2019
MCM/ICM
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Ecosystems provide many natural processes to maintain a healthy and sustainable environment after human life. However, over the past decades, rapid industrial development and other anthropogenic activities have been limiting or removing ecosystem services. It is necessary to access the impact of human activities on biodiversity and environmental degradation.
The main purpose of this work is to understand the true economic costs of land use projects when ecosystem services are considered. To this end, we propose an ecological service assessment model to perform a cost benefit analysis of land use development projects of varying sites, from small-scale community projects to large national projects. We mainly focus on the treatment cost of environmental pollution in land use from three aspects: air pollution, solid waste and water pollution. We collect pollution data nationwide from 2010 to 2015 to estimate economic costs. We visually analyze the change in economic costs over time via some charts. We also analyze how the economic cost changes with time by using linear regression method. We divide the data into small community projects data (living pollution data) and large natural data (industrial pollution data). Our results indicate that the economic costs of restoring economical services for different scales of land use are different. For small-scale land, according to our analysis, the treatment cost of living pollution is about 30 million every year in China. With the rapid development of technology, the cost is lower than past years. For large-scale land, according to our analysis, the treatment cost of industrial pollution is about 8 million, which is lower than cost of living pollution. Meanwhile the cost is trending down due to technology development. The theory developed here provides a sound foundation for effective decision making policies on land use projects.
Key words: economic cost , ecosystem service, ecological service assesment model, pollution.
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E
Content
1. Introduction (3)
2. Variable Description (3)
2.1 Definitions (3)
3. Model Definitions and Results (4)
3.1 2010-2015 Air Pollution Virtual Governance Cost (4)
3.2 2010-2015 Solid Waste Virtual Governance Cost (8)
3.3 2010-2015 Water Pollution Virtual Governance Cost (11)
3.4 Total Governance Data Analysis (14)
3.5 Model Analysis Over Time (15)
4. Conclusions (16)
4.1 Strengths (17)
4.2 Weakness (17)
4.3 Model Improvement (17)
5. References (18)
1.Introduction
Today, with the rapid development of social industrialization and modernization, one thing we must admit is that in the process of industrialization in different regions, countries and even the whole world, we are trying to maximize the economic benefits of limited development space, but at the same time, the impact of decision-making on the biosphere is also ignored.
It is well known that the biosphere provides many natural processes to maintain healthy and sustainable human living environments, which are called ecosystem services. It not only provides food, medicine and raw materials for industrial and agricultural production, but also maintains the life support system that human beings rely on for survival and development. At present, the internationally recognized ecosystem service function classification system is a classification method proposed by MA working group. MA's ecosystem service classification system divides the main service function types into four function groups: product, rule, culture and support. Thus, the ecosystem service function is the foundation of human civilization and sustainable development.
But as we use and update our environment, we may limit or eliminate ecosystem services. Although these activities seem insignificant, they do affect the ecosystem to some extent.
Therefore, we introduce the virtual cost management method, which aims to evaluate the cost of environmental degradation by calculating the cost of pollution control. This allows for a comprehensive assessment of projects under construction, thus ensuring the resilience and sustainability of ecosystem services while utilizing land resources.
To ensure the integrity and the sustainable development of ecological system is the premise and foundation of development, If we simply pursue the speed of development and neglect the pressure that construction activities bring to the ecosystem, will inevitably produce the bad consequences, we must protect our earth, because it is not only our planet, but also the planet of our descendants.
2.Variable Description
2.1 Definitions
To measure the cost of environmental degradation, we introduced the following variables:
Virtual governance costs: The environmental degradation value calculated by the pollution loss method is called the environmental degradation cost, which refers to the various damages caused by the pollutants discharged in the production and consumption process to the environmental function, human health and crop yield under the current governance level.
Environmental loss method: In the SEEA framework, pollution loss method refers to the environmental value assessment method based on damage. This method uses certain technical means and pollution loss investigation to calculate all kinds of damages caused by environmental pollution.
Biodiversity: Refers to the variety of life in an ecosystem; all of the living organisms within a given area.
Biosphere: The part of the Earth that is occupied by living organisms and generally includes the interaction between these organisms and their physical environment.
Ecosystem: A subset of the biosphere that primarily focuses on the interaction between living things and their physical environment.
Ecosystem Services: The many benefits and assets that humans receive freely from our natural environment and a fully functioning ecosystem.
Environmental Degradation: The deterioration or compromise of the natural environment through consumption of assets either by natural processes or human activities.
Mitigate: To make less severe, painful, or impactful.
Valuation: Refers to the estimating or determining the current worth of something.
