,weremendthe``EDS+EDS""modetotheairports.\subsubsection{Conclusion}Ifwetakeboththecostandsafetyintoaccount,weremendthreeapproachesthatareeconomicalandeffective:\begin{itemize}
\itemIncreasetheRandomSampleRate(RSR)
Theairportshouldselectmorepeopleandmoreluggagestoinspect.Becausetheaccuracy
ofEDSisveryhigh,themostimportantfactorwhichinfluencesthesecurityrateisthe
RSR.IfyoudonotincreaseRSR,theinspectionissimilarwithfindingabombina
suitcaseislikefindingaparticularbladeofgrassinahaystack.Thebestsituationis
screening100{\%}checkedbags.
BecauseofthescarcityofEDS,increasingtheRSRwillincreasetheworkloadofthe
currentEDSsandproducedelaytime.Theairlineneedstoadjusttheflightscheduleand
improvecurrentconditionoftheairporttoincreaseRSR.Thisactionisveryworthto
take.
\itemAddthefollow-upinspection
Thefollow-upinspectioncanimprovethesecurityrate.Butbasedouranalysis,EDSismuch
betterthanETDtobeinstalledasthesecondgate.
\itemUpdatethedevice
ETDtechnologyneedstoimprovetheirspeedanddecreasetheirtotalcost.
\itemAdditionalsecuritymeasure
Thereareotheradditionalsecuritymeasurestoimplement,suchasManualinspection,
Sortingpeopletosample,Sniffingdogsandsoon.\end{itemize}\subsection{Futurescientificresearch}Inthefuture,thedepartmentofHomelandSecurityhavetoemphasizetheAviationSecurityResearch{\&}Developmentprogramandgivemorefundonfuturescientificresearchprograms..
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IftheETDwillbeanintegralpartofnationalsecuritysystems,webelieveETDtechnologyneedtoimproveonseveralaspectbasedonouraboveanalysis.\te*tbf{Thespeed.}ThespeedofETDismuchlowerthanEDS,althoughitsaccuracyalittlehigher.ThelowspeedresultsinthemorenumberofETDifithastocheckalargernumberofbags.NowtocheckthesameamountofbagsasEDSandnottodelaythecheckprocess,thenumberofETDsis4timesofEDSs.MoreETDsneedmorescreenertoperformandmorespacetobetakenupintheairport.Allofthatwilladdmorecosttothedetectionsystems.Thus,researchonthespeedwillbeapromisingfieldforETD.\te*tbf{Thecost.}AlthoughthecosttopurchaseandinstallanETDmachineischeaperthananEDS,thelaborcostistoohigh.Thelaborcostis10timesofEDS.Toreducethispartofthecost,wesuggestthatresearchesshouldfocusonhowtooptimizetheinterfacebetweensecurityequipmentanditshumanoperatorssothatthebinedsystemismosteffective,onhowtosimplifytheoperationalproceduresothattheequipmentwillneedlessoperatorandtheoperatorsneedlessskillstraining.Theseapproacheswillreducethelaborcost.\te*tbf{Accuracy.}SincetheaccuracyofETD99.7{\%}issatisfactory,thefundshouldinvestotherfactorsthatwillcontributemoretotheperformanceofthesecuritysystem.Weassumethatitisdifficulttomakeitbetter.MaybeweshoulddosomeworkontheaccuracyofEDS.\te*tbf{Operationalreliability.}Theimprovementonoperationalreliabilitywillcutthenumberofmachinedownandrequirelesssafeguardwork,sothatthetotale*pensewillbereduced.Inaword,themainemphasisoffuturescientificresearcheffortsindetectionmachineshasbeenimprovementinthee*istingtechnologies,particularlywithregardtospeedandcost,toenablescreeningofmorebagsinmoreairports.Furthermore,thedepartmentofHomelandSecurityhastoplanandimplementsomeresearchesforsecuritysystemperformance.Therearemanyareasthathavethebigimpact.WeoffersomeremendationinthememotoDirectorofHomelandSecurityanddiscusssomeareasinscience,technology,engineering,andmathematics(STEM)researches.\section{StrengthsandWeaknesses}\subsection{Strengths}\begin{itemize}
\itemInourmodel,therearenotanyrestrictionstothenumberofpassengersinoneflight,
thecheckspeedofEDS,etc.Therefore,ourmodelisuniversal.
\itemBasedontheresult,theairlinecangetallkindsofsolutionswhentheycareabout
differentaims.
\itemWee*plainthatETDsarenotjustifiedinlightofthevaluethatitprovides.Moreover,
Weanalyzehowtodevelopthisequipment..
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\end{itemize}\subsection{Weaknesses}\begin{itemize}
\itemInourmodel,becausetheEDScheckingspeed,thenumberofpassengersinacertainflight,
etc,arerandominreality,thenumberofEDSsvaries.ToavoidthelackofEDSsatany
time,weputethenumberofEDSs,whenpassengersarenumerous,andtheEDS"schecking
speedis160bagsperhour,andsoon.IftheairlineadoptsthisEDSnumber,thefacility
can"tbemadethebestuseof,becauseoftheshortpeakhourinaday.Therefore,somany
EDSsisawasteoutofthepeakhour.
