美模B题最终答案Word文档下载推荐.docx
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美模B题最终答案Word文档下载推荐.docx
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●Maximizetheuseofthecampsites,thusmakingtheBigLongRiveracceptmoretourists.
●Trytoreducetheencounterbetweentrips,namelyreducedthecatchupphenomenon.
●Touristscangotomoredifferentcampstoenjoydifferententertainmentandappreciatethescenery.
Wewillusethreemodelstoachievetheaboveobjects.
2.FurtherConsiderations
Theproblemisatypicaldynamicplanningissue,accordingtothetotaldaysofthetravelwedividetheriverintoevensections,andthetripsneedadaytotravelthrougheachsection.Sincecampingpointisevenlydistributed,soifeachcampsiteisbestused,allthecampsiteswillbeofutmostused.Sonow,weneedtomakemaximumuseofcampsiteinonesection,thenusingrecursionrelationwecanmakeallcampsitesbeofutmostused.
Ifassumeintervaltendingtozerohere,justdon'
tconsiderthegapbetweenthetrips.Accordingtolimitprinciple,wecanissueacontinuousofboatsinonetype.Becauseasingletypeofboatsoperationatthesamerate,sotheywillnevermeet.Theoreticallythereisenoughspacetocamping,rivercanaccommodategreatnumberofships,butitdoesn'
tfitwiththepracticalsituation.Inpractice,thenumberofcampsitesislimited,thusweshouldconsiderthegapbetweenthetrips,itisnotonlyrelatedtowhetherpassengerscanenjoywildexperience,butmoreimportantisrelatedtothesafetyofthepassengers.
3.AssumptionsandHypotheses
Thefollowingassumptionsweremadewhentacklingtheproblem.
●Thenumberofvisitorsuniformdistributioninsixmonths.
●Thespeedoftheboatsisnotinfluencedbytheflowofwater.
●Themovementdirectionoftripscanonlyfromupstreamtodownstream,andwon'
tretrograde.
●Ycampsitesarefixed,hereweassumethatthereare224campsites,andisometricevenlydistributed.Thusthereisacampsiteevery1mile.Eachcampsiteisasightport,andwewanttomaximizetheuseofresources.
●Eachgrouphasalotofboats,andisonetypeoftwovarietiesboats,oar-poweredboatsormotorizedboats.
●Oar-poweredboatsgroupandmotorizedboatsratioofgroupm:
n.
●Alltripsmusthavearestoncampsiteintheevening,onecampsitecanonlyallowatriptorest,weregulate8pmand6amastheresttimeduringwhichalltripsmustbeinthecampsite.
●Duringtheday,eachtripcandecidetorestincampsiteaccordingtotheirdemands.
●Thedistributionof6-18nights’campingarrangementisdecidedbypassengers’demands,anditisnotmandatory.
●Iftwotripswillmeetwitheachotherinacampsite,andonecanenterthecampsiteforarest,inthiscaseitisnotthemeetwedefine.
4.AnalysisoftheProblem
ThemainproblemnowishowwecanmaketheBidLongRiverholdmoreofthetrips.Accordingtotheactualsituationofhistoricaldata,thenumberofcampingare200orso,herewedefineY=200.Wethink,thelimittoallthetripsinatimeofthetourshouldbemainlyforthefollowingtwoconstraints:
●Theaveragetraveltimeoftheproject.Thistime,inthisproblemis6to18nights(tospend6-18nights).Theshorterthetime,themoreboatsthrough,thusabsorbingmoretourists.
●Thenumberofthecampsites.Becauseeverytriphavetorestonshoreinthecampsiteintheevening,andeachcampsitecanonlyholdonetrip,sothenumberofcampsiteshouldbetheupperlimitofallgroupnumber.
Wearerequestedtodesignthetravelplanforeachtrip,includingeachplacetocampandtheresttime.Howeverthereisnoneedtodesignonebyoneforeachtripsinceatimescheduleisenough,whichallowsthemtoplay6-18nights,andthetripshaveaplacetoresteverynight.Anothergoalistomakethetripaslessaspossiblecontactwithothertrips.Thespeedofthemotorizedboatsiseightmiles/hour,andthespeedoftheoar-poweredboatsis4miles/hour.Thedemandsoftouristsleadtotheremustbeaccompaniedmotorizedboatsandoar-poweredboats.Wetemporarilyhypothesizethattheratioofoar-poweredboatandmotorizedboatis1:
1.Asweallknow,themotorizedboatsbehindiseasytocatchupoar-poweredboats.