3.Model Definitions and Results
3.1 2010-2015 Air Pollution Virtual Governance Cost
The natural gas use proportion c1,c2 and c3 are collectively recorded as c, the gas use amount d1,d2 and d3are collectively recorded as d, and the natural gas operation cost f1,f2 and f3 are collectively recorded as f.
In the modeling process, it is assumed that the garbage disposal cost, gas operation cost and central heating operation cost will not change in the next few years.
Urbanization is often accompanied by land development and utilization. Urban construction is inseparable from industrial construction and improvement of human living environment. In this process, the continuous development and utilization of land, or the construction of large factories, or the increase of communities and parks, has a certain impact on the local ecology. Factory waste emissions and gas consumption to a certain extent polluted the air, causing irreversible damage to the ecological environment.
The impact of land development and utilization on the atmosphere is manifold. In large national projects such as industrial projects, we focus on the costs of sulphur dioxide emissions and dust emissions. In small-scale community projects such as community life, we mainly study the governance cost from the perspective of gas use, and establish an ecological service evaluation model related to air pollution.
When considering the function of ecological services, we first study the economic cost of land development and utilization from the perspective of large-scale land development and utilization. Large-scale land development generally includes the establishment and relocation of large companies, the laying of pipelines nationwide, and the establishment of large state-owned enterprises. The construction of large chemical plants in land development produces polluting gases during the development process or after the plant is put into use. Among them, sulfur dioxide and dust emissions accounted for a large proportion. Let's use these two types of pollution as an example to calculate the economic cost.
Collecting China's SO2 and dust emissions from 2010 to 2015:
The unit cost of SO2 and dust
It should be noted that in the process of treatment, the exhaust gas can not be completely treated. The virtual removal rate of SO2 was a2=90%, and the virtual removal rate of dust was b2=97%. The cost of waste gas treatment should be calculated by virtual management method. It is that the total amount of emissions× virtual removal rate× unit governance cost.
SO2 governance cost=a×a2×a1
Dust governance cost=b×b2×b1
The calculations above can be used to estimate the cost of governance. Governance cost=SO2 governance cost+ dust governance cost.
Secondly, when considering the function of ecological services, the cost of land development and utilization is studied from the perspective of small-scale land development and utilization. The development and utilization of small-scale land generally includes the construction of roads, sewers, houses and Bridges. Let's take the development of land for residential areas as an example. When people live in communities, using natural gas for heating and living also pollutes the air. We mainly consider the impact of artificial gas, natural gas and liquefied petroleum gas.
Collecting data on gas use in urban areas of China from 2010 to 2015:
Gas operating costs, urban population, urban gasification rate:
The cost of domestic gas treatment is related to urban population, urban gas rate, gas consumption, various proportions of gas consumption, heating area and operating cost. We use hypothetical assumptions to define the cost of gas pollution control.
Gas pollution control cost=（）+（s1-s2）×e Where n=1 is artificial gas, n=2 is natural gas, and n=3 is liquefied petroleum gas.
The following estimates of governance costs can be obtained by calculation:
3.2 2010-2015 Solid Waste Virtual Governance Cost
In the calculation process, we assume that the unit governance cost is the same, including the cost of general solid waste management, the cost of hazardous waste management, the cost of household garbage removal, the cost of sanitary landfill, and the cost of harmless incineration.
In the process of land development and utilization, both large-scale land use and small-scale land use will inevitably produce solid waste.
In the process of construction and normal use, large factories mainly produce general solid waste and hazardous waste. There are two ways to treat solid waste: storage and disposal. When calculating the cost of industrial solid waste treatment, we can start with the cost of waste storage and management and the cost of waste disposal.
Collecting data on China's industrial solid waste treatment from 2010 to 2015:
HS means hazardous waste storage HD means hazardous waste disposal The unit cost of industrial solid waste:
According to the above data, the virtual governance method is used to calculate the cost of large-scale land development and utilization when the ecological service function is considered.
Virtual governance cost of industrial solid waste=virtual waste management cost of storage waste+ virtual governance cost of disposal waste
Virtual governance cost of storage waste=e1+e2
Virtual governance cost of disposal waste=f1+f2
e1=a× (b1-a1)
e2=c× (d1-c1)
f1=b×b1
f2=d×d1
The virtual governance cost of industrial solid waste can be obtained by calculation:
When small-scale land is used for community construction, a certain amount of household garbage will be produced. There are many ways to deal with household garbage. When calculating the treatment cost, we mainly follow three treatment methods: cleaning, sanitary landfill and innocuous incineration.
