数学建模美赛2012MCM B论文

Camping along the Big Long River

Summary

In this paper,the problem that allows more parties entering recreation system is investigated.In order to let park managers have better arrangements on camping for parties,the problem is divided into four sections to consider.

The first section is the description of the process for single-party's rafting.That is, formulating a Status Transfer Equation of a party based on the state of the arriving time at any campsite.Furthermore,we analyze the encounter situations between two parties.

Next we build up a simulation model according to the analysis above.Setting that there are recreation sites though the river,count the encounter times when a new party enters this recreation system,and judge whether there exists campsites available for them to station.If the times of encounter between parties are small and the campsite is available,the managers give them a good schedule and permit their rafting,or else, putting off the small interval time t∆until the party satisfies the conditions.

Then solve the problem by the method of computer simulation.We imitate the whole process of rafting for every party,and obtain different numbers of parties,every party's schedule arrangement,travelling time,numbers of every campsite's usage, ratio of these two kinds of rafting boats,and time intervals between two parties' starting time under various numbers of campsites after several times of simulation. Hence,explore the changing law between the numbers of parties(X)and the numbers of campsites(Y)that X ascends rapidly in the first period followed by Y's increasing and the curve tends to be steady and finally looks like a S curve.

In the end of our paper,we make sensitive analysis by changing parameters of simulation and evaluate the strengths and weaknesses of our model,and write a memo to river managers on the arrangements of rafting.

Key words:Camping；Computer Simulation;Status Transfer Equation

1Introduction

The number of visits to outdoor recreation areas has increased dramatically in last three decades.Among all those outdoor activities,rafting is often chose as a family get-together during May to September.Rafting or white water rafting is a kind of interesting and challenging recreational outdoor activity,which uses an inflatable raft to navigate a river or sea [1].It is very popular in the world,especially in occidental countries.This activity is commonly considered an extreme sport that usually done to thrill and excite the raft passengers on white water or different degrees of rough water.It can be dangerous.

During the peak period,there are many tourists coming to experience rafting.In order to satisfy tourists to the maximum,we must make full use of our facilities in hand,which means we must do the utmost to utilize the campsites in the best way possible.What's more,to make more people feel the wildness life,we should minimize the encounters to the best extent;meanwhile no two sets of parties can occupy the same campsite at the same time.It is naturally coming into mind that we should consider where to stop,and when to stop of a party [2].

In previous studies [3-5],many researchers have simulated the outdoor creation based on real-life data,because the approach is dynamic,stochastic,and discrete-event,and most recreation systems share these traits.But there exists little research aiming at describing the way that visitors travel and distribute themselves within a recreation system [6].Hence,in our paper,we consider the whole process of parties in detail and simulate every party ’s behavior,including the location of their campsites,and how long it will last for them to stay in a campsite to finish their itineraries.Meanwhile minimize the numbers of encounters.

Aiming at showing the whole process of rafting,we firstly focus on analyzing the situation s of a single-party's rafting by using status transfer equation,then consider the problems of two parties'encounters on the river.Finally,after several times of simulation on the whole process of rafting,we obtain the optimal value of X .2Symbols and Definitions

In this section,we will give some basic symbols and definitions in the following for the convenience.

Table 1.Variable Definition Symbols Definition

i v i p j i q ,S d

The velocity of oar or motor

0-1variables on choosing rafting transportation

0-1variables on the occupation of campsites

Length of the river

Average distance between two campsites