建模美赛排版.docx

建模美赛排版.docx

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建模美赛排版

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8631

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145B

Summary

Inordertodeterminethemixoftrips,fromthepointofviewofthemanagersandthepassengers,dependonusingthedynamicprogramming,MonteCarlomethodsandgeneticalgorithmoptimizationtosetuptwomodels,wedeterminetheoptimalmixoftrips.

ForModel1:

fromthepointofviewofthemanagers,,duetothelargenumberofcampsalongtheRiverisunknown,andinordertoensuretheutilizationrateofcampat100%Wedeterminethe26kindsoftripsas26trippackagestobeusedbyanalyzingvaryingdurationandpropulsioninacertaincondition.

ForModel2:

fromthepointofviewofthemanagers,tobeginwith,byconsideringhowtochoosetwovesselsinAtrip.Therefore,theaveragespeedsofthevessels,aswellaswhethercampsitesareoccupied,thedriftingtimebetweenthetwocampsitesaredetermined.Then,wetaketheanytwovesselsencounterproblemintoaccount.Wedividethewholeproblemintoseveralphases,andsimulatethewholetripbyusingMonteCarlomethods.Afterthetripsimulation,Andthenusingdynamicprogrammingandgeneticalgorithmstosolvetheproblem.Weconcludethatcarryingcapacityoftheriveris1854vesselsandallowforelevenvesselstobelaunchedeachdayoftheseason.

Contents

1.Introduction......................................................................................................................................................1

1.1ProblemBackground.........................................................................................1

1.2OurWork.............................................................................................................1

2.SymbolDefinitions......................................................................................................................................3

3.ModelAssumptions.......................................................................................................................................3

4.ProblemAnalysis............................................................................................................................................5

5.Model1................................................................................................................................................................5

4.1TheFoundationofModel…………………………….……………………………………….…....5

4.2SolutionandResult…………………………………….…………………………………………....5

4.3AnalysisoftheResult………………………………….……………………………………......…..5

6.Model2……….....................................................................................................................................................5

5.1TheFoundationofModel…………………………….…………………………………...….......5

5.2SolutionandResult……………………………...….……………………………………..…...…...6

5.3AnalysisoftheResult………………………………….…………………………………..…..…..7

7.DiscussionandConclusion.....................................................................................................................7

7.1StrengthandWeakness………………………..…………………………...……7

7.2Conclusions…………………………………..…………………………………8

8.References........................................................................................................................................................23

9.Appendix...........................................................................................................................................................23

1Introduction

1.1ProblemBackground

TheBigLongRiver（225milesdownstream）,therearetwokindsofvesselscouldbetakenbythepassengers:

oar-poweredrubberrafts,whichtravelonaverage4mph,ormotorizedboats,whichtravelonaverage8mph.Theparkmanagerswanttodeterminehowtheymightscheduleanoptimalmixoftrips,andhowmuchmoreboattripscouldbeaddedtotheBigLongRiver’sraftingseason.

Wearenowfacedwiththefollowing:

●Howtooptimizethemixoftripsandtheschedule?

●Byconsideringthecarryingcapacityoftheriver,howtodeterminethetimesboattripscouldbeaddedtotheBigLongRiver’sraftingseason?

1.2Ourwork

Asweknow,X tripstraveldowntheBigLongRivereachyearduringasixmonthperiod.Thereare Y campsitesontheBigLongRiver,distributedfairlyuniformlythroughouttherivercorridor.Thetripsrangefrom6to18nightsofcampingontheriver,starttofinish.Thuswewillconsiderasfollowing:

●BasedontheY campsites'certainconditions,determinevaryingduration（measuredinnightsontheriver）andpropulsion（motororoar）toutilizethecampsitesinthebestwaypossible,withminimalcontactwithothergroupsofboatsontheriver.

●AftermathematicallyanalyzingtheCampingschedule,ourmodelinggroupwouldliketodescribeourkeyfindingstothemanagersoftheriver.

2.SymbolDefinitions

Variable

Definition

Thespeedofthei-thdrifting

i-thdriftingpushmode（motororoar）Variable（0or1）

Campsiteoccupiedvariable（0or1）

S

Thelengthoftheriver

d

Theaveragedistancebetweenthetwocampsites

Y

Thenumberofcampsites

X

Thenumberofpackages

Thetimeofstartingati-thdriftingtothecampsitej-th

Randomresidencetimeinthecampsite

x-thdaysinthesix-monthopenperiod（

）

y

y-thmotorizedboatinaday

x

x-thoar-poweredrubberraftsinaday

Thefirstmotorizedboatdeparturetimeeveryday

Theoar-poweredrubberraftsdeparturetimeeveryday

Motorizedboatdriftingspace（

）

oar-poweredrubberraftsdriftingspace（

）

M

atotalofvesselsinaday

Thenumberofmotorizedboateveryday

b

Thedriftingtimeofmotorizedboateveryday.

