1、For office use only T1 _ T2 _ T3 _ T4 _ Team Control Number 80386 Problem Chosen D For office use only F1 _ F2 _ F3 _ F4 _ 2018 MCM/ICM Summary Sheet As the tail of the heavy Falcon rocket dissipated in the atmosphere, Tesla should know that it is more difficult to hand over a reliable production to

2、 consumers than sending a car into outer space. How should Tesla find the development plan to meet the needs of customers and deliver Tesla electric cars to every family? To solve the task 1, we make a regression analysis to the number of American cars and found that we need at least 1,463,222 charg

3、ing stations after 15 years. Then, discuss the number of the charging stations by regression analysis. After calculating, we can easily know that it is impossible for Tesla to complete the switch to all-electricity in the US, even in 2030. Finally, in order to set up the charging pile more reasonabl

4、y, we give the suburban space a definition. According to the research, we divide the data into three ratios of urban, suburban and rural area as 27.7%, 56.48% and 15.82%. As for task 2, we choose South Korea as the research object and generalization of the first question model. We can calculate that

5、 they need at least 124,798 charging stations in 2018 and the distribution of urban, suburban and rural area. Then the optimal layout model of the charging station is established by using the maximum cover model and the central ground theory. The development plan of the layout for the charging stati

6、on is set up at the same time. The key factor affecting the development model of our charging station is the charging demand in the future regions, which will directly determine the layout of the future charging station. In the part of 2b, our conclusion is to build the charging stations in a balanc

7、ed construction in each region, and the amount of construction is slightly larger than the demand. When solving the problem 2c, we set up an competitive exclusion model for automobile and electric vehicle. The numerical solution of the equation is obtained by using the ode45 of Matlab. From the valu

8、e, we can easily know that it takes about 13 years, 16 years, 18 years and 55 years for South Koreas electric car to reach the required percentages. The key factor that affect our competition model is the competitive advantage of the car to electric vehicles. By making sensitive analysis on these tw

9、o parameters, we found that the inherent growth rate has little impact on the process of all-electricity and the competitive advantage of the automobile to electric vehicle has significant influence on the process of all-electricity. The problem get a great change when it comes to task 3. The standa

10、rd deviation elliptical method is used to get the index of population distribution equilibrium and Gini coefficient to measure the uneven distribution of wealth in countries. Discriminant analysis realizes the classification of equilibrium country and gives the criterion. In task 4, through the calc

11、ulation progress, we can find that when the fast replacement station replaced all the existing slow charging stations, the number of charging piles will be 97% less than before. So we think that the fast changing technology will significantly reduce the number of required charging stations In the en

12、d, we write a handout for the leaders all over the world and hope to help them to determine the most suitable strategy for the successful completion of the electrification for their country. Key Words: Balanced Development; Queuing Theory; Logistic Population Competition; Standard Deviation Ellipse;

13、 Discriminant Analysis 數(shù)學(xué)家（原校苑數(shù)模）整理請(qǐng)關(guān)注“校苑數(shù)?！蔽⑿殴娞?hào)，獲取更多資料w w w .m a t h o r .co m 版權(quán)所有COMAP 僅供學(xué)習(xí) 請(qǐng)勿傳播 Content 1 Introduction . 1 1.1 Background . 1 2 Problem Restatement . 1 3 General Assumptions . 1 4 Model Parameters . 2 5 Model Construction . 2 5.1 Installation of Charging Station Model . 2 5.1.1

14、Total Number of Charging Station . 2 5.1.2 Charging stations in urban, suburban, and rural areas . 4 5.2 Use the Model in South Korea . 5 5.2.1 Test the Model in South Korea . 5 5.2.2 Build the General Layout Model of Charging Station . 6 5.2.3 Taking South Korea as an Example to Solve the Model . 7

15、 5.2.4 Commercial Model of Electric Vehicle Charging Station . 8 5.2.5 The Competitive Exclusion Model of Biological Groups . 8 5.3 Consideration of regional differences . 10 5.3.1 Use the Gini Coefficient to measure the degree of distribution imbalance. . 10 5.3.2 Standard Deviation Ellipse Algorit

16、hm . 10 5.3.3 Discriminant Model . 12 5.3.4 The Classification System. 15 6 The Influence of High-tech on Electric Vehicles . 15 6.1 The influence of new transportation methods on electric vehicles . 16 6.1.1 Car-Share services: . 16 6.1.2 Self-Driving Cars: . 17 6.1.3 Flying Cars: . 17 6.2 The infl

17、uence of new technology on electric vehicles . 17 6.3 Wireless Charging Technology. 18 7 The Sensitivity Analysis . 18 8 Strengths and Weaknesses . 19 8.1 Strengths . 19 8.2 Weaknesses . 19 9 The handout for the leaders. 20 數(shù)學(xué)家（原校苑數(shù)模）整理請(qǐng)關(guān)注“校苑數(shù)?！蔽⑿殴娞?hào)，獲取更多資料w w w .m a t h o r .co m 版權(quán)所有COMAP 僅供學(xué)習(xí) 請(qǐng)勿傳