Collecting the amount of domestic garbage generated by Chinese Residents from 2010 to 2015:
Domestic garbage unit treatment cost:
Virtual governance cost of domestic garbage=x1+y1+z1
x1=m×(z-x)
y1=n×(y+ z)
z1=r× z
The processing cost of domestic garbage can be obtained by calculation:
3.3 2010-2015 Water Pollution Virtual Governance Cost
The next section considers the cost of water pollution control for land use projects. Based on the above two treatment costs, we still choose the virtual
treatment cost method to calculate the annual water pollution treatment cost from 2010 to 2015. By looking up relevant materials, we know that water pollution involves a wide range of fields, including planting, livestock and poultry breeding, industry, urban life and rural life. However, due to the lack of systematic treatment of sewage in agricultural production, we only consider the cost of virtual pollutants in industry and urban life. Here, we consider the water pollution of small community projects as urban life water pollution, while large national projects are considered as industrial sector water pollution.
Pollutants in industrial wastewater include COD, ammonia nitrogen, petroleum and heavy metals. Here we consider the virtual governance cost of four pollutants, then the calculation formula of the virtual governance cost of industrial enterprises is:
The virtual governance cost of the industrial sector=∑(pollutant emissions×virtual governance costs per unit of pollutants× virtual removal rate of pollutants), the total virtual governance cost is the sum of the virtual governance costs of various pollutants.
Virtual domestic wastewater treatment costs include virtual management cost of COD and ammonia nitrogen virtual governance cost, namely virtual wastewater treatment cost = ∑(pollutant discharge unit pollutant of virtual management cost virtual pollutants removal rate), namely industrial COD discharge quantity A1, industrial ammonia nitrogen emissions B1, C1 oil discharge, heavy metal emissions D1, cities COD discharge E1 and ammonia nitrogen emissions for F1.
The cost of treatment of each pollutant is:
Table 19 The cost of treatment of each pollutant
It should be noted that the virtual removal rate of pollutants is not 100%, the removal rate of COD is 80%, the removal rate of ammonia nitrogen is 50%, the removal rate of petroleum is 80%, and the removal rate of heavy metals is 50%. The annual emissions of various pollutants are:
Then calculated by the above data:
Industrial COD Treatment Cost=A1*80%*800
Industrial Ammonia Nitrogen Treatment Cost=B1*50%*100
Petroleum treatment cost=C1*80%*500
Heavy metal treatment cost=D1*90%*1000
Urban COD Treatment Cost=E1*80%*800
Urban Ammonia Nitrogen Treatment Cost=F1*50%*100 Virtual cost of industrial water pollution=industrial COD treatment cost+ industrial ammonia nitrogen treatment cost+ petroleum treatment cost+ heavy metal treatment cost, namely:
Virtual cost of industrial water pollution=industrial COD treatment cost+
industrial ammonia nitrogen treatment cost+ petroleum treatment cost+ heavy metal treatment cost, namely:
3.4 Total Governance Data Analysis
Based on the above three data, we put the three aspects of governance cost together to form the time governance cost chart, as shown in the figure below:
Chart 1 Industrial integrated virtual governance cost
Chart 2 life total virtual governance cost from 2010 to 2015
The cost of industrial governance in 2011 was relatively larger than that in 2010. However, after 2011, the cost of industrial governance began to decline. Compared with the cost of industrial pollution governance, the cost of living management was much higher. The trend is to increase, then decrease, then increase and then decrease. Overall, the cost of living treatment fluctuates between about 245 billion yuan. According to the overall data trend, we find that both the cost of industrial governance and the cost of living governance are decreasing year by year. The main reason for the decrease is that the negative impacts of land use decrease year by year, which also reflects the global increasing attention to the impact of human activities on ecosystem services.
3.5 Model Analysis Over Time
From the above data, we use the linear regression method to calculate the trend of the model with time. For the industrial governance cost, we set the year=x, the governance cost(10000yuan)=y, and then use the regression line equation to calculate The coefficients a~, b~
:
Calculate a~=8000000 b~=-214213The relationship between x and y can be obtained as follows: y=-214213x+8000000, that is, the governance cost decreases with time, so the following trend graph can be obtained:
Chart 3 industrial governance cost
For the cost of urban life governance, it can be seen from the above data that the governance cost changes periodically with time. It is preferable to consider the trend of moving average to predict the future cost of governance. Let be the forecast of governance cost for the next year. The number of periods in which n is moving average; is the pre-treatment cost, and represent the actual values of the first three periods of the previous two periods until the first n periods, then:
In summary, the trend graph of life governance costs over time can be obtained:
Chart 4 Life governance cost
As can be seen from the above figure, the cost of urban living governance changes periodically with time, but it is still decreasing.