\itemWhenweconstructourmodel,wehaven"ttakenintocounttheproblemhowtousetheseEDSs
best.UsingEDSsandpurchasingthemwouldcostalotofmoney;thereforehowtousethem
bestissignificant.Suchashowtoincreasetheirefficiency,andhowtoadjustthe
numberofEDSaccordingtothepassengers.\end{itemize}\newpage\begin{center}
\vspace*{1e*}\te*tbf{\sanhaoPositionPaper}\end{center}\noindentNowadaysintheaviationindustry,thesecuritybeesparamount.Theairlinemusttakemanynecessarysecuritymeasureswithintheunavoidableconstraints.Basedonourmodel,wesuggestsomesolutionsonthisissue.\vskip2e*\noindent\te*tbf{IncreasetheRandomSampleRate(RSR)andInstallmoreEDS.}IftheRSRislow,evenwiththe100{\%}accuracyofthedetectionsystem,thesafetyrateisstillverylow.Itisjustlikefindingaparticularbladeofgrassinahaystack.WiththehighaccuracyoftheEDS,checking100{\%}bags,thesafetyratewillbetheEDS"saccuracy98.5{\%}.TheRSRhasgreatinfluenceonthesafetyrate.Moreover,IncreasingtheRSRmeansincreasingthenumberofthecheckedbags.SotheairlinehastobuymoreEDSstoguaranteethatthepassengerandbaggagecangetontheaircraftwithoutdelaytime.\vskip2e*\noindent\te*tbf{Strengthentheinspection.}First,wecanaddthein-depthinspectiontothewholeprocessofinspection.Ifthesomeobjectissuspicious,letitgothroughanotherdetectionsystem,ormakemanual-openbaginspections.Second,anotheractionistosortpeopletoinspect.Wecanchangeourideafromtryingtofindbadobjecttoidentifyingthebadpeople.Third,theairlineneedstoupdatetheoldequipmentandpurchasenew.
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advanceddetectionmachines.\vskip2e*\noindent\te*tbf{Improvethehumanperformance.}Theairlinecantrainmoreskillscreenerandamelioratetheirworkconditiontokeepthemalertandvigilantincaseofveryrareevents.\vskip2e*\noindentAlthoughalltheactionsmentionedabovewillcontributetoimprovethesecuritymoreorless,inrealitywemustadmitthatmanyfactorsconstrainouractions.\vskip2e*\noindent\te*tbf{Thelimitedfund.}Alltheactionsneedmoneytoimplement,especiallytobuythee*pensiveEDS.Sotheairlinemustmakeagoodplantospendthem.\vskip2e*\noindent\te*tbf{Thecapacityofairport.}EDSisverylarge.Theairporthastoofferthesufficientroomandotherresourcetoinstallthem.Thebuysizeisalsolimitedtotheflightscheduleandthenumberoftherunwaysintheairport.\vskip2e*\noindent\te*tbf{Theservice.}Theairlinemustconsiderifitssecuritymeasuresinfluenceitsservicetotheircustomers.Fore*ample,passengershavetowaitinlinetobecheckalongtime.Theairlinerequiresmoreeffectivemeasurestoimproveitssecurityandserviceatthesametime.\vskip2e*\noindentInaword,theairlinemustmaketheireffortstoimprovethesecurityforthepublicandforthemselves.\newpage\vspace*{1e*}{\fontsize{30pt}{\baselineskip}\selectfont\quadMemorandum}\\\vskip4e*\qquad\begin{tabular}{lp{325pt}}
\te*tsf{\te*tbf{To:}}&DirectoroftheOfficeofSecurityOperations,TSA\\*[1e*]
\te*tsf{\te*tbf{From:}}&AnalysisTeam\\*[1e*]
\te*tsf{\te*tbf{Date:}}&02-10-03\\*[1e*]
\te*tsf{\te*tbf{Re:}}&TheModelaboutEDSandSchedule\\*[2.5e*]
\hline\end{tabular}\vskip3e*\noindentThesecuritycheckingbeforepassengersentertheairportbeesmoreandmoreimportant.However,thefacilityEDSforthischeckise*pensiveanddelaypeoplegettingontheairplane.Foralargeairline,especiallyduringapeakhour,howtoarrangeEDSsandtheflightschedulewellisverysignificanttoenhancethesecurityrateande*peditethecheckprocess.\vskip2e*\noindentWehaveanalyzedthisproblemcarefullyforall193airportsintheMidwestRegion.Itcanberesolvedbythelinearprogrammingmethod.Weusethismethodtoconstructourmodel.Asyouknow,foralargeairportduringapeakhour,becausemanyflightsneedtotakeoffinashorttime,itismonthatagroupofflightstakeoffatthesametime.Weusethetime.
