1、For office use onlyT1_T2_T3_T4_Team Control Number11111 Problem ChosenABCDFor office use onlyF1_F2_F3_F4_2015Mathematical Contest in Modeling (MCM/ICM) Summary SheetIn order to evaluate the performance of a coach, we describe metrics in five aspects: historical record, game gold content, playof

2、f 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. First, *grade. To ev

3、al* , 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 ranking. We conduct s

4、ensitivity 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 Washington, Franklin D. R

5、oosevelt. At last, the strength and weakness of our mode are discussed, non-technical explanation is presented and the future work is pointed as well.Key words: Ebola virus disease; Epidemiology; West Africa; *ContentsI. Introduction21.121.221.321.421.521.62II. The Description of the Problem32.1 How

6、 do we approximate the whole course of paying toll?32.2 How do we define the optimal configuration?32.3 The local optimization and the overall optimization32.4 The differences in weights and sizes of vehicles32.5 What if there is no data available?3III. Models33.1 Basic Model33.1.1 Terms, Definition

7、s and Symbols33.1.2 Assumptions33.1.3 The Foundation of Model33.1.4 Solution and Result33.1.5 Analysis of the Result33.1.6 Strength and Weakness43.2 Improved Model43.2.1 Extra Symbols43.2.2 Additional Assumptions43.2.3 The Foundation of Model43.2.4 Solution and Result43.2.5 Analysis of the Result53.

8、2.6 Strength and Weakness5IV. Conclusions54.1 Conclusions of the problem54.2 Methods used in our models54.3 Applications of our models5V. Future Work65.1 Another model65.1.1 The limitations of queuing theory66665.2 Another layout of toll plaza65.3 The newly- adopted charging methods7VI. References7V

9、II. Appendix7I. IntroductionIn 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 Problem2.1 How do we approximate the whole course of paying toll?llll2.2 How do we define the optimal configuration? 1

10、) From the perspective of motorist: 2) From the perspective of the toll plaza: 3) Compromise: 2.3 The local optimization and the overall optimizationlll Virtually: 2.4 The differences in weights and sizes of vehicles 2.5 What if there is no data available?III. Models3.1 Basic Model3.1.1 Terms, Defin

11、itions and SymbolsThe signs and definitions are mostly generated from queuing theory. l l l l l 3.1.2 Assumptionsl l l l l3.1.3 The Foundation of Model1) The utility functionl The cost of toll plaza: l The loss of motorist: l The weight of each aspect: l Compromise: 2) The integer programmingAccordi

12、ng to queuing theory, we can calculate the statistical properties as follows.3) The overall optimization and the local optimizationl The overall optimization: l The local optimization: l The optimal number of tollbooths: 3.1.4 Solution and Result1) The solution of the integer programming:2) Results:

13、 3.1.5 Analysis of the Resultl Local optimization and overall optimization: l Sensitivity: The result is quite sensitive to the change of the three parameters l Trend: l Comparison: 3.1.6 Strength and Weaknessl Strength: In despite of this, the model has proved that . Moreover, we have drawn some us

14、eful conclusions about . The model is fit for, such as l Weakness: This model just applies to . As we have stated, . Thats just what we should do in the improved model.3.2 Improved Model3.2.1 Extra SymbolsSigns and definitions indicated above are still valid. Here are some extra signs and definition

15、s.l l l l3.2.2 Additional Assumptionslll Assumptions concerning the anterior process are the same as the Basic Model.3.2.3 The Foundation of Model1) How do we determine the optimal number?As we have concluded from the Basic Model, 3.2.4 Solution and Result1) Simulation algorithmBased on the analysis

16、 above, we design our simulation arithmetic as follows.l Step1: l Step2: l Step3: l Step4: l Step5: l Step6: l Step7: l Step8: l Step9: 2) Flow chartThe figure below is the flow chart of the simulation.3) Solution3.2.5 Analysis of the Result3.2.6 Strength and Weaknessl Strength: The Improved Model a

17、ims 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.l Weakness: . Thus the model is still an approximate on a large scale. This has doomed to limit the applications of it. IV. Conclusions4.1 Conclusions of the problemll