4.Conclusions
Based on our analysis, we draw the following conclusions:
In the process of social construction, we must recognize the construction of economic society, the development of land use cannot be separated from the existence of ecosystem services and environmental sustainable development, but should be developed in parallel. Thus in the process of land development and utilization, we should pay attention to protecting the ecological environment and correctly assess the economic cost of land development projects.
In the analysis process, we found that the environmental degradation cost of large-scale industrial project construction is declining year by year, and the environmental degradation cost of small-scale project construction is not particularly large each year, we can reasonably extrapolate the results, the decline in environmental degradation costs for large industrial projects may be due to the increased efficiency of industrial waste treatment, as well as the application of clean energy, and more non-high environmentally hazardous industrial projects to replace
high environmentally hazardous industrial projects. The changing trend of environmental degradation costs for small-scale project construction also reminds us of the need to find new and more economical ways to deal with domestic pollution.
Based on the virtual governance cost analysis, we put forward the policy of open land use in the future: Improving the ecological environment, Promoting sustainable development, Ensuring the normal operation of ecological environment services. In the future land development and construction projects, we should pay more attention to the assessment of ecological services, so that the development and utilization rate of land tends to be highly rationalized.
4.1 Strengths
●The model simulates the annual virtual governance cost and makes the result
accurate and reliable.
●In selecting the samples, we selected China's annual data on pollution control.
China is a representative country. Therefore, the sample is representative and persuasive.
●In the measurement model, linear regression and moving average are used to
simplify the model and ensure the rationality of data. As a result, the entire model is relatively easy to implement.
●The model is used to simulate the data obtained, and the change trend is
represented by graph at last, so that the result is more clear.
4.2 Weakness
●The linear equation is used to simplify the model and make the result more
intuitive, but due to the unpredictability and diversity of some factors, the regression analysis is limited in some cases.
●Due to the limited space, we only considered the three main factors for
calculating the low cost of environmental degradation,which means that there are still some factors that will affect the correctness of the model we built.
●We only analyzed the data for six years, which means our results may still be
inaccurate.
●In addition, our model simulates the situation that unit governance cost remains
unchanged, without taking into account the fact that scientific progress reduces unit governance cost. In fact, this is unscientific.
4.3 Model Improvement
In the construction of the model, we assume that the unit governance cost remains unchanged, but with the progress of science and technology, the pollution governance technology will certainly increase and the governance cost will also
decrease, so if this important factor is not evaluated, it is not scientific to make the model in real life. In addition, our consideration of the model still requires a lot of data to simulate, and we do not use enough data in the validation process. We also need to further add factors that may affect model evaluation to the models we build to make them more practical.
5. References
[1]Ministry of Environmental Protection of the People's Republic of China. China Environmental Statistics Annual Report [R] China Environmental Press, 2011
[2]Ministry of Environmental Protection of the People's Republic of China. China Environmental Statistics Annual Report[R] China Environmental Press, 2012
[3]Ministry of Environmental Protection of the People's Republic of China. China Environmental Statistics Annual Report[R] China Environmental Press, 2013
[4]Ministry of Environmental Protection of the People's Republic of China. China Environmental Statistics Annual Report[R] China Environmental Press, 2014
[5]Ministry of Environmental Protection of the People's Republic of China. China Environmental Statistics Annual Report[R] China Environmental Press, 2015
[6]Ministry of Environmental Protection of the People's Republic of China. China Environmental Statistics Annual Report[R] China Environmental Press, 2016