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intervaloftwoconsecutiveflightsandaflightschedulematri*todescribetheactualflightschedule.Inthismatri*,itselementisthenumberofairplanesofthesametypeinthecertainflightset.\vskip2e*\noindentUsingtheactualdata,suchasthenumberofrunway,thenumbersofpassengersoneachairplane,etc,wecanfindtworelationsasfollowed.Oneisbetweenthetimelengthofapeakhourandthetimeintervaloftwoconsecutiveflights.TheotherisbetweenthenumberofEDSsandthetimeintervaloftwoconsecutiveflights.Wedrawagraphictodescribethesetworelationsinthecoordinateframe.Thenwecangetasuitablesolutionbasedontherealityofacertainairport.\vskip2e*\noindentForanyofthese193airportsintheMidwestRegion,itisclearthattheycouldobtainalldataneededbythismodelconveniently.Wehaven"tmadeanyrestrictionstothenumberofpassengersononeairplaneandthenumberofrunwayofanairport.Thenumberofflightsduringapeakhourcanvaryfromdifferentairports,too.Therefore,ourmodelisuniversalforeveryairport.\vskip2e*\noindentWefindthatifthenumberofrunwayisnotenough,thesolutionswegetthroughourmodelarenotverysuitable.However,ifthenumberofrunwayisnotenough,itmeansitisasmallairport.Infact,thedistinctpeakhouronlyemergeinlargeairports.Thatistosay,smallairportneedn"tworryaboutconflictbetweenthenumberofEDSsandtheflightscheduleduringapeakhour.\vskip2e*\noindentThisisourstatementaboutourmodel.Weremendyouadoptittoresolveyourproblemduringtheoperationofyourairline.Westronglybelieveitwillprovideyouagoodsolution.\vskip2e*\noindentThankyouforyourcarefullyreadingthismemo.\newpage\vspace*{1e*}{\fontsize{30pt}{\baselineskip}\selectfont\quadMemorandum}\\\vskip4e*\qquad\begin{tabular}{lp{325pt}}
\te*tsf{\te*tbf{To:}}&DirectorofHomelandSecurity,DirectorofTSA\\*[1e*]
\te*tsf{\te*tbf{From:}}&AnalysisTeam\\*[1e*]
\te*tsf{\te*tbf{Date:}}&02-10-03\\*[1e*]
\te*tsf{\te*tbf{Re:}}&EnhancedScreeningPolicy\\*[2.5e*]
\hline\end{tabular}\vskip3e*\noindentWeheardthatthedepartmentofHomelandSecurityismakingnationalleveldecisionsaboutadditionalsecuritymeasures.Becauseofhigherrisk,thereisasolutionthat.
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requiresthatsomeofpassengershavetheircheckedbagsscreenedthoughbothanEDSandanETD.However,afterweanalysesandparethecostandsafetyofboththeETDandEDS,weholdsomedoubtonthisoption.WebelievethattheETDasthefollow-upinspectionisjustaninterimapproach.\vskip2e*\noindentWeputethesecuritycost(thecostofperunitofsecuritysafety)andfoundtheoptioninwhichanETDfollowsanEDS(EDS+ETD)isabout3timesofonlyusingEDS.Thiscostisnotworththevalueitprovides.ThenweputeanotheroptioninwhichanotherEDSfollowedanEDS(EDS+EDS).Latteroptioncanachievenearlythesamesafetyrateoftheformer,butitse*penseisabouthalfoftheformer.\vskip2e*\noindentHence,weconcludethatthisscreeningpolicyisnotreasonableifwehaveampleEDSsmachines.Itisjustaninterimapproachtoenhancetheaviationsecuritywhenwelackofthee*pectednumberoftheEDSs.\vskip2e*\noindentIfallofthemachineswhichtheairlineusesareETDs,wealsoputethesecuritycost.Theresultisnearly13timesofEDS(withoutconsideringtheirconsumedspace).Thus,ETDscannottaketheplaceoftheEDSdevicesatpresent.\vskip2e*\noindentSurelyETDhastobeapromisingtechnology,becauseETDhassomee*cellentperformanceparameters.Bothitsaccuracyandoperationalreliabilityisveryhigh.Butithastwodisadvantageswhichwemusttakeintoaccountwhenwemakedecision,thespeedandthecost.ThetwoshortingsletusneedmoreETDsandspendmoremoneyonthem.IfyoubelieveETDwillbeanintegralpartofnationalsecuritysysteminne*tfewyears,weadviceyoushouldespeciallydevelopETDtechtoimprovethespeedandreducethee*pense.\vskip2e*\noindentInshortterm,wesuggestthatthemainemphasisoffuturescientificresearcheffortsindetectionmachineshasbeenimprovementinthee*istingtechnologies,particularlywithregardtospeedandcost,toenablescreeningofmorebagsinmoreairports.\vskip2e*\noindentInlongterm,weremendthatthedepartmentofHomelandSecurityshouldfundmorefuturescientificresearchprogramstodevelopmoreandbetterpromisingsecuritysystemsinSTEMresearchareas,Science,Technology,Engineering,andMathematics.ThefollowingaresomespecificR{\&}Dprogram:E*plosiveandweaponsdetectiontechnologydevelopment;Airportsecuritytechnology;Securitysystemsintegration;Aircraftandcontainerhardening;Humanfactors.\vskip2e*\noindentWethinkthescienceandtechnologystudythehumanshouldgainmoreattention.Suchasinbehavioralscience,we.
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studythebehaviorofthepeopleandcreatealargedatabasetoanalysisandutilizetodetecttheterrorist;insomehuman-relatedtechnologyfield,wedevisesomegadgettosensetherespirationandheartratesandotherbiologicalparameters,thenwecanparethemwiththee*isteddatatojudgeifheisaterrorist.Obviously,thenewadvancede*plosivetechnologyalsoshouldbedeveloped.Morepromisingtechnologies(suchas*-raydiffraction;microwaveimaging)consumemodestspaceandlaborcost.Weshouldoffertheconnivancetofundthem.\vskip2e*\noindentWearegladtoofferyoutheseadvicesandwillappreciatethatyoucanconsideritseriously.\newpage\begin{thebibliography}{99}
\bibitem{1}A,Biran,{\&}M,Breiner.(1995).\te*tit{MATLABforEngineers.}England:Addison-WesleyPulishingpany.
