2016数学建模美赛F题论文文档格式.docx
- 文档编号:980573
- 上传时间:2023-04-29
- 格式:DOCX
- 页数:25
- 大小:1.39MB
2016数学建模美赛F题论文文档格式.docx
《2016数学建模美赛F题论文文档格式.docx》由会员分享,可在线阅读,更多相关《2016数学建模美赛F题论文文档格式.docx(25页珍藏版)》请在冰点文库上搜索。
ProblemChosen
F
F1
F2
F3
F4
2016
MCM/ICM
SummarySheet
(Yourteam'
ssummaryshouldbeincludedasthefirstpageofyourelectronicsubmission.)
Typeasummaryofyourresultsonthispage.Donotinclude
thenameofyourschool,advisor,orteammembersonthispage.
Summary
Ouranalysisandtargets:
Inessence,thisproblemiskindofacaseofmaximumflowandminimumconsumptionwithmultiplesourcesandtargets.“Multiplesources”referstodifferentoriginalcountriesofrefugeesinvolvedinthecase,while“multipletargets”referstodifferenttargetcountrieswhererefugeesarrive.It’souraimtorationalizetheflowsofrefugeesandtooptimizethetargetcountryforeachrefugee,i.e.tooptimizethechoiceoftransmittingroutesandtheallocationofavailableresourceswithvariousconditionfactors.
Thegeneralideaandmethod:
Setanindicatorwhichconsistsofdifferentpartsofdifferentfactors.Theindicatorisdesignedtoreflecttheseverityofbothtransportationandresourcesconsumption.Everysub-factorshouldinflectthegapbetweentheoreticalvalueandactualconditions.Fortheactualconditions,wecangetenoughdatatodescribeorestimateit.Asforthetheoreticalvalue,weintroducetheadvancedDijkstraalgorithminspiredbyEdmond-Karpalgorithm.Besides,weproposedtheconceptions:
weightingfactormatrix,resourcesfactormatrix,aseriessubfactormatriceswhichisdesignedtodescribetheeffectcausedbydifferentfactors.Theproblemisquitesimilartothemodelofwatersupplysystem.Soweusethesimilardefiningmethodtotackletheproblems.
Mainresultsandconclusions:
Themodelworkswellunderdynamicconditionsandtheresultsfittherealsituationwell,whilethefactorofpoliticsandthefactorofadjustmentscanbechangedthusitisabletoassessthecascadingeffects.ItishelpfulwhenthepopulationofrefugeesgrowsrapidlyandisabletomakepredictionofthemaximumcapacityofEuropeanmainlandtoconsumetheflowofrefugees.
Keypoints:
Maximumflowandminimumexpense/Watersupplynetworkmodel
Dijkstraalgorithm
UnstoppableRefugees
1Introduction
1.1Background
Asaresultofmajorpoliticalandsocialunrestandwarfare,amassivesurgeofrefugeesemigratingfromtheMiddleEasttoEuropeancountries.WithhundredsofthousandsofrefugeesmovingacrossEuropeandmorearrivingeachday,muchattentionhasbeengiventorefugeeintegrationpoliciesandpracticesinmanycountriesandregions.Thechallengesbroughtbytherefugeesmustbemanagedcarefullythrougheffectivepolicies.
1.2AnOverViewofTasks
1)Metricsofrefugeecrises.Developasetofmeasuresandparameterstofortherefugeecrisesassessment.
2)Flowofrefugees.Createamodelofoptimalrefugeemovementthatwouldincorporateprojectedflowsofrefugeesacrosssixtravelrouteswithconsiderationofseveralimportantfactors,liketransportations/accessibility,safetyandcountriescapacities.Determinethenumberofrefugeesandtherateofpointsofentry.Justifythenewelementsaddedinthemodelandanalyzethesensitivity.
3)Dynamicsofthecrisis.Refinethemodeltoadaptthedemandofchangingenvironmentalfactors.Herewehavetotakethecascadeeffectoftheresourceconsumptionintoconsideration.What’smore,aplanshouldbegiventoallocatetheresourceproperlyandrankthepriorityofdifferentkindofresources.AnalyzetheeffectsofNGOsandthenewdestinationsforrefugees.
4)Policytosupportrefugeemodel.Weareaskedtowriteareportonourmodelandproposeasetofpoliciesthatwillsupporttheoptimalpattern.Considerandprioritizethehealthandsafetyofrefugeesandlocalpopulations.TakethelawsandculturalconstraintsandroleofNGOSintoconsideration.
5)Exogenousevents.Analyzetheexogenousevents’influenceonthesituationparametersandthecascadingeffectoftherefugeeflows.Howyourplanisdesignedtoberesilienttotheseevents?
6)Scalability.DiscusstheScalabilityofyourmodelwhenyourmodelisappliedforamuchlargerscale
1.3OurGeneralAnalysisandWork
1.3.1Analysis:
Theindexforthecrisisassessmentshouldbecomposedoftwoparts:
1)Theburdenoftherefugeetransitionforthecountryonthepath
2)Theburdenoftheresourceconsumptionforcountrieswithrefugees
Eachpartaboveshouldindicatethedifferencebetweenidealsituationsandpracticalones.
Thepracticalsituationcanbeknownorbeestimatedfromstatisticdata,soourfocusisthetheoreticoridealrefugeeflowpattern.