[7]Fang Yu,《China Environmental Economic Accounting Technical Guide》，[M],2009
[8]Wupeng Du, Qingxian Gao, Enchen zhang, Qilong Miao, Jianguo Wu, The Emission Status and Composition Analysis of Municipal Solid Waste in China,[J],Research of Environmental Sciences,2006,(19)
[9]Feng Cai, Gangcai Chen, Feng Peng, Qingling Yang, Shibo Zhao, Sishu Xian, Fei Wu, Quantitative assessment of eco-environmental damage based on virtual diaposal cost approach,[J],Chinese Journal of Environmental Engineering,2015,(9)
[10]National Bureau of Statistics: https://www.doczj.com/doc/3b10330307.html,/
[11]Ministry of Housing and Urban-Rural Development of the People’s Republic of China (MOHURD):https://www.doczj.com/doc/3b10330307.html,/xytj/tjzljsxytjgb/jstjnj/index.html
问题A：除非超车否则靠右行驶的交通规则 在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。建立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的表现。你不妨考察一下流量和安全的权衡问题,车速过高过低的限制，或者这个问题陈述中可能出现的其他因素。这条规则在提升车流量的方面是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替代品（包括完全没有这种规律）并加以分析。在一些国家，汽车靠左形式是常态，探讨你的解决方案是否稍作修改即可适用，或者需要一些额外的需要。最后，以上规则依赖于人的判断，如果相同规则的交通运输完全在智能系统的控制下，无论是部分网络还是嵌入使用的车辆的设计，在何种程度上会修改你前面的结果？ 问题B：大学传奇教练 体育画报是一个为运动爱好者服务的杂志，正在寻找在整个上个世纪的“史上最好的大学教练”。建立数学模型选择大学中在一下体育项目中最好的教练：曲棍球或场地曲棍球，足球，棒球或垒球，篮球，足球。 时间轴在你的分析中是否会有影响？比如1913年的教练和2013年的教练是否会有所不同？清晰的对你的指标进行评估，讨论一下你的模型应用在跨越性别和所有可能对的体育项目中的效果。展示你的模型中的在三种不同体育项目中的前五名教练。 除了传统的MCM格式，准备一个1到2页的文章给体育画报，解释你的结果和包括一个体育迷都明白的数学模型的非技术性解释。 使用网络测量的影响和冲击 学术研究的技术来确定影响之一是构建和引文或合著网络的度量属性。与人合写一手稿通常意味着一个强大的影响力的研究人员之间的联系。最著名的学术合作者是20世纪的数学家保罗鄂尔多斯曾超过500的合作者和超过1400个技术研究论文发表。讽刺的是,或者不是,鄂尔多斯也是影响者在构建网络的新兴交叉学科的基础科学,尤其是，尽管他与Alfred Rényi的出版物“随即图标”在1959年。鄂尔多斯作为合作者的角色非常重要领域的数学,数学家通常衡量他们亲近鄂尔多斯通过分析鄂尔多斯的令人惊讶的是大型和健壮的合著网络网站(见http:// https://www.doczj.com/doc/3b10330307.html,/enp/)。保罗的与众不同、引人入胜的故事鄂尔多斯作为一个天才的数学家,才华横溢的problemsolver,掌握合作者提供了许多书籍和在线网站(如。,https://www.doczj.com/doc/3b10330307.html,/Biographies/Erdos.html)。也许他流动的生活方式,经常住在带着合作者或居住,并给他的钱来解决问题学生奖,使他co-authorships蓬勃发展并帮助构建了惊人的网络在几个数学领域的影响力。为了衡量这种影响asErdos生产,有基于网络的评价工具,使用作者和引文数据来确定影响因素的研究,出版物和期刊。一些科学引文索引,Hfactor、影响因素,特征因子等。谷歌学术搜索也是一个好的数据工具用于网络数据收集和分析影响或影响。ICM 2014你的团队的目标是分析研究网络和其他地区的影响力和影响社会。你这样做的任务包括: 1)构建networkof Erdos1作者合著者(你可以使用我们网站https://files.oak https://www.doczj.com/doc/3b10330307.html,/users/grossman/enp/Erdos1.htmlor的文件包括Erdos1.htm)。你应该建立一个合作者网络Erdos1大约有510名研究人员的文件,与鄂尔多斯的一篇论文的合著者,他但不包括鄂尔多斯。这将需要一些技术数据提取和建模工作获
For office use only T1________________ T2________________ T3________________ T4________________ Team Control Number 55069 Problem Chosen A For office use only F1________________ F2________________ F3________________ F4________________ 2017 MCM/ICM Summary Sheet The Rehabilitation of the Kariba Dam Recently, the Institute of Risk Management of South Africa has just warned that the Kariba dam is in desperate need of rehabilitation, otherwise the whole dam would collapse, putting 3.5 million people at risk. Aimed to look for the best strategy with the three options listed to maintain the dam, we employ AHP model to filter factors and determine two most influential criteria, including potential costs and benefits. With the weight of each criterion worked out, our model demonstrates that option 3is the optimal choice. According to our choice, we are required to offer the recommendation as to the number and placement of the new dams. Regarding it as a set covering problem, we develop a multi-objective optimization model to minimize the number of smaller dams while improving the water resources management capacity. Applying TOPSIS evaluation method to get the demand of the electricity and water, we solve this problem with genetic algorithm and get an approximate optimal solution with 12 smaller dams and determine the location of them. Taking the strategy for modulating the water flow into account, we construct a joint operation of dam system to simulate the relationship among the smaller dams with genetic algorithm approach. We define four kinds of year based on the Kariba’s climate data of climate, namely, normal flow year, low flow year, high flow year and differential year. Finally, these statistics could help us simulate the water flow of each month in one year, then we obtain the water resources planning and modulating strategy. The sensitivity analysis of our model has pointed out that small alteration in our constraints (including removing an important city of the countries and changing the measurement of the economic development index etc.) affects the location of some of our dams slightly while the number of dams remains the same. Also we find that the output coefficient is not an important factor for joint operation of the dam system, for the reason that the discharge index and the capacity index would not change a lot with the output coefficient changing.
