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VIP专享美国数学建模竞赛优秀论文阅读报告

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2.优秀论文一具体要求:1月28日上午汇报

1)论文主要内容、具体模型和求解算法(针对摘要和全文进行概括);

In the part1, we will design a schedule with fixed trip dates and types and also routes. In the part2, we design a schedule with fixed trip dates and types but unrestrained routes.

In the part3, we design a schedule with fixed trip dates but unrestrained types and routes.

In part 1, passengers have to travel along the rigid route set by river agency, so the problem should be to come up with the schedule to arrange for the maximum number of trips without occurrence of two different trips occupying the same campsite on the same day.

In part 2, passengers have the freedom to choose which campsites to stop at, therefore the mathematical description of their actions inevitably involve randomness and probability, and we actually use a probability model. The next campsite passengers choose at a current given campsite is subject to a certain distribution, and we describe events of two trips occupying the same campsite y probability. Note in probability model it is no longer appropriate to say that two trips do not meet at a campsite with certainty; instead, we regard events as impossible if their probabilities are below an adequately small number. Then we try to find the optimal schedule.

In part 3, passengers have the freedom to choose both the type and route of the trip; therefore a probability model is also necessary. We continue to adopt the probability description as in part 2 and then try to find the optimal schedule.

In part 1, we find the schedule of trips with fixed dates, types (propulsion and duration) and routes (which campsites the trip stops at), and to achieve this we use a rather novel method. The key idea is to divide campsites into different “orbits”that only allows some certain trip types to travel in, therefore the problem turns into several separate small problem to allocate fewer trip types, and the discussion of orbits allowing one, two,

three trip types lead to general result which can deal with any value of Y. Particularly, we let Y=150, a rather realistic number of campsites, to demonstrate a concrete schedule and the carrying capacity of the river is 2340 trips.

In part 2, we find the schedule of trips with fixed dates, types but unrestrained routes. To better describe the behavior of tourists, we need to use a stochastic model(随机模型). We assume a classical probability model and also use the upper limit value of small probability to define an event as not happening. Then we use Greedy algorithm to choose the trips added and recursive algorithm together with Jordan Formula to

calculate the probability of two trips simultaneously occupying the same campsites. The carrying capacity of the river by this method is 500 trips. This method can easily find the

2 Definitions

1 Introduction

4 Assumptions

排的结构);

3 Specific formulation of problem

unrestrained routes.

6.1 Method

6.1.1 Motivation and justification6.1.2 Key ideas

6.2 Development of the model6.2.1 Calculation of p(T,x,t)

6.2.2 Best schedule using Greedy algorithm

6.2.3 Application to situation where X trips are given

5.1 Method

5.1.1 Motivation and justification5.1.2 Key ideas

5.2 Development of the model

5.2.1Every campsite set for every single trip type5.2.2 Every campsite set for every multiple trip types5.2.3One campsite set for all trip types

6 Part 2 Best schedule of trips with fixed dates and types, but

5 Part 1 Best schedule of trips with fixed dates, types and also routes.

2)论文结构概述(列出提纲,分析优缺点,自己安

optimal schedule with X given trips, no matter these X trips are with fixed routes or not.In part 3, we find the optimal schedule of trips with fixed dates and unrestrained types and routes. This is based on the probability model developed in part 2 and we assign the choice of trip types of the tourists with a uniform distribution to describe their freedom to choose and obtain the results similar to part 2. The carrying capacity of the river by this method is 493 trips. Also this method can easily find the optimal schedule with X given trips, no matter these X trips are with fixed routes or not.

7 Part 3 Best schedule of trips with fixed dates, but unrestrained types

and routes.

11 References

10 Conclusions

9.1 Strengths and weaknesses9.1.1 Strengths9.1.2 Weakness

9.2 Further discussion

7.1 Method

7.1.1 Motivation and justification7.1.2 Key ideas

7.2 Development of the model

9 Evaluation of the model

12 Letter to the river managers

用于问题的转化

We regard the carrying capacity of the river as the maximum total number of trips available each year, hence turning the task of the river managers into looking for the best schedule itself.

表明我们在文中所做的工作

We have examined many policies for different river…..问题的分解

We mainly divide the problem into three parts and come up with three different….对我们工作的要求:

we develop a rather novel method here.

8.1Stability with varying trip types chosen in 6

8.2The sensitivity analysis of the assumption 4④8.3 The sensitivity analysis of the assumption 4⑥

8 Testing of the model----Sensitivity analysis

Given the above considerations, we want to find the optimal。。阐述对问题研究后的发现和成果

3)论文中出现的好词好句(做好记录);

The advantages of this model are that it provides with a simple but almost optimal schedule and that it is able to control the proportions of the number of all trip types, which makes sense to you for easier management of the river trips.

We have undertaken an extensive examination of the problem and here are our key findings, hope they are beneficial to your management of the river.自我评价(夸奖)自己的模型(模型的方法新颖)

初始化设定Y>=306。。。做,。。。达到了。。。的简化,使得更易求解。。。

数学描述,为了…我们令…;用…表示…

For better description we assign a natural number to every campsite in the downstream direction, from 0 to Y+1.

修正如下:(采用多样化的图框进行描述,显得更漂亮,清楚,明确)

4)论文中的图表(图表样式和图表说明)。

如下图表:优点是,采用图表对模型的整个过程进行了描述,表意清晰,明确。

We use ???? to denote the average time tourists travel per day for a certain trip

The key idea is to divide the campsites into separate “which”are for some certain trip types to travel in, and we only need to find the optimal schedule for every orbit with fewer trip types. This reduces the problem to be simple and solvable.

否是…

… ……

同上:

论文内部的公式:

概率论中的容斥原理:

此说明,阅卷人对论文的内容的重视程度不是很重要,重要的是:

语言的贯通,论文的整体结构,模型的优缺点,和作者针对于模型对于实际提出的建设性意见…

VIP专享美国数学建模竞赛优秀论文阅读报告

2.优秀论文一具体要求:1月28日上午汇报1)论文主要内容、具体模型和求解算法(针对摘要和全文进行概括);Inthepart1,wewilldesignaschedulewithfixedtripdatesandtypesandalsoroutes.Inthepart2,wedesignaschedulewith
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