国际竞赛题英文版Word文件下载.docx
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Problem3
DataSets3
Summary3
ProblemBGradeInflation3
Background3
DataSets4
MathematicalContestinModeling1999Problems4
ProblemB-UnlawfulAssembly4
2000MathematicalContestinModeling4
ProblemAAirtrafficControl4
ProblemBRadioChannelAssignments5
2001MathematicalContestinModeling(MCM)5
ProblemA:
ChoosingaBicycleWheel5
ProblemB:
EscapingaHurricane'
sWrath(AnIllWind...)6
2002ContestProblems7
ProblemAWindandWaterspray7
ProblemBAirlineOverbooking7
2003ContestProblems7
ProblemATheStuntPerson7
ProblemBGammaKnifeTreatmentPlanning8
2004MCM8
PROBLEMA:
AreFingerprintsUnique?
8
PROBLEMB:
AFasterQuickPassSystem8
ProblemC
ToBeSecureorNottoBe?
9
2005MCMProblem11
2006年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题12
PositioningandMovingSprinklerSystemsforIrrigation12
WheelChairAccessatAirports13
PROBLEMC:
Trade-offsinthefightagainstHIV/AIDS13
2007年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题PROBLEMA:
Gerrymandering19
TheAirplaneSeatingProblem19
ProblemCOrganTransplant:
TheKidneyExchange19
2008年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题23
TakeaBath23
PROBLEMB:
CreatingSudokupuzzles23
2008ICMProblemCFindingtheGoodinHealthCareSystems23
2009年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题24
2009MCMA:
DesigningaTrafficCircle24
2009MCMB:
EnergyandtheCellPhone25
2009ICM:
CreatingFoodSystems:
Re-BalancingHuman-InfluencedEcosystems26
2010年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题26
2010MCMA:
TheSweetSpot26
2010MCMB:
Criminology26
2010ICM:
TheGreatPacificOceanGarbagePatch27
2011年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题28
SnowboardCourse28
RepeaterCoordination28
Howenvironmentallyandeconomicallysoundareelectricvehicles?
Istheirwidespreadusefeasibleandpractical?
29
1996AmericanMCMProblems
ProblemA
Theworld'
soceanscontainanambientnoisefield.Seismicdisturbances,surfaceshipping,andmarinemammalsaresourcesthat,indifferentfrequencyranges,contributetothisfield.Wewishtoconsiderhowthisambientnoisemightbeusedtodetectlargemovingobjects,e.g.,submarineslocatedbelowtheoceansurface.Assumingthatasubmarinemakesnointrinsicnoise,developamethodfordetectingthepresenceofamovingsubmarine,itssize,anditsdirectionoftravel,usingonlyinformationobtainedbymeasuringchangestotheambientnoisefield.Beginwithnoiseatonefixedfrequencyandamplitude.
ProblemB
WhendeterminingthewinnerofacompetitionliketheMathematicalContestinModeling,therearegenerallyalargenumberofpaperstojudge.Let'
ssaythereareP=100papers.AgroupofJjudgesiscollectedtoaccomplishthejudging.Fundingforthecontestconstainsboththenumberofjudgesthatcanbeobtainedandamountoftimethattheycanjudge.ForeampleifP=100,thenJ=8istypical.Ideally,eachjudgewouldreadpaperandrank-orderthem,buttherearetoomanypapersforthis.Instead,therewillbeanumberofscreeningroundsinwhicheachjudgewillreadsomenumberofpapersandgivethemscores.Thensomeselectionschemeisusedtoreducethenumberofpapersunderconsideration:
Ifthepapersarerank-ordered,thenthebottom30%thateachjudgerank-orderscouldberejected.Alternatively,ifthejudgesdonotrank-order,butinsteadgivethemnumericalscore(say,from1to100),thenallpapersbelowsomecut-offlevelcouldberejected.
Thenewpoolofpapersisthenpassedbacktothejudges,andtheprocessisrepeated.AconcernisthenthetotalnumberofpapersthatjudgereadsmustbesubstantiallylessthanP.TheprocessisstoppedwhenthereareonlyWpapersleft.Therearethewinners.TypicallyforP=100,W=3.
Yourtaskistodetermineaselectionscheme,usingacombinationofrank-ordering,numericalscoring,andothermethods,bywhichthefinalWpaperswillincludeonlypapersfromamongthe"
best"
2Wpapers.(By"
weassumethatthereisanabsoluterank-orderingtowhichalljudgeswouldagree.)Forexample,thetopthreepapers.Amongallsuchmethods,theonethatrequiredeachjudgetoreadtheleastnumberofpapersisdesired.
Notethepossibilityofsystematicbiasinanumericalscoringscheme.Forexample,foraspecificcollectionofpapers,onejudgecouldaverage70points,whileanothercouldaverage80points.Howwouldyouscaleyourschemetoaccommodateforchangesinthecontestparameters(P,J,andW)?