Camping along the Big Long River Summary In this paper, the problem that allows more parties entering recreation system is investigated. In order to let park managers have better arrangements on camping for parties, the problem is divided into four sections to consider. The first section is the description of the process for single-party's rafting. That is, formulating a Status Transfer Equation of a party based on the state of the arriving time at any campsite. Furthermore, we analyze the encounter situations between two parties. Next we build up a simulation model according to the analysis above. Setting that there are recreation sites though the river, count the encounter times when a new party enters this recreation system, and judge whether there exists campsites available for them to station. If the times of encounter between parties are small and the campsite is available, the managers give them a good schedule and permit their rafting, or else, putting off the small interval time t until the party satisfies the conditions. Then solve the problem by the method of computer simulation. We imitate the whole process of rafting for every party, and obtain different numbers of parties, every party's schedule arrangement, travelling time, numbers of every campsite's usage, ratio of these two kinds of rafting boats, and time intervals between two parties' starting time under various numbers of campsites after several times of simulation. Hence, explore the changing law between the numbers of parties (X) and the numbers of campsites (Y) that X ascends rapidly in the first period followed by Y's increasing and the curve tends to be steady and finally looks like a S curve. In the end of our paper, we make sensitive analysis by changing parameters of simulation and evaluate the strengths and weaknesses of our model, and write a memo to river managers on the arrangements of rafting. Key words: Camping；Computer Simulation; Status Transfer Equation
２01４高教社杯全国大学生数学建模竞赛 承诺书 我们仔细阅读了《全国大学生数学建模竞赛章程》和《全国大学生数学建模竞赛参赛规则》(以下简称为“竞赛章程和参赛规则”，可从全国大学生数学建模竞赛网站下载)。 我们完全明白,在竞赛开始后参赛队员不能以任何方式(包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师)研究、讨论与赛题有关的问题。 我们知道，抄袭别人的成果是违反竞赛章程和参赛规则的，如果引用别人的成果或其他公开的资料(包括网上查到的资料),必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。 我们郑重承诺，严格遵守竞赛章程和参赛规则，以保证竞赛的公正、公平性。如有违反竞赛章程和参赛规则的行为,我们将受到严肃处理。 我们授权全国大学生数学建模竞赛组委会，可将我们的论文以任何形式进行公开展示(包括进行网上公示，在书籍、期刊和其他媒体进行正式或非正式发表等)。 我们参赛选择的题号是(从Ａ/B/C/Ｄ中选择一项填写)：B 我们的报名参赛队号为（8位数字组成的编号）: 所属学校（请填写完整的全名)： 参赛队员(打印并签名) :1. 2． 3．
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The Keep-Right-Except-To-Pass Rule Summary As for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic. As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left. As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow . Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall. Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic control
电力市场输电阻塞管理模型 摘要 本文通过设计合理的阻塞费用计算规则，建立了电力市场的输电阻塞管理模型。 通过对各机组出力方案实验数据的分析，用最小二乘法进行拟合，得到了各线路上有功潮流关于各发电机组出力的近似表达式。按照电力市场规则，确定各机组的出力分配预案。如果执行该预案会发生输电阻塞，则调整方案，并对引起的部分序内容量和序外容量的收益损失，设计了阻塞费用计算规则。 通过引入危险因子来反映输电线路的安全性，根据安全且经济的原则，把输电阻塞管理问题归结为：以求解阻塞费用和危险因子最小值为目标的双目标规划问题。采用“两步走”的策略，把双目标规划转化为两次单目标规划：首先以危险因子为目标函数，得到其最小值；然后以其最小值为约束，找出使阻塞管理费用最小的机组出力分配方案。 当预报负荷为982.4MW时，分配预案的清算价为303元/MWh，购电成本为74416.8元，此时发生输电阻塞，经过调整后可以消除，阻塞费用为3264元。 当预报负荷为1052.8MW时，分配预案的清算价为356元/MWh，购电成本为93699.2元，此时发生输电阻塞，经过调整后可以使用线路的安全裕度输电，阻塞费用为1437.5元。 最后，本文分析了各线路的潮流限值调整对最大负荷的影响，据此给电网公司提出了建议；并提出了模型的改进方案。