18、播 Team # 80386 Page 4 of 21 Where 1 is the proportion of supercharging, 2 is the proportion of destination charging piles. Then we get: = 2 =1 , = 1,2 (5.1.9) Then we get the data of 1. According to 1, we can calculate the whole number of charging piles by equation (5.1.7) and (5.1.9). Thus, =11,705

19、,777, so the number of the charging station is 1,463,222. 5.1.2 Charging stations in urban, suburban, and rural areas Because in most cases the definition of urban, suburban and rural areas is not very clear. We developed a standard definition of suburban that reflects what residents experience. A s

20、uburb is a mixed-use or residential area, existing either as part of a city or urban area or as a separate residential community within commuting distance of a city. In most English-speaking countries, suburban areas are defined in contrast to central or inner-city areas, but in Australian English a

21、nd South African English, suburb has become largely synonymous with what is called a neighborhood in other countries and the term extends to inner-city areas. In some areas, such as Australia, China, New Zealand, the United Kingdom, and a few U.S. states, new suburbs are routinely annexed by adjacen

22、t cities. In others, such as Saudi Arabia, Canada, France, and much of the United States, many suburbs remain separate municipalities or are governed as part of a larger local government area such as a county. It turns out that many cities legal boundaries line up poorly with what local residents pe

23、rceive as urban. Nationally, 26 percent of Americans described where they live as urban, 53 percent said suburban and 21 percent said rural. (This comes close to the census estimate that 81 percent of the population is urban if “urban” is understood to include suburban areas.) 2 Once we know the rur

24、al population, we can calculate the other two parts population by the proportion above. (suburban population: rural population=53:21) Figure1: Rural population forecast in the United States 數(shù)學(xué)家（原校苑數(shù)模）整理請(qǐng)關(guān)注“校苑數(shù)?！蔽⑿殴娞?hào)，獲取更多資料w w w .m a t h o r .co m 版權(quán)所有COMAP 僅供學(xué)習(xí) 請(qǐng)勿傳播 Team # 80386 Page 5 of 21 From f

25、igure 1, we can know the United States population in 2030, and work out the population of suburb and city. The result as follows: Population ratio of the United States in 2030: Urban: 27.70%; Suburban: 56.48%; Rural: 15.82%. Based on the ratio of the United States in 2030, we can get the number of c

26、harging piles that required in each region as follows: Urban: 3,243,085; Suburban: 6,610,905; Rural: 1,851,787. Thus, we can get the number of charging stations in different areas as: Urban: 405,386; Suburban: 826,363; Rural: 231,473. 5.2 Use the Model in South Korea 5.2.1 Test the Model in South Ko

27、rea We can use the method mentioned in 5.1.Based on the number of current cars, the proportion of the charging piles , and the service strength of the charging pile 1,2, we can also use (5.1.7) and (5.1.9) to calculate . We can get that = 419,059, and the charging stations are 52,382 in South Korea.

28、 Figure2: Korean Rural population projection From the figure above, we can get the population of South Korea in 2018, and the proportion of population in each region. Then finally get the needs of charging piles and stations in different areas in the table below: Table1: The needs of the charging pi

29、les and charging stations Charging piles Charging stations The whole country 998,380.01 124,797.50 Urban 272,097.73 34,012.22 Suburban 554,660.76 69,332.59 Rural 171,621.52 21,452.69 數(shù)學(xué)家（原校苑數(shù)模）整理請(qǐng)關(guān)注“校苑數(shù)?！蔽⑿殴娞?hào)，獲取更多資料w w w .m a t h o r .co m 版權(quán)所有COMAP 僅供學(xué)習(xí) 請(qǐng)勿傳播 Team # 80386 Page 6 of 21 5.2.2 Build t

30、he General Layout Model of Charging Station The Maximum Coverage Theory In order to achieve the maximum coverage in South Korea, we build a Layout Model of Charging Station. The model form of the theory of the center to divide the service area, the primary site method by gravity in every service are

31、a, and we supposed that we have “m” rechargeable charging stations, “n” demand points and going to build “p” stations. Set up the requirement at j as , and take to express the distance from the station i to the demand point j. Then we set up the decision variables as = 1 0 Where 1 indicates that the

32、 i alternative is building a charging station and providing service at the j demand point of the charging station. On the contrary, 0 means that build the station at i but do not provide service at the j demand point of the charging station Then we can get: =1 =1 (5.2.2) Our goal is to work out the

33、formula and get the maximum. =1 ( = 1,2,3,) 1 =1 ( = 1,2,3,) ( =1 ) =1 () (5.2.3) Where: Dm is the maximum number of cars that a charging station can serves in one day. P is the maximum number of charging stations that can only be built on the alternative address. rm refers to service radius. In our

34、 model, each of the demand point can only serve for one charging station, and the indicative function in the above formula is: (x) = 1, 0 0, = 0 (5.2.4) The Central Ground Theory The determination of the scope of service is in fact the maximum service radius of the charging station. It should be aim