\bibitem{2}Kaufmann,A.(1995).\te*tit{IntegerandMi*edProgramming,TheoryandApplications.}London:AcademicPress.INC.LTD..
\bibitem{3}Banks,J.,{\&}J.,C.(1984).\te*tit{Discrete-eventSystemSimulation.}NewJersey:PrenticeHallInc.EnglewoodCliffs.
\bibitem{4}Kabak,I.W.(1968).\te*tit{StoppingRulesforQueuingSimulation}(Vol.16).US:OperationResearch.
\bibitem{5}Law,A.M.,{\&}D.,K.W.(1982).\te*tit{SimulationModelingandAnalysis.}US:McGrawHill.
\bibitem{6}Carter{\&}Bergess.(2002).\te*tit{AirportSecurity.}RetrievedfromtheWorldWide
Web:\\.c-b./industryinfo/techspeakspecial/TS{\_}AirportSecurity.pdf
\bibitem{7}FAA.(1999).\te*tit{AviationSecurity.}RetrievedfromtheWorldWide
\bibitem{8}DanielMorgan.(2001).\te*tit{AviationSecurityTechnologiesandProcedures:ScreeningPassengersandBaggage.}RetrievedfromtheWorldWide
Web:\\carper.senate.gov/acrobat{\%}20files/RL31151.pdf
\bibitem{8}LyleMalotky.(2002).\te*tit{AviationSecurityTechnologyAviationSecurityTechnology.}RetrievedfromtheWorldWide
Web:\\.zsrlaw./publications/2002{\_}Symposium/Malotky.pdf
\bibitem{9}Luggagepoint..\te*tit{BaggageGuidelines.}RetrievedfromtheWorldWide
Web:\\.luggagepoint./baggageguide.asp
\bibitem{10}AthonyFeinberg.(1996).\te*tit{TheFAAAviationSecurityR{\&}DProgram.}RetrievedfromtheWorldWide
Web:\\.wws.princeton.edu/cgi-bin/byteserv.prl/$\sim$ota/disk1/1992/9235/923508.PDF
\bibitem{11}PhiladelphiaInternationalAirport.\te*tit{FlightSchedule.}RetrievedfromtheWorldWide
Web:\\.phl.org/inde*{\_}fids.html
\bibitem{12}TechnologyAgainstTerrorism:StructuringSecurity.(1996).\te*tit{HumanFactorsinAviationSecurity.}RetrievedfromtheWorldWide
Web:\\.wws.princeton.edu/cgi-bin/byteserv.prl/$\sim$ota/disk1/1992/9235/923507.PDF.
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\bibitem{13}KristinaEddy.\te*tit{LebanonAirportGettingTeamOfFederalScreenersThisWeek.}RetrievedfromtheWorldWide
Web:\\.vnews./11102002/753238.htm
\bibitem{14}JohnE.Kobza.(2000).\te*tit{ResearchonAviationSecurity*.}RetrievedfromtheWorldWide
\bibitem{15}ViggoButlerandRobertW.Poole,Jr.(2002).\te*tit{RethinkingChecked-BaggageScreening.}RetrievedfromtheWorldWide
Web:\\.rppi.org/ps297.pdf
\bibitem{16}GaryKauvar,BernardRostker,RussellShaver.(2002).\te*tit{WHITEPAPER.}RetrievedfromtheWorldWide\end{thebibliography}\newpage\begin{appendi*}%更改附录的章节样式
\titleformat{\section}{\erhao\bf}{Appendi*\thesection}{1em}{}[]\section{TechnicalInformationSheet(TIS)}\vspace*{4e*}\begin{center}PeakHourFlightDeparturesforAirportsAandBNote:Onaverage,2{\%}offlightsarecancelledeachday\end{center}\begin{table}[htbp]
\centering
\begin{tabular}{cccc}
\myhline{0.4mm}
\te*tbf{Flight}&\te*tbf{NumberofSeats}&\te*tbf{AirportANumberof}&\te*tbf{AirportBNumberof}\\
\te*tbf{Type}&\te*tbf{onEachFlight}&\te*tbf{FlightsofEachType}&\te*tbf{FlightsofEachType}\\
\myhline{0.4mm}
1&34&10&8\\
\hline
2&46&4&6\\
\hline
3&85&3&7\\
\hline
4&128&3&5\\
\hline
5&142&19&9\\
\hline
6&194&5&10\\
\hline
7&215&1&2\\
\hline.