一、问题的重述 我国电力系统的市场化改革正在积极、稳步地进行，随着用电紧张的缓解，电力市场化将进入新一轮的发展，这给有关产业和研究部门带来了可预期的机遇和挑战。 电网公司在组织电力的交易、调度和配送时，必须遵循电网“安全第一”的原则，同时按照购电费用最小的经济目标，制订如下电力市场交易规则： 1、以15分钟为一个时段组织交易，每台机组在当前时段开始时刻前给出下一个时段的报价。各机组将可用出力由低到高分成至多10段报价，每个段的长度称为段容量，每个段容量报一个段价，段价按段序数单调不减。 2、在当前时段内，市场交易-调度中心根据下一个时段的负荷预报、每台机组的报价、当前出力和出力改变速率，按段价从低到高选取各机组的段容量或其部分，直到它们之和等于预报的负荷，这时每个机组被选入的段容量或其部分之和形成该时段该机组的出力分配预案。最后一个被选入的段价称为该时段的清算价，该时段全部机组的所有出力均按清算价结算。 电网上的每条线路上有功潮流的绝对值有一安全限值，限值还具有一定的相对安全裕度。如果各机组出力分配方案使某条线路上的有功潮流的绝对值超出限值，称为输电阻塞。当发生输电阻塞时，需要按照以下原则进行调整： 1、调整各机组出力分配方案使得输电阻塞消除； 2、如果1做不到，可以使用线路的安全裕度输电，以避免拉闸限电，但要使每条 线路上潮流的绝对值超过限值的百分比尽量小； 3、如果无论怎样分配机组出力都无法使每条线路上的潮流绝对值超过限值的百分 比小于相对安全裕度，则必须在用电侧拉闸限电。 调整分配预案后，一些通过竞价取得发电权的发电容量不能出力；而一些在竞价中未取得发电权的发电容量要在低于对应报价的清算价上出力。因此，发电商和网方将产生经济利益冲突。网方应该为因输电阻塞而不能执行初始交易结果付出代价，网方在结算时应该适当地给发电商以经济补偿，由此引起的费用称之为阻塞费用。网方在电网安全运行的保证下应当同时考虑尽量减少阻塞费用。 现在需要完成的工作如下： 1、某电网有8台发电机组，6条主要线路，附件1中表1和表2的方案0给出了各机组的当前出力和各线路上对应的有功潮流值，方案1~32给出了围绕方案0的一些实验数据，试用这些数据确定各线路上有功潮流关于各发电机组出力的近似表达式。 2、设计一种简明、合理的阻塞费用计算规则，除考虑电力市场规则外，还需注意：在输电阻塞发生时公平地对待序内容量不能出力的部分和报价高于清算价的序外容量出力的部分。 3、假设下一个时段预报的负荷需求是982.4MW，附件1中的表3、表4和表5分别给出了各机组的段容量、段价和爬坡速率的数据，试按照电力市场规则给出下一个时段各机组的出力分配预案。 4、按照表6给出的潮流限值，检查得到的出力分配预案是否会引起输电阻塞，并在发生输电阻塞时，根据安全且经济的原则，调整各机组出力分配方案，并给出与该方案相应的阻塞费用。 5、假设下一个时段预报的负荷需求是1052.8MW，重复3~4的工作。 二、问题的分析
Team Control Number For office use only 13215 For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ Problem Chosen F3 ________________ T4 ________________ F4 ________________ C 2012 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to each copy of your solution paper.) Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page. Message Network Modeling for Crime Busting Abstract A particularly popular and challenging problem in crime analysis is to identify the conspirators through analysis of message networks. In this paper, using the data of message traffic, we model to prioritize the likelihood of one’s being conspirator, and nominate the probable conspiracy leaders. We note a fact that any conspirator has at least one message communication with other conspirators, and assume that sending or receiving a message has the same effect, and then develop Model 1, 2 and 3 to make a priority list respectively and Model 4 to nominate the conspiracy leader. In Model 1, we take the amount of one’s suspicious messages and one’s all messages with known conspirators into account, and define a simple composite index to measure the likelihood of one’s being conspirator. Then, considering probability relevance of all nodes, we develop Model 2 based on Law of Total Probability . In this model, probability of one’s being conspirator is the weight sum of probabilities of others directly linking to it. And we develop Algorithm 1 to calculate probabilities of all the network nodes as direct calculation is infeasible. Besides, in order to better quantify one’s relationship to the known conspirators, we develop Model 3, which brings in the concept “shortest path” of graph theory to create an indicator evaluating the likelihood of one’s being conspirator which can be calculated through Algorithm 2. As a result, we compare three priority lists and conclude that the overall rankings are similar but quite changes appear in some nodes. Additionally, when altering the given information, we find that the priority list just changes slightly except for a few nodes, so that we validate the models’ stability. Afterwards, by using Freeman’s centrality method, we develop Model 4 to nominate three most probable leaders: Paul, Elsie, Dolores (senior manager). What’s more, we make some remarks about the models and discuss what could be done to enhance them in the future work. In addition, we further explain Investigation EZ through text and semantic network analysis, so to illustrate the models’ capacity of applying to more complicated cases. Finally, we briefly state the application of our models in other disciplines.