35、ed at the convenience of electric vehicle users charging. In the initial stage of promoting the use of electric vehicles, the number of pure 數(shù)學(xué)家（原校苑數(shù)模）整理請(qǐng)關(guān)注“校苑數(shù)?！蔽⑿殴娞?hào)，獲取更多資料w w w .m a t h o r .co m 版權(quán)所有COMAP 僅供學(xué)習(xí) 請(qǐng)勿傳播 Team # 80386 Page 7 of 21 electric vehicles is relatively small. At this time, th

36、e service scope of charging stations is larger, and the number of charging facilities is infrequency. With the increasing number of electric vehicles, the service radius of the charging station will be gradually shortened, and the number of charging stations should be increased to meet the needs of

37、the users. 3 We assumed that the maximum time for a driver to find a charging station is 10 minutes. When the driver finds that the battery is not enough, he tries to find a charging station near the nearest minute to recharge the vehicle. Based on the central ground theory, we can get: = (5.2.5) Wh

38、ere: : The speed of a vehicle (km/h) : The longest searching time that the customers use. : The curvature coefficient of the road. The ratio between the actual traffic distance and the linear distance between two points. can be calculated in the equation shown below: = 16 8 1+ (1 )2(5.2.6) So, we ca

39、n get 94.18. Thus, the maximum number of cars that a charging station can serves in one day is almost 95. Figure3: The primary site we choose Figure4: The development period network 5.2.3 Taking South Korea as an Example to Solve the Model Our paper starts with the model of network layout theory to

40、divide the service area, and we can choose the service area by this theory. Because the site of the center of gravity method may not be achieved in reality, we need to choose a coordinate near feasible site as an alternative site. Then calculate the distance matrix of each demand point and each alte

41、rnative charging station. We can use the Lingo software to solve the equations (5.2.3) and (5.2.4), and get 數(shù)學(xué)家（原校苑數(shù)模）整理請(qǐng)關(guān)注“校苑數(shù)?！蔽⑿殴娞?hào)，獲取更多資料w w w .m a t h o r .co m 版權(quán)所有COMAP 僅供學(xué)習(xí) 請(qǐng)勿傳播 Team # 80386 Page 8 of 21 the optimal charging station layout according to the General Layout Model. 5.2.4 Commerc

42、ial Model of Electric Vehicle Charging Station Due to the short range of electric vehicles and the lack of charging stations, it is difficult for consumers to use electric vehicles to complete all their travel needs and this make them feel nervous and generate anxiety. According to the literature“Th

43、e Commercial Model of Electric Vehicle Charging Station”, we can get the anxiety () as: () = (5.2.7) Where: : is an exogenous parameter that represents the initial anxiety of the consumer. dc is the length of a linear city. t: is the average distance between two charging stations Then we can get the

44、 consumer purchase benefit: 1 () + (5.2.8) Where: : A random variable. A consumer can get a value if he uses an electric car to complete all his travel needs. p: The sale price of an electric car. b: Government subsidies We can know from the above equations that build the charging station first can

45、reduce peoples anxiety effectively. Without the charging station: = , () = Have a charging station: = 1 2 ,() = 1 2 . Then it lowers the anxiety of people and raises the enthusiasm to by the electric vehicles of consumers. In summary, the economically developed areas government or companies should b

46、uild more charging stations according to the amount of car purchases by consumers. This is mainly because that the relatively high economic level of the users who with their own garage value the convenience of products more than the costs of small, pure electric cars. 5.2.5 The Competitive Exclusion

47、 Model of Biological Groups Choosing the competitive exclusion model of biological groups to simulate the market competition of electric vehicles and traditional automobiles. We assumed x1() as the number of electric vehicles on the change of time variable t, and x2() as the traditional automobiles

48、on the change of time variable t. Then we can write the competitive exclusion model of electric vehicles and traditional automobiles: 1 = 11(1 1 1 2 1 ) 2 = 22(1 2 2 1 2 ) (5.2.9) 數(shù)學(xué)家（原校苑數(shù)模）整理請(qǐng)關(guān)注“校苑數(shù)?！蔽⑿殴娞?hào)，獲取更多資料w w w .m a t h o r .co m 版權(quán)所有COMAP 僅供學(xué)習(xí) 請(qǐng)勿傳播 Team # 80386 Page 9 of 21 Where: 1: The in

49、herent growth rate of electric vehicles 2: The inherent growth rate of traditional cars. 1: The maximum number of electric vehicles allowed in the country. 2: The maximum number of traditional cars allowed in the country. : The competitive advantage of electric vehicles over traditional cars. : The

50、competitive advantage of traditional cars over electric vehicles. To make electric cars completely replace traditional cars, we need to let the autonomous equation above to reach the balance point P1 ( 1,0). According to the equilibrium stability criterion of the autonomous equation, if and only if

51、1 2 and 2 1 , 1 , and only when the data turned into this, can electric vehicles replace the traditional automobiles. Because of the autonomous equation above is very hard to work out, we make use of numerical solution function Ode45 in MATLAB to solve the problem. Where the inherent growth rate in the model 1= 0.3 , 2= 4.7. We hope the value that r be obtained can calculated and has a very small error with the historical data. Figure5: The electric vehicles and traditional cars quantitative changing trend in Sou