美赛论文优秀模版

2015

Mathematical Con test in Modeli ng (MCM/ICM) Summary Sheet

In order to evaluate the performanee of a coach, we describe metrics in five aspects: historical

record, game gold content, playoff performanee, honors and contribution to the sports. Moreover, each aspect is subdivided into several sec on dary metrics. Take playoff performa nce as example, we collect postseas on result (Sweet Sixtee n, Final Four, etc.) per year from NCAA official website, Wikimedia and so on.

First, ****grade.

To eval*** , in turn, are John Wooden, Mike Krzyzewski, Adolph Rupp, Dean Smith and Bob Kni ght.

Time line horizon does make a difference. According to turning points in NCAA history, we divide the

previous century into six periods with different time weights which lead to the cha nge of ranking.

We con duct sen sitivity an alysis on FSE to find best membership fun cti on and calculati on rule.

Sensitivity analysis on aggregation weight is also performed. It proves AM performs better tha n sin gle

model. As a creative use,top 3 preside nts (U.S.) are picked out: Abraham Lincoln, George Washi ngton, Fran kli n D. Roosevelt

At last, the stre ngth and weak ness of our mode are discussed, non-tech ni cal expla nati on is prese nted and the future work is poin ted as well.

Key words: Ebola virus disease; Epidemiology ; West Africa; ******

Con te nts

I. I ntroduct ion (2)

1.1 ............................................................................................................................................................................... 2 For office use only Team Con trol Number For office use only T1 _____________________ 11111 T2 _____________________ F1 ____________________ F2 _____________________ T3 ____________________ T4 ____________________ Problem Chose n

ABCD F3 _____________________ F4 _____________________

1.2 (2)

1.3 (2)

1.4 (2)

1.5 (2)

1.6 (2)

II.The Descripti on of the Problem (2)

2.1How do we approximate the whole course of pay ing toll? (2)

2.2How do we defi ne the optimal configuration? (3)

2.3The local optimizati on and the overall optimization (3)

2.4The differe nces in weights and sizes of vehicles (3)

2.5What if there is no data available? (3)

III....................................................................................................................................................................................... M odels (3)

3.1Basic Model (3)

3.1.1Terms, Definitions and Symbols (3)

3.1.2Assumpti ons (3)

3.1.3The Foun datio n of Model (4)

3.1.4Soluti on and Result (4)

3.1.5An alysis of the Result (4)

3.1.6Stren gth and Weakness (4)

3.2Improved Model (4)

3.2.1Extra Symbols (5)

3.2.2Additi onal Assumpti ons (5)

3.2.3The Foun datio n of Model (5)

3.2.4Soluti on and Result (5)

3.2.5An alysis of the Result (6)

3.2.6Stren gth and Weakness (6)

IV.Con clusi ons (6)

4.1Con clusi ons of the problem (6)

4.2Methods used in our models (6)

4.3Applicati ons of our models (6)

V.Future Work (6)

5.1Ano ther model (6)

5.1.1The limitations of queuing theory (6)

5.1.2 (6)

5.1.3 (7)

5.1.4 (7)

5.2Ano ther layout of toll plaza (7)

5.3The n ewly- adopted chargi ng methods (7)

VI.References (8)

VII.Appe ndix (8)

I.I ntroducti on

In order to indicate the origin of the toll way problems, the following background is worth men ti oning.

1.1

1.2

1.3

1.4

1.5

1.6

II.The Description of the Problem

2.1How d o we approximate the whole course of pay ing toll?

2.2How d o we defi ne the optimal con figurati on?

1)From the perspective of motorist:

2)From the perspective of the toll plaza:

3)Compromise:

2.3The l ocal optimization and the overall optimization

Virtually:

2.4The differe nces in weights and sizes of vehicl es

2.5What if there is no data availabl e?

III.Models

3.1 Basic Model

3.1.1Terms, Definitions and Symbols

The sig ns and defi niti ons are mostly gen erated fronqueu ing theory.

3.1.2Assumpti ons

3.1.3The Foun dation of Model

1)The utility fun ctio n

The cost of toll plaza:

The loss of motorist:

The weight of each aspect:

Compromise:

2)The in teger program ming

Accord ing to queu ing theory, we can calculate the statistical properties as follows.

3)The overall optimization and the local optimization

The overall optimizati on:

The local optimization:

The optimal nu mber of tollbooths:

3.1.4Solution and Result

1)The solution of the integer programming:

2)Results:

3.1.5An alysis of the Result

Local optimization and overall optimization:

Sensitivity: The result is quite sensitive to the change of thehree parameters

Trend:

Comparis on:

3.1.6Stre ngth and Weak ness

Strength: In despite of this, the model has provedhat . Moreover, we have drawn some useful

con clusi on sabout . The model is fit for, such as

Weakness: This model just applies to . As we havestated, . That' s just what

we should do in the improved model.

3.2 Improved Model

3.2.1Extra Symbols

Signs and defi niti ons in dicated above are still valid. Here are some extra sig ns and defi niti ons.

3.2.2Additi onal Assumpti ons

Assumpti ons concerning the an terior process are the same as the Basic Model.

3.2.3The Foun dation of Model

1) How do we determ ine the optimal nu mber?

As we have con cluded from the Basic Model,

3.2.4Solution and Result

1) Simulati on algorithm

Based on the analysis above, we design our simulation arithmetic as follows.

Step1:

Step2:

Step3:

Step4:

Step5:

Step6:

Step7:

Step8:

Step9: 2) Flow chart

The figure below is the flow chart of the simulatio n.

3)Solution

3.2.5 Analysis of the Result

3.2.6 Stre ngth and Weak ness

Strength: The Improved Model aims to make up forthe neglect of . The result seems to declare that this model is more reas on able tha n the Basic Model and much more effective tha n the existi ng desig n.

Weak ness: . Thus the model is still an approximate on a large scale. This has

doomed to limit the applications of it.

IV. Con clusi ons

4.1 Con clusi ons of the probl em

4.2 Methods used in our mod els

4.3 Applicati ons of our mod els

V. Future Work

5.1 Ano ther model

5.1.1 The limitations of queuing theory

5.1.2

5.1.3

5.1.4

1)

2)

3)

4)

5.2 Ano ther layout of toll plaza

5.3 The newly- ad opted charging methods

VI. Refere nces

[1]

[2]

[3]

[4]

VII. Appe ndix