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2021年2月11日发(作者：篮球女孩钱红艳)

美国数学建模论文格式

【篇一：

2013

美国数学建模论文模版】

title

abstract:

key words:

contents

1.

introduction............ .................................................. .........................

.............. ..............................................3

1.1 why does toll way collects

toll? ………………………………………….…………………….3

1.2 toll

modes………………………………………………………………… …

…………………………3

1.3 toll collection

methods………………………………………… ………………………

…….……3

1.4 annoyance in toll

plazas…………………………… …………….………….………………

…….3

1.5 the origin of the toll way

problem……………………...……………………………………...3

1.6 queuing

theory………………… ……………………………………………………

…………...…...4

2. the description of

problem….......................................... ................................................

...................5

2.1 how do we approximate the whole course of paying

toll? ................ ............................5

2.2 how do we define the optimal

configuration? ........................…………….………….5

2.2.1 from the perspective of

< br>motorist…………………………………….………………….5

2.2.2 from the perspective of the toll

plaza…………………………………………………6

2.2.3

compromise…………………………… ……...…………………………

…………...………..6

2.3 overall optimization and local

optimization……………………………..……………….…6

< br>

2.4 the differences in weights and sizes of

vehicles………………………………………..…7

2.5 what if there is no data

available? ............................ .................................................. ...........

.....7

3.

models……………............. .................................................. ..............

......................... .....................................7

3.1 basic

model............ .................................................. ...................................

.... ........................................7

3.1.1 symbols and

defini tions………………………………..…...…………………………

…...7< /p>

3.1.2

assumption s……………………………………………………………

….……..……………..8< /p>

3.1.3 the foundation of

model………………………………………………………………….9

3.1.4 solution and

result ……………………………………………………………….………

...11

3.1.5 analysis of the

result……………………………………………….………………………

..…… ….….11

3.1.6 strength and < /p>

weakness………………………………………………….…………….

…..13

3.2 improved

model..................................... .................................................. ..........

14

3.2.1 extra

symbols……………………………………..………… ……………...…

………………......................

14

3.2.2 additional

assumptions…………………………………………… …...…..………

…………………..14

3.2.3 the foundation of

mod el………………………………..……………………………………

……….14

3.2.4 solution and

result………………………………………….……………………………

..…… ………...15

3.2.5 analysis of the

result…………………………………………….……………………..…

………….….18

3.2.6 strength and

weakness……………………………………………… .……………….

…..19

4.

conclusions............................ .................................................. .........

.............................. .............................19

4.1 conclusions of the

prob lem……………………………………..……………..19

4.2 methods used in our

mod els…………………………………...……………………..…………

19

4.3 application of our

models…………………………………………………..………………..

….19

5. future

w ork............................................... .................................................. ..

..................................... ......19

5.1 another

model………………………………………………………………………

…… …………19

5.2 another layout of toll

plaza………………………………………………………..……… ……2

3

5.3 the newly- adopted charging

methods………………………………………..……………23 6

.

references............... .................................................. .........................

.............. ...........................................23 7. < /p>

appendix................................ .................................................. ..........

............................. .............................23programs and

codes………………………………………………………………..……

… ……………24

i. introduction

in order to indicate the origin of the toll way problems, the

following background is worth mentioning.

1.1

1.2

1.3

1.4

1.5

1.6

ii. the description of the problem

2.1 how do we approximate the whole course of paying toll?

?

?

?

?

2.2 how do we define the optimal configuration?

1) from the perspective of motorist:

2) from the perspective of the toll plaza:

3) compromise:

2.3 the local optimization and the overall optimization

?

?

?virtually:

2.4 the differences in weights and sizes of vehicles

2.5 what if there is no data available?

iii. models

3.1 basic model

3.1.1 terms, definitions and symbols

the signs and definitions are mostly generated from queuing

theory.

?

?

?

?

?

3.1.2 assumptions

?

?

?

?

?

3.1.3 the foundation of model

1) the utility function

? the cost of toll plaza:

? the loss of motorist:

? the weight of each aspect:

? compromise:

2) the integer programming

according to queuing theory, we can calculate the statistical

properties as follows.

3) the overall optimization and the local optimization

? the overall optimization:

? the local optimization:

? the optimal number of tollbooths:

3.1.4 solution and result

1) the solution of the integer programming:

2) results:

3.1.5 analysis of the result

? local optimization and overall optimization:

? sensitivity: the result is quite sensitive to the change of the

three

parameters

? trend:

? comparison:

3.1.6 strength and weakness

? strength: in despite of this, the model has proved that .

moreover, we

have drawn some useful conclusions about. the model is fit

for, such as ? weakness: this model just applies to. as we

have stated,. that’s

just what we should do in the improved model.

3.2 improved model

< br>【篇二：

2015

年数学建模美赛论文格式】

< p>

2015

年美国数学建模要求

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文章标题居中用宋体

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第一

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第二

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第三 作者宋体

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