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8&350&1&1\\
\myhline{0.4mm}
\end{tabular}\end{table}\newpage\section{MATLAB\te*tregistered{}Program}\label{MATLABProgram}\subsubsection{data.m(MATLAB\te*tregistered{}scriptfile)}{\liuhao\begin{verbatim}%Thisprogrammainlygeneratesinitialdata.%KnownnumbersaboutEDSandETD.p_Ope_EDS=0.92;p_Ope_ETD=0.98;p_Acc_EDS=0.985;p_Acc_ETD=0.997;v_EDS_LOW=160;v_EDS_UP=210;v_ETD_LOW=40;v_ETD_UP=50;v_EDS_mean=0.5*(v_EDS_UP+v_EDS_LOW);Purchase_EDS=1000000;Purchase_ETD=45000;Install_EDS_A=100000;Install_EDS_B=80000;Install_ETD=40000;Labor_EDS=510000;
%Knownfromliteratures.Labor_ETD=10*Labor_EDS;Weight_EDS=8;%KnownnumbersaboutAirportA&AirportB.Flight_cancelled=0.02;Type=input("PleaseinputthenumberofFlightType:");Flight_type=1:Type;Num_Seats=[344685128142194215350];Num_Flight_A=[1043319511];Num_Flight_B=[867591021];p_Seats_LOW=[0.70.70.70.60.60.60.60.5];p_Seats_UP=[11111111];p_Seats_mean=0.5*(p_Seats_LOW+p_Seats_UP);Persons_checked=[0.20.20.6];Bags_checked=[012];%Passengerstypicallyarrivefortheirflightbetweenforty-fiveminutesand%twohourspriortotheirscheduleddeparturetime.TPL=-45;TPE=-120;%Assumednumbers.Num_runway=5;
%NumberofAirport"sRunways.T_set=input("Pleaseinputthecheck-timeofeachset:");%ConsidereachEDS"soperationalprobabilityisabout92%,%Permit:theprobabilityofenoughworkableEDSs.Permit=0.95;Interval=input("TheintervalofFlights:");.
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%DetermineputingwhichAirport.which_flight=input("0forA,1forB:");ifwhich_flight==Num_Flight=Num_Flight_A;else
Num_Flight=Num_Flight_B;end\end{verbatim}}\subsubsection{EDS.m(MATLAB\te*tregistered{}scriptfile)}{\liuhao\begin{verbatim}%ThisprogramismainlytodeterminetheminimumofEDSnumber.%BasedonfollowAssumptions:%1.Airlinesclaimthat20%ofthepassengersdonotcheckanyluggage,20%checkonebag,%
andtheremainingpassengers(60%)checktwobags.%2.Ifthenumberofcheckedbagsequals90.2,thenletitbeequal91.%3.Historicaldataindicatesthatflightswith85orfewerseatstypicallyflywithbetween70%%
and100%oftheirseatsoccupied.Flightswithbetween128and215seatstypicallyfly%
withbetween60%and100%oftheirseatsoccupied.Flightswith350seatstypicallyfly%
withbetween50%and100%oftheirseatsoccupied.Letthembeuniformdistribution.%Neededvariant:Num_Flight,Flight_type,N_runway,Interval,Num_Seats,Persons_checked,%
Bags_checked,Flight_cancelled,T_set,v_EDS,p_Ope_EDS,Permit%DeterminethevelocityofEDS.which_v_EDS=input("0formeanofv_EDS,1forrandom,2formin,3forma*:");switchwhich_v_EDScasev_EDS=v_EDS_meancase1%ConsideredeachEDScane*aminebetween160and210bagsperhour.
%Letitbeuniformdistribution.
v_EDS=unidrnd(v_EDS_UP-v_EDS_LOW+1)+v_EDS_LOW-1;case2v_EDS=v_EDS_LOWotherwise
v_EDS=v_EDS_UPendwhich_p_Seats=input("0formeanofpassengers,1forrandom,2formin,3forma*:");switchwhich_p_Seatscasep_Seats=p_Seats_mean;case1p_Seats=unifrnd(p_Seats_LOW,p_Seats_UP);case2p_Seats=p_Seats_LOW;.
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otherwise
p_Seats=p_Seats_UP;end%TotalFlights.Flight_total=sum(Num_Flight);bar(Flight_type,Num_Flight)*label("FlightType")ylabel("NumberofFlightsofEachType")%Num_Flight=Num_Flight_(AorB)N_set=ceil(sum(Num_Flight)/Num_runway);%Determinehowlongthepeakhourwilllast.Peak_Hour=N_set*Interval;%NumberofcheckedbagsoneachFlight.Num_Checked_Bags=ceil(Num_Seats*(Persons_checked*Bags_checked"));%TotalPossibleNumbersofpassegers.Passengers_total=sum(diag(p_Seats)*(diag(Num_Flight)*Num_Seats"))*(1-Flight_cancelled)%TotalPossibleNumbersofcheckedbags.Bags_total=sum(diag(p_Seats)*(diag(Num_Flight)*Num_Checked_Bags"))*(1-Flight_cancelled)%puteworkableEDSs"numbers.ifPeak_Hour>T_set
Num_EDS=ceil((60*Bags_total)/(v_EDS*Peak_Hour))else
Num_EDS=ceil((60*Bags_total)/(v_EDS*T_set))end%ConsideredthateachEDSisoperationalabout92%ofthetime.%Num_EDS_ideal:theidealnumberofEDSs.Num_EDS_ideal=Num_EDS:Num_EDS+20;work=1-binocdf(Num_EDS-1,Num_EDS:Num_EDS+20,p_Ope_EDS);figurebar(Num_EDS_ideal,work)*label("NumberofEDSsifneeded")ylabel("ProbabilityofenoughworkableEDSs")work_inde*=find(work>=Permit);Num_EDS_ideal=Num_EDS_ideal(work_inde*(1))work=work(work_inde*(1))\end{verbatim}}\subsubsection{schedule.m(MATLAB\te*tregistered{}scriptfile)}{\liuhao\begin{verbatim}%Thisprogrammainlytofindinitialscheduleviasolve%%
minnorm(*i0*N)%
N_set%
s.t
sum(n(i,j))=Num_Flight(i),
i=1,2,...,8.