B

Thedriftingtimeofoar-poweredrubberraftseveryday.

DriftdaysofythMotorizedboatinx-thday

Driftdaysofythoar-poweredrubberraftsinx-thday

j

j-thCampsite

ythmotorizedboatinx-thdaytothej-thcampsiteatk-thday

ythoar-poweredrubberraftsinx-thdaytothej-thcampsiteatk-thday

Probabilityofythoar-poweredrubberraftsinx-thdaytothej-thcampsiteatk-thday

Probabilityofythmotorizedboatinx-thdaytothej-thcampsiteatk-thday

3.ModelAssumptions

Weassumethat:

●Forcamping6to12nightstourists,weonlyprovideoar-poweredrubberrafts,calledpackage1-7;

●Forcamping13to18nightstourists,weonlyprovideoar–poweredmotorizedboats,calledpackage8-13;

●Forthesamekindoftravelpackage,everydayinthebigriverraftingdistanceisthesame,starttofinish;

●Theoar-poweredrubberraftswhichtravelonconstantaverage4mph.

●Themotorizedboatswhichtravelonconstantaverage8mph.

●Changingvesselsinatripcanbeneglected;

●Thetravelingdistanceofeachvesselinadaymustbepositive.

●Theimpactofnaturalfactorsofthetripcanbetemporarilyignored.

4.ProblemAnalysis

Tothequestion1:

Thequestion1belongstoakindofoptimizationprobleminmathematics,whichis,namely,withthedifferenttimeandthedifferentpromotionmethods（motororplasma）,arrangeanoptimalmixedtravelplan,makemaximumuseofcamp,andtomakeshipsaslittleaccesstoothershipsontheriver.Inthispaperweusethecomputersimulation,theMonteCarlomethod,integerprogramming,geneticalgorithmandotherrelatedtheorytoestablishandsolutionmodel.

Tothequestion2:

Wemustcalculatehowmanytimesoftripscanbescheduledperdayonthebasisofthequestion1.Onlyinthiswaycanwemakethemaximumuseofcamp,thusfurtherfindouthowmanytimesoftripscanbescheduledinthesixmonths.Then,thecarryingcapacityoftheriverisconcluded.Torealizethebearingcapacityoftherivertomaximize,wemustbothconsidereveryhairshiptime,andtoconsiderthemaximizationofunreasonableshiptimeminimization.Then,weanalyzethebearingcapacityoftheriverandstateourownopinions.

Aftersolvingandanalyzingtheproblem,wesetuptwomodels.

5.Model1

Model1:

Fromtheviewoftourismmanager

Becausethenumberofcampsalongthecoastisunknown,andfortheconvenienceoftourismmanagerstomanage,thetourismstrategywehaveformulatedisbasedonthenumberofcamps.Underthepremiseofthecamputilizationrateof100%,wemakesurethedaysoftripswecanprovideforvisitors.

Takingbothtraveltimeandtraveltoolintoconsideration,wedividetravelmodeinto13*2=26kindsoftravelpackage.Butbecausethenumberofcampsalongtheriverisunknown,andwehavetomakeassumptions:

thedistanceoftravelingeverydayineachpackageissameanddriftconstantprogress.Soaccordingtothenumberofunknowncamps,weneedtoprovidethecombinationoftravelingdayssoastomakethesumofallcombinationsofthetravelingdaysequalthesumofthenumberofthecamps.Andthenputallthecampondistribution,makeallkindsofcampingdaysdrifthasadefinitecampwiththecorresponding,i.e.,Beforethetouristssetoff,thegivencampvisitorsshouldstayinhasbeenmadesure.Sotheutilizationrateofcampcanreach100%.Andthen,thetouristschoosefrombyoar-powereddrift,orbyrubberraftsdriftbythemselves.Finallywhichkindsofthepackagetypesshouldbeprovidedforpassengersisdetermined.

During6monthsofthetouristseason,inadditiontothelast17days,theremaining163daysofeverydayarethesame,soforthefirst163days,weonlyneedtodeterminethetourarrangementofthefirstday,andthenthetravelarrangementsoftherestofthe163daysarethesa