1997AmericanMCMProblems
ProblemATheVelociraptorProblem
Thevelociraptor,Velociraptormongoliensis,wasapredatorydinosaurthatlivedduringthelateCretaceousperiod,approximately75millionyearsago.Paleontologiststhinkthatitwasaverytenacioushunter,andmayhavehuntedinpairsorlargerpacks.Unfortunately,thereisnowaytoobserveitshuntingbehaviorinthewildascanbedonewithmodernmammalianpredators.Agroupofpaleontologistshasapproachedyourteamandaskedforhelpinmodelingthehuntingbehaviorofthevelociraptor.Theyhopetocompareyourresultswithfielddatareportedbybiologistsstudyingthebehaviorsoflions,tigers,andsimilarpredatoryanimals.
Theaverageadultvelociraptorwas3meterslongwithahipheightof0.5metersandanapproximatemassof45kg.Itisestimatedthattheanimalcouldrunextremelyfastatspeedof60km/hrforabout15seconds.Aftertheinitialburstofspeed,theanimalneededtostopandrecoverfromabuildupoflacticacidinitsmuscles.
SupposethatvelociraptorpreyedonThescelosaurusneglectus,aherbivorousbipedapproximatelythesamesizeastheVelociraptor.AbiomachanicalanalysisofafossilizedThescelosaurusindicatesthatitcouldrunataspeedofabout50km/hr.forlongperiodoftime.
Part1
Assumingthevelociraptorisasolitaryhunter,designamathematicalmodelthatdescribeahuntingstrategyforasinglevelociraptorstalkingandchasingasingleThescelosaurusaswellastheevasivestrategyoftheprey.AssumethattheThescelosauruscanalwaysdetectthevelociraptorwhenitcomeswithin15meters.butmaydetectthepredatoratevengreaterranges(upto50metersdependinguponthehabitatandweatherconditions.Additionally,duetoitsphysicalstructureandstrength,thevelociraptorhasalimitedturningradiuswhenrunningatfullspeed.Thisradiusisestimatedtobethreetimestheanimal'
shipheight.Ontheotherhand,theThescelosaurusisextremelyagileandhasaturningradiusof0.5meters.
Part2
Assumingmorerealisticallythatthevelociraptorhuntedinpairs,designanewmodelthatdescribesahuntingstrategyfortwovelociraptorstalkingandchasingasingleThescelosaurusaswellastheevasivestrategyoftheprey.UsetheotherassumptionsandlimitationsgiveninPart1.
ProblemBMixWellForFruitfulDiscussions
Smallgroupmeetingforthediscussionsofimportantissues,particularlong-rangeplanning,aregainingpopularity.Itisbelievedthatlargegroupsdiscourageproductivediscussionandthatadominantpersonalitywillusuallycontrolanddirectthediscussion.Thus,incorporate boardmeetingstheboardwillmeetinsmallgroupstodiscussissuesbeforemeetingasawhole,thesesmallergroupsstilltuntheriskofcontrolbyadominantpersonality.Inanattempttoreducethisdangeritiscommontoscheduleseveralsessionswithadifferentmixofpeopleineachgroup.
AmeetingofAnTostalCorporationwillbeattendedby29BoardMembersofwhichninearein-housemembers(i.e.,corporateemployees).Themeetingistobeanall-dayaffairwiththreesessionsscheduledforthemorningandfourfortheafternoon.Eachsessionwilltake45minutes,beginningonthehourfrom9:
00A.M.to4:
00P.M.,withlunchscheduledatnoon.Eachmorningsessionwillconsistofsixdiscussiongroupswitheachdiscussiongroupledbyoneofthecorporation'
ssixseniorofficers.Noneoftheseofficersareboardmembers.Thuseachseniorofficerswillnotbeinvolvedintheafternoonsessionsandeachofthesesessionswillconsistofonlyfourdifferentdiscussiongroups.
Thepresidentofthecorporationwantsalistofboard-memberassignmenttodiscussiongroupsforeachofthesevensessions.Theassignmentsshouldachieveasmuch ofamixofthemembersasmuchaspossible.Theidealassignmentwouldhaveeachboardmemberinadiscussiongroupthesamenumberoftimeswhileminimizingcommonmembershipofgroupsforthedifferentsessions.
Theassignmentshouldalsosatisfythefollowingcriteria:
1.Forthemorningsessions,noboardmembershouldbeinthesameseniorofficer'
sdiscussiongrouptwice.
2.Nodiscussiongroupshouldcontainadisproportionatenumberofin-housemembers.
Givealistofassignmentsformembers1-9and10-29andofficers1-6.Indicatehowwellthecriteriainthepreviousparagraphsaremet.Sinceitispossiblethatsomeboardmemberswillcancelatthelastminuteorthatsomenotscheduledwillshowup,analgorithmthatthesecretarycouldusetoadjusttheassignmentswithanhour'
snoticewouldbeappreciated.Itwouldbeidealifthealgorithmcouldalsobeusedtomakeassignmentsforfuturemeetingsinvolvingdifferentlevelsofparticipationforeachtypeofattendee.
1998AmericanMCMProblems
ProblemAMRIScanners
IndustrialmedicaldiagnosticmachinesknownasMagneticResonanceImager(MRI)scanathree-dimensionalobjectsuchasabrain,anddelivertheirresultsintheformofathree-dimensionalarrayofpixel.Eachpixelconsist