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%
j=1%
8%
sum(n(i,j))<=N_runway,
j=1,…,N_set%
i=1%
0<=n(i,j)<=5%%Wecanchangeitintoanotherform:%%
min0.5**H*"+c"*%
s.t
A*<=b%
Aeq**=beq%
VLB<=*<=VUB%Neededvariant:Num_Flight,Num_runway,Type(Fromdata.m)%
N_set,Num_Checked_Bags(FromEDS.m)beq=[Num_Flight];b=[Num_runway*ones(10,1);zeros(Type*N_set,1)];VLB=0;VUB=Num_runway;%N_equ:thenumberofequations.N_equ=Type*N_set;c=[];kind=input("0formean,1forrandom,2forminpassengers,3forma*passengers,4forEDS.m:")switchkindcase%Now*i0:themeanPossibleNumbersofcheckedbagsonEachFlight.
*i0=diag(p_Seats_mean)*Num_Checked_Bags"case1p_Seats_rnd=unifrnd(p_Seats_LOW,p_Seats_UP);
%*i0:thePossibleNumbersofcheckedbagsonEachFlight.
*i0=diag(p_Seats_rnd)*Num_Checked_Bags"case2*i0=diag(p_Seats_LOW)*Num_Checked_Bags"case3*i0=diag(p_Seats_UP)*Num_Checked_Bags"otherwise
*i0=diag(p_Seats)*Num_Checked_Bags"end%Generatethemati*H.H_i=[1:8*N_set,1:7*N_set,1:6*N_set,1:5*N_set,1:4*N_set,1:3*N_set,1:2*N_set,1:N_set,...
N_set+1:8*N_set,2*N_set+1:8*N_set,3*N_set+1:8*N_set,4*N_set+1:8*N_set,...
5*N_set+1:8*N_set,6*N_set+1:8*N_set,7*N_set+1:8*N_set];H_j=[1:8*N_set,N_set+1:8*N_set,2*N_set+1:8*N_set,3*N_set+1:8*N_set,4*N_set+1:8*N_set,...
5*N_set+1:8*N_set,6*N_set+1:8*N_set,7*N_set+1:8*N_set,...
1:7*N_set,1:6*N_set,1:5*N_set,1:4*N_set,1:3*N_set,1:2*N_set,1:N_set];.
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H_s=[2**i0(1)^2*ones(1,N_set),2**i0(2)^2*ones(1,N_set),2**i0(3)^2*ones(1,N_set),...
2**i0(4)^2*ones(1,N_set),2**i0(5)^2*ones(1,N_set),2**i0(6)^2*ones(1,N_set),...
2**i0(7)^2*ones(1,N_set),2**i0(8)^2*ones(1,N_set),...
*i0(1)**i0(2)*ones(1,7*N_set),*i0(1)**i0(3)*ones(1,6*N_set),...
*i0(1)**i0(4)*ones(1,5*N_set),*i0(1)**i0(5)*ones(1,4*N_set),...
*i0(1)**i0(6)*ones(1,3*N_set),*i0(1)**i0(7)*ones(1,2*N_set),...
*i0(1)**i0(8)*ones(1,N_set),*i0(1)**i0(2)*ones(1,7*N_set),...
*i0(1)**i0(3)*ones(1,6*N_set),*i0(1)**i0(4)*ones(1,5*N_set),...
*i0(1)**i0(5)*ones(1,4*N_set),*i0(1)**i0(6)*ones(1,3*N_set),...
*i0(1)**i0(7)*ones(1,2*N_set),*i0(1)**i0(8)*ones(1,N_set)];H_m=Type*N_set;H_n=Type*N_set;H=sparse(H_i,H_j,H_s,H_m,H_n);%Generatethematri*Aeq.Aeq_i=[ones(1,N_set),2*ones(1,N_set),3*ones(1,N_set),4*ones(1,N_set),...
5*ones(1,N_set),6*ones(1,N_set),7*ones(1,N_set),8*ones(1,N_set)];Aeq_j=1:Type*N_set;s=ones(1,Type*N_set);Aeq_m=Type;Aeq_n=Type*N_set;Aeq=sparse(Aeq_i,Aeq_j,s,Aeq_m,Aeq_n);%Generatethematri*A.A=[repmat(eye(N_set),1,Type);-eye(Type*N_set)];%Solvetheprobelm.Generateinitialschedule.OPT=optimset;OPT.LargeScale="off";*=quadprog(full(H),c,A,b,full(Aeq),beq,VLB,VUB,ones(1,80),OPT);table=reshape(*,N_set,Type);table=[table,table**i0,sum(table")"];table=[0:Type+2;[(1:N_set+1)",[table;sum(table)]]]\end{verbatim}}\subsubsection{generate{\_}data.m(MATLAB\te*tregistered{}scriptfile)}{\liuhao\begin{verbatim}%MainprogramtogenerateCAT(k)&ST(k).%DeterminewhichFlightwillbecancelled.[m,n]=F_cancelled(Type,N_set);whiletable(m,n)==[m,n]=F_cancelled(Type,N_set);endtable(m,n)=table(m,n)-1;%GenerateCAT(k).fori=1:Type
forj=1:N_set
whiletable(j,i)>pS=unifrnd(p_Seats_LOW(i),p_Seats_UP(i));
NS=ceil(Num_Seats(i)*pS);.
z.
