数学建模美赛F题论文.docx

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

（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.

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

TotalCapacityofi