Wethinkthatvisitorshasthespecificdemandfortheplaytime,sowewon’treducetheirplaytimetoincreasethenumberoftourists,afterall,thelongtimevisitorsspentoncampsitealsomeansvisitorsneedhigherconsumption,won'
tcauseinvestorsincomedecrease.
5.ModelOne
ConsideringthepreferencelifestyleandtravelstyleofAmericanpeople,visitorshopetohavemoreautonomyspacetospendtheirtraveltimes,soinmostcasestheadministratorsshallnotinterfereintheirspecifictravelwhichlastsfor6to18days.Inviewofthis,thescheduleprohibitedbytheinvestorisonlythedeparturetime.TheobligationofvisitorsistoleavetheBigLongRiverfromtheendexitafterspending6-18nightsontheriver.
Sincethemanagersdonotarrangespecificschedulesoftheplaytimeforthetourists,theplaytimesofeachtripisrandomwhiletherandomnessofeachtrip’splaytimecancausethephenomenonthatsomecampsitesareleftatnightwhilesomegroupsneedtospendalotoftimelookingforcampsitestorest,someevencan'
tfindacampsitewhichleadingtothegreatdecreaseoftourists’pleasure.
Goals
●Thebiglongrivercanaccommodatemoretouriststomeettheneedsofthetourists,thusimprovingtheincomeofthemanager.
●Visitorscanfreetolookforcampsitetoresteasily(thesatisfactionofthetouristsatisfactiondecreasewiththeincreasetimelookingforcampsites,untilthetouristscannottolerate);
Touristscanvisittheplacetheywant,thatiswhentheywanttovisitaplace,theprobabilityofachievingthisgoalishigh;
●Campsitescanbeoccupiedasmanyaspossibleatnight,butthisgoalisconflicttothefirstgoal;
●Thenumberofcontactsbetweentripsshouldbeasfewaspossible.
ConsiderationoftheModel
●Thepreferencestoacampsitewhentouristsvisitthecampsiteareinfluencedbytwofactors.
Oneisthepopularityofcampsitewhichisdeterminedbythenumberofbeingvisitedandtherankinthepast.
Here,weassumethatitsubjectstouniformdistribution,randomlygeneratedbythecomputer.
isonbehalfofthelikelihoodofthisattractionbeacceptedbytourists;
;
Thesecondfactoristhewilltouristswanttolandonthecampsite,thewilloflandingchangeswithtime.Forexample,ifagroupjuststartsitstravel,touriststendtodriftingaperiodoftimebeforelanding,especiallyafteranightresting,touristswouldmorelikelytocontinuedriftingalongertimebeforelanding;
afterdriftingalongtime,theirdriftingwillwouldbereduced.Overall,theprobabilitiesofvisitorslandinginasubsequentdistancearenormaldistribution.
Inconsiderationoftheattractiondegreesofscenicspots,wenormalizedtheattractiondegreesofsomecampsiteswhicharelikelytobevisited,andmakethesumofthemequal100%.
Wecangetanewdistributionbynormalizingthisdistributionwiththenormaldistribution.Thelandingprobabilitiesoftouristsobeythisnewdistribution.Underthenewdistribution,thecomprehensiveprobabilityforvisitorslandingoncampsitexis:
(Note:
thenormaldistributioniscontinuousdistribution,butthedistributionhereisdiscretedistribution,soitneedsnecessaryprocessing.)
(1)Theprobabilitiesforagrouptolandonacampsitearetheintegralsoftheintervalitisin
(2)Inthenormaldistribution,95%probabilitiesfallintheinterval
sothepartoutside
canbeneglectedwhichcanbeaddedtothemiddlecampsite
(3)
Representsthecomprehensivewillfortouriststolandoncampsitex,srepresentshalfofthedistancebetweentwoadjacentcampsites.μstandsforthecampsitepointwhichtouristsaremostlikelytoland,thepointisamongtheseveralcampsitepointsafterpointx.
●Thetimestouristsstayingoncampsitesarenormaldistribution.Touristswon'
trushtoleaveacampsite,thelongertimetouristsstayonthecampsite,andthegreatertouristswanttoleave.
●Whenthecampsitetouristswanttolandisoccupied,touristswouldhavetocontinueflowdowntheriver.Inthiscasethewillsoflandingfortouristsobeytheindexdistribution,becausetouristshaveastrongwilltoland.Whenthiscasehappensmanytime
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