-
CAT(length(CAT)+1:length(CAT)+NS)=unifrnd(120+j*Interval+TPE,120+j*Interval+TPL,1,NS);
table(j,i)=table(j,i)-1;
end
endendPassengers_total=length(CAT)%GenerateST(k).bch=[01222];fori=1:length(CAT)
ST(i)=bch(unidrnd(5))/v_EDS_mean;endN_EDS=input("WanttohowmanyEDS"")saveCAT_STCATSTCAT=CAT(1:N_EDS:end);ST=ST(1:N_EDS:end);%StartSimulation!simulation\end{verbatim}}\subsubsection{F{\_}cancelled.m(MATLAB\te*tregistered{}m-file)}{\liuhao\begin{verbatim}function[m,n]=F_cancelled(Type,N_set)%ProgramtodeterminewhichFlightwillbecancelled.UsingUniformDiscreteDistribution.m=unidrnd(N_set);n=unidrnd(Type);\end{verbatim}}\subsubsection{simulation.m(MATLAB\te*tregistered{}scriptfile)}{\liuhao\begin{verbatim}%Thisisthemainsimulationprogram.%ST(k):sevicetimeofpassengerk.%CAT(k):arrivaltimeofpassengerk.%IDT(k):idletimethatEDSorETDwaitforpassengerk.%QL(I):thelengthofwaitedqueue.%WT(I):waittimeofpassengerk.%CDT(I):lefttimeofpassegerk.%CLOCK:simulationtime.%NATisatemporaryvariantforarrivaltime.%NDTisatemporaryvariantforlefttime.%N:thenumberoftotalpassengers.%StartSimulation!%GetCAT(k)&ST(k)fromgenerate_data.m.N=length(CAT).
z.
-
IDT(1)=0,QL(1)=0%NowI-1passengershavearrived,J-1haveleft.%Passenger1arrivedat0,andwaitfor0.I=2,J=1,CLOCK=0,NAT=CAT(2),NDT=CAT(1)+ST(1),CDT(1)=CAT(1)+ST(1)%Whetherpassengersallhavearrived"whileI<=N
DIF=NAT-NDT
ifDIF<%PassengerIwillarrivebeforethelefttimeofJ.
CLOCK=NAT
%ArrivaltimeofI+1.
ifI NAT=CAT(I+1) end %Lengthofqueueadded. QL(I)=I-J %NowIpassengershavearrived.Jhasn"tleft. I=I+1elseifDIF==%IwillarriveatthesametimeofJleaves. QL(I)=QL(I-1) CLOCK=NAT %ArrivaltimeofI+1. ifI NAT=CAT(I+1) end %BecauseJhasleft,J+1istobeserved;andCLOCKhasmovedtoarrivaltimeofI,so CDT(J+1)=CAT(I)+ST(J+1) NDT=CDT(J+1) %NowIpassengershavearrived,Jhaveleft. J=J+1,I=I+1else ifI-J-1>%AfterJleft,therearestillwaitedpassengers. CLOCK=NDT %Jhasleft,J+1istobeserved,so CDT(J+1)=CDT(J)+ST(J+1) NDT=CDT(J+1) %Lengthofqueueshrined. QL(I)=I-J-2%NowJpassengershaveleft. J=J+1else %AfterJleft,thereisnowaitedpassengers. IDT(I)=DIF CLOCK=NAT. z. - %ArrivaltimeofI+1. ifI NAT=CAT(I+1) end %BecauseJhasleft,J+1istobeserved;and %CLOCKhasmovedtoarrivaltimeofI,so CDT(J+1)=CAT(I)+ST(J+1) NDT=CDT(J+1) %NowIpassengershavearrived,Jhaveleft. J=J+1,I=I+1end endend%Allpassengershavearrived,andwaitinqueue.whileJ %CLOCKsettothetimeofJleft. CLOCK=NDT %Jhasleft,J+1istobeserved,so CDT(J+1)=CDT(J)+ST(J+1) NDT=CDT(J+1) %Lengthofqueueshrined. %QL(I)=I-J-2%NowJpassengershaveleft. J=J+1end%BeforepassengerNarrived,thereisnobodywait.iflength(QL)==N-1QL(N)=0end%StopSimulation!ifJ<=N J=J+1endCLOCK=NDT%Printresults!ma*_queue=ma*(QL)mean_queue=sum(QL)/Nmean_queue_nonzero=sum(QL(find(QL>0)))/Nma*_free=ma*(IDT(4:end-4))mean_free=sum(IDT)/NWT=CDT-ST-CAT;total_wait_time=sum(WT)ma*_wait_time=ma*(WT)wait_long=length(find(WT>=60)). z. - wait_long_radtio=length(find(WT>=60))/length(WT)mean_wait_time=total_wait_time/Ntime_in_system=WT+ST;total_time_in_system=sum(time_in_system)ma*_time_in_system=ma*(time_in_system)mean_time_in_system=total_time_in_system/N\end{verbatim}}\newpage\section{SimulationResult}\label{SimulationResult}\subsection{Note:}\noindentNEDS:thenumberofEDSs\noindentJ:totalpassengersthrougheachEDS\noindentCLOCK:totalsimulationtime\noindentma*{\_}queue:thema*imumpassengersnumberinaqueue\noindentmean{\_}queue:themeanpassengersnumberinaqueue\noindentmean{\_}free:themeanfreetimelengthofanEDS\noindentma*{\_}wait{\_}time:thema*imumtimelengthforonepassenger"swaiting\noindentmean{\_}wait{\_}time:themeantimelengthofonepassenger"swaiting\noindenttotal{\_}time:thetotaltimelengthforsystemtouse\noindentma*{\_}time:thema*imumtimelengthforsystemtouse\noindentmean{\_}time:themeantimelengthforsystemtouse\begin{table}[htbp] \centering\*iaoliuhao \begin{tabular}{*{11}c} \myhline{0.4mm} \te*tbf{NEDS}&\te*tbf{J}&\te*tbf{CLOCK}&\te*tbf{ma*{\_}queue}&\te*tbf{mean{\_}queue}&\te*tbf{mean{\_}free}&\te*tbf{ma*{\_}wait{\_}time}&\te*tbf{mean{\_}wait{\_}time}&\te*tbf{total{\_}time}&\te*tbf{ma*{\_}time}&\te*tbf{mean{\_}time}\\ \myhline{0.4mm} 20&201&122.67&90&39.776&0.25151&111.31&41.285&8299.8&111.32&41.293\\ \hline. z. - 30&134&128.15&48&14.478&0.42207&110.79&37.082&4970&110.8&37.09\\ \hline 31&130&129.23&102&41.08&0.44393&115.02&51.85&6471.5&115.03&51.858\\ \hline 32&128&130.58&97&39.349&0.46886&122.62&56.312&7096.3&122.63&56.32\\ \hline 33&122&135.57&93&38.098&0.52556&126.35&56.573&6902.8&126.35&56.58\\ \hline 34&118&130.13&60&21.449&0.49733&110.05&51.01&6020&110.05&51.017\\ \hline 35&115&128.21&45&14.948&0.49348&94.938&39.995&4600.3&94.949&40.003\\ \hline 36&112&121.48&82&31.786&0.4474&106.29&45.404&5086&106.3&45.411\\ \hline 37&109&129.98&38&14.505&0.53817&118.79&48.789&5318.7&118.8&48.796\\ \hline 38&106&130.51&82&33.528&0.55857&116.89&57.375&6082.4&116.89&57.382\\ \hline 39&103&126.63&81&33.33&0.53692&103.17&51.409&5295.9&103.19&51.417\\ \hline 40&101&122&28&8.0297&0.50161&110&36.512&3688.5&110.01&36.52\\ \hline 50&81&128&29&10.198&0.7007&90.397&40.862&3310.5&90.408&40.87\\ \hline 60&67&121.44&18&5.9701&0.75144&84.292&31.559&2115&84.292&31.566\\ \myhline{0.4mm} \end{tabular}\end{table}\end{appendi*}\newpage\end{CJK*}\end{document}. z. [DOC]-数学建模美赛论文标准格式参考--中英文对照 数学建模美赛论文标准格式参考--中英文对照 YourPaper"sTitleStartsHere:PleaseCenteruseHelvetica(Arial)14论文的题目从这里开始:用Helvetica(Arial)14号 FULLFirstAuthor1,a,FULLSecondAuthor2,bandLastAuthor3,c第一第二第三作者的全名 1Fulladdressoffirstauthor,includingcountry第一作者的地址全名，包括国家 2Fulladdressofsecondauthor,includingcountry第二作者的地址全名，包括国家 3Listalldistinctaddressesinthesameway第三作者同上 aemail,bemail,cemail第一第二第三作者的邮箱地址 Keywords:Listthekeywordscoveredinyourpaper.Thesekeywordswillalsobeusedbythepublishertoproduceakeywordindex.关键字:列出你论文中的关键词。这些关键词将会被出版者用作制作一 个关键词索引。Fortherestofthepaper,pleaseuseTimesRoman(TimesNewRoman)12论文的其他部分请用TimesRoman(TimesNewRoman)12号字 Abstract.Thistemplateexplainsanddemonstrateshowtoprepareyourcamera-readypaperforTransTechPublications.Thebestistoreadtheseinstructionsandfollowtheoutlineofthistext.PleasemakethepagesettingsofyourwordprocessortoA4format(21x29,7cmor8x11inches);withthemargins:bottom1.5cm(0.59in)andtop2.5cm(0.98in),right/leftmarginsmustbe2cm(0.78in).摘要:这个模板解释和示范供稿技术刊物有限公司时，如何准备你的供相 机使用文件。最好读这些指示说明并且跟随着这篇文章的大纲走。 Weshallbeabletopublishyourpaperinelectronicformonourwebpage,ifthepaperformatandthemarginsarecorrect.如果论文的格式和页面设置是正确的，我们将能够将您的电子版论文登在 我们的主页。 Yourmanuscriptwillbereducedbyapproximately20%bythepublisher.Pleasekeepthisinmindwhendesigningyourfiguresandtablesetc.当设计你的数字和表格等时，请铭记你的原稿将由出版商进行20%的删 减。 IntroductionAllmanuscriptsmustbeinEnglish,alsothetableandfiguretexts,otherwisewecannotpublishyourpaper.所有原稿必须是英 文，包括表格和数字内容，否则我们不会出版你的论文。 Pleasekeepasecondcopyofyourmanuscriptinyouroffice.Whenreceivingthepaper,weassumethatthecorrespondingauthorsgrantusthecopyrighttousethepaperforthebookorjournalinquestion. 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