数学建模美赛F题论文.docx
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数学建模美赛F题论文
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2016
MCM/ICM
SummarySheet
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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.
Reason:
Humannatureisnearlyallthesame.Thedesiretohighincomeandrestsocialenvironmentandbetterwelfarepolicyissimilartoeachother.
3)Noteverycountrywillbeincludedinthismodel.Onlytypicalandcrucialcountriesareselectedinourmodel.
Reason:
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
overloadingindex
theallocationofrefugeeswiththereasonableadjustment
TotalCapac