Theessenceofthisproblemiskindofacaseofmaximumflow(profit)andminimumconsumption(cost)withmultiplesourcesandtargets.Here,itmeansmultiplesourceofrefugeesamultipledestinationsinEuropecountries.Thisissimilartothepatternofcitywatersupplement,sowecalldrawsomeconceptionofwatersupplementintothisproblem.
It’souraimtorationalizetheflowsofrefugeesandtooptimizethetargetcountryforeachrefugee,i.e.tooptimizethechoiceoftransmittingroutesandtheallocationofavailableresources.
1.3.2Ourwork
1)WebuildabasicrefugeeflowmodelbasedonthewatersupplypipenetworkmodelandMaximumflowandminimumexpensemodel.
2)ThebasicalgorithmsareDijkstra(optimalrouteforflowfromasingleorigin)algorithmandEdmond-Karp(maximumflowwithmultipleorigins)algorithm.Wemodifiedthistwoalgorithmstoadaptthismultiplesourceandmultipletargetsproblems.
3)Theconceptsofweightingfactormatrixandavailableresourcematrixareintroducedintoourmodel.Bothmatricesarecomposedofvariousfactormatriceswhichrepresentdifferentsituationparameters.
4)Weproposedaseriesofformulastocalculatedifferentfactors.
5)Weextendedandmodifiedthemodelunderdifferentnewconditions,andintroducedcorrespondingfactormatrixtomeasurethesituation.Forexample,feedbackfactormatrix,cascadingeffectfactormatrix.
6)Sensitivityofthemodelhasbeenanalyzedunderdifferentsituations.
7)Anoptimalpolicyhasbeenproposedaccordingtotheresultofourmodel.
8)Scalabilityisdiscussedindifferentsituations.
2AssumptionandJustification
2.1BasicAssumptions
1)Terrainfactorisoutofotherconsideration.
Reason:
Theterrainofthemostregionsreferencedintheproblemisflat.Soitcanbetakenasaplaneproblem.
2)Everyrefugeeisregardasequivalent
individualsexceptfortheirpositionandreligionattributes.
Humannatureisnearlyallthesame.Thedesiretohighincomeandrestsocialenvironmentandbetterwelfarepolicyissimilartoeachother.
3)Noteverycountrywillbeincludedinthismodel.Onlytypicalandcrucialcountriesareselectedinourmodel.
Thereisnearlynorefugeesoncertainroutesoutofpositionorotherfactorsandtheadjustmentofpolicywon’tchangethissituationwhichmeansitmeansnothingforourmodel.
2.2SpecialAssumptionsfordifferentsituations
1) Atthebeginningofmodeling,apartfromthesixroutesmentionedinthequestion,wedonotconsiderotherroutesthatrefugeesmaychooseandassumealltherefugeewewillconcerningchooseoneofthesixroutes.
2) Second,atthebeginningofmodeling,wedonotconsiderallthecountriesthathaveacceptedtherefugee,maincountriesproducingrefugeesandmaincountriesacceptingrefugees,suchasGermany,France,Spain,Sweden,Afghan,Iran,Iraq,Syria,Turkey,Greece,Albania,Macedonia,Bulgaria,Rumania,Serbia,Montenegro,Bosnia,Croatia,Hungary,Austria,Ukraine,Slovakia,Czechoslovakia,Poland,Germany,France,Spain,Morocco,Italy,Libya,UnitedKingdom,Denmark,Norway,Sweden,Finland,Russia,Belgium,Hollandandsoon,othercountriesthatthenumberofrefugeesproducedoracceptedisquitesmallarenotbeingconsidered.Ofcourse,thereisnorefugeewhoconsidersflowingtoregionslikeAmerica,CanadaorChina.
3) Themeansoftransportationassumedinourmodelarebyhighway,byrailway,byshippingandbywalking.Andwemakeasimplificationtoletthesemeansoftransportationrunatacertainrate,forexamplethemilesthatrailwayrunperday.Besides,atthebeginningofthemodel,weassumethatthereisnosuddenaccident.
4) Inourmodel,weassumethatallrefugeescouldreachthedestinationsafeandsound.
5) Assumethatcountriesacceptingrefugeesdon’tchangetheirrefugeepolicyduringtheperiodofrefugeecrisis.
6) Assumeeveryrefugeemovealongtheroutestraightlytoreachthedestinationwithoutdetouringorchangingtheroute.
7) Assumetheresourcesthatsuppliedbyeverycountryacceptingrefugeesarestableinaperiod,theseresourceswillnotincreasebecauseofrefugeecrisisordecreasebecauseofthenumberofacceptedrefugeelessthanbudgeted.
8) Originalmodeldoesnotconsidertheinfluenceofnon-governmentagenciesandonlygovernmenttakestheresponsibilityofacceptingrefugees.
3notations
Indicatorofthedegreeofrefugeecrisis
theactualnumberofrefugeesonsuchacertainroute
factoroftransportationpressureofrefugees
theidealnumberofrefugeesonsuchacertainroute
thefactorofresourceconsumptionofrefugees
thenumberofallroutes
factorofinequality
degreeofdanger
factorofoverload
numberofdeathpeopleontheroutes
thepracticalnumberofpeopleontheroute
time-consumingindex
theallocationofrefugeesundertheknownconditionwithoutadjustment
overloading
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 2016 数学 建模 论文