关于中国人口增长趋势的研究 【摘要】 本文从中国的实际情况和人口增长的特点出发，针对中国未来人口的老龄化、出生人口性别比以及乡村人口城镇化等，提出了Logistic、灰色预测、动态模拟等方法进行建模预测。 首先，本文建立了Logistic阻滞增长模型，在最简单的假设下，依照中国人口的历史数据，运用线形最小二乘法对其进行拟合，对2007至2020年的人口数目进行了预测，得出在2015年时，中国人口有13.59亿。在此模型中，由于并没有考虑人口的年龄、出生人数男女比例等因素，只是粗略的进行了预测，所以只对中短期人口做了预测，理论上很好，实用性不强，有一定的局限性。 然后，为了减少人口的出生和死亡这些随机事件对预测的影响，本文建立了GM(1,1) 灰色预测模型，对2007至2050年的人口数目进行了预测，同时还用1990至2005年的人口数据对模型进行了误差检验，结果表明，此模型的精度较高，适合中长期的预测，得出2030年时，中国人口有14.135亿。与阻滞增长模型相同，本模型也没有考虑年龄一类的因素，只是做出了人口总数的预测，没有进一步深入。 为了对人口结构、男女比例、人口老龄化等作深入研究，本文利用动态模拟的方法建立模型三，并对数据作了如下处理：取平均消除异常值、对死亡率拟合、求出2001年市镇乡男女各年龄人口数目、城镇化水平拟合。在此基础上，预测出人口的峰值，适婚年龄的男女数量的差值，人口老龄化程度，城镇化水平，人口抚养比以及我国“人口红利”时期。在模型求解的过程中，还对政府部门提出了一些有针对性的建议。此模型可以对未来人口做出细致的预测，但是需要处理的数据量较大，并且对初始数据的准确性要求较高。接着，我们对对模型三进行了改进，考虑人为因素的作用，加入控制因子，使得所预测的结果更具有实际意义。 在灵敏度分析中，首先针对死亡率发展因子θ进行了灵敏度分析，发现人口数量对于θ的灵敏度并不高，然后对男女出生比例进行灵敏度分析得出其灵敏度系数为0.8850，最后对妇女生育率进行了灵敏度分析，发现在生育率在由低到高的变化过程中，其灵敏度在不断增大。 最后，本文对模型进行了评价，特别指出了各个模型的优缺点，同时也对模型进行了合理性分析，针对我国的人口情况给政府提出了建议。 关键字：Logistic模型灰色预测动态模拟 Compertz函数
2019 MCM/ICM Summary Sheet (Your team's summary should be included as the first page of your electronic submission.) Type a summary of your results on this page. Do not include the name of your school, advisor , or team members on this page. Ecosystems provide many natural processes to maintain a healthy and sustainable environment after human life. However, over the past decades, rapid industrial development and other anthropogenic activities have been limiting or removing ecosystem services. It is necessary to access the impact of human activities on biodiversity and environmental degradation. The main purpose of this work is to understand the true economic costs of land use projects when ecosystem services are considered. To this end, we propose an ecological service assessment model to perform a cost benefit analysis of land use development projects of varying sites, from small-scale community projects to large national projects. We mainly focus on the treatment cost of environmental pollution in land use from three aspects: air pollution, solid waste and water pollution. We collect pollution data nationwide from 2010 to 2015 to estimate economic costs. We visually analyze the change in economic costs over time via some charts. We also analyze how the economic cost changes with time by using linear regression method. We divide the data into small community projects data (living pollution data) and large natural data (industrial pollution data). Our results indicate that the economic costs of restoring economical services for different scales of land use are different. For small-scale land, according to our analysis, the treatment cost of living pollution is about 30 million every year in China. With the rapid development of technology, the cost is lower than past years. For large-scale land, according to our analysis, the treatment cost of industrial pollution is about 8 million, which is lower than cost of living pollution. Meanwhile the cost is trending