美賽論文優(yōu)秀模版

1、Team Control Number For office use only For office use only 11111 _ _F1 T1 _ T2 _ F2 F3T3 _ _ Problem Chosen F4 T4 _ _ ABCD 2015 Mathematical Contest in Modeling (MCM/ICM) Summary Sheet In order to evaluate the performance of a coach, we describe metrics in five aspects: historical record, game gold

2、 content, playoff performance, honors and contribution to the sports. Moreover, each aspect is subdivided into several secondary metrics. Take playoff performance as example, we collect postseason result (Sweet Sixteen, Final Four, etc.) per year from NCAA official website, Wikimedia and so on. Firs

3、t, *grade. To eval* , in turn, are John Wooden, Mike Krzyzewski, Adolph Rupp, Dean Smith and Bob Knight. 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 change of rank

4、ing. We conduct sensitivity analysis on FSE to find best membership function and calculation rule. Sensitivity analysis on aggregation weight is also performed. It proves AM performs better than single model. As a creative use, top 3 presidents (U.S.) are picked out: Abraham Lincoln, George Washingt

5、on, Franklin D. Roosevelt. At last, the strength and weakness of our mode are discussed, non-technical explanation is presented and the future work is pointed as well. West Africa; *; Epidemiology; Ebola virus diseaseKey words: Team #12345 Page 1 of 9 Contents I. Introduction . 2 1.1 . 2 1.2 . 2 1.3

6、 . 2 1.4 . 2 1.5 . 2 1.6 . 2 II. The Description of the Problem . 2 2.1 How do we approximate the whole course of paying toll? . 2 2.2 How do we define the optimal configuration? . 3 2.3 The local optimization and the overall optimization . 3 2.4 The differences in weights and sizes of vehicles. 3 2

7、.5 What if there is no data available? . 3 III. Models . 3 3.1 Basic Model . 3 3.1.1 Terms, Definitions and Symbols . 3 3.1.2 Assumptions . 3 3.1.3 The Foundation of Model . 4 3.1.4 Solution and Result . 4 3.1.5 Analysis of the Result . 4 3.1.6 Strength and Weakness . 4 3.2 Improved Model . 4 3.2.1

8、Extra Symbols . 5 3.2.2 Additional Assumptions . 5 3.2.3 The Foundation of Model . 5 3.2.4 Solution and Result . 5 3.2.5 Analysis of the Result . 6 3.2.6 Strength and Weakness . 6 IV. Conclusions . 6 4.1 Conclusions of the problem . 6 4.2 Methods used in our models . 6 4.3 Applications of our models

9、 . 6 V. Future Work . 6 5.1 Another model . 6 5.1.1 The limitations of queuing theory . 6 5.1.2 . 6 5.1.3 . 7 5.1.4 . 7 5.2 Another layout of toll plaza . 7 5.3 The newly- adopted charging methods . 7 VI. References . 8 VII. Appendix . 8 Team #12345 Page 2 of 9 I. Introduction In order to indicate t

10、he 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? ? ? ? ? Team #12345 Page 3 of 9 2.2 How do we define the optimal configuration? 1) From the perspect

11、ive 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 Sym

12、bols The signs and definitions are mostly generated from queuing theory. ? ? ? ? ? 3.1.2 Assumptions ? ? Team #12345 Page 4 of 9 ? ? ? 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 program

13、ming According to queuing theory, we can calculate the statistical properties as follows. 3) The overall optimization and the local optimization ? The overall optimization: ? Thelocal optimization: ? The optimal number of tollbooths: 3.1.4 Solution and Result 1) The solution of the integer programmi

14、ng: 2) Results: 3.1.5 Analysis of the Result ? Local optimization and overalloptimization: ? 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 ha

15、ve drawn some useful conclusions about . The model is fit for, such as ? Weakness: This model just applies to . As we have stated, . Thats just what we should do in the improved model. 3.2 Improved Model Team #12345 Page 5 of 9 3.2.1 Extra Symbols Signs and definitions indicated above are still vali

16、d. Here are some extra signs and definitions. ? ? ? ? 3.2.2 Additional Assumptions ? ? ? Assumptions concerning the anterior process are the same as the Basic Model. 3.2.3 The Foundation of Model 1) How do we determine the optimal number? As we have concluded from the Basic Model, 3.2.4 Solution and

17、 Result 1) Simulation 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 simulation. 3) Solution Team #12345 Page 6 of 9 3.2.5 Ana

18、lysis of the Result 3.2.6 Strength and Weakness ? Strength: The Improved Model aims to make up for the neglect of . The result seems to declare that this model is more reasonable than the Basic Model and much more effective than the existing design. Weakness: . Thus the model is still an approximate on a large scale. This has ?doomed to limit the applications of it. IV. Conclusions 4.1 Conclusions of the problem ? ? ? 4.2 Methods used in our models ? ? ? 4.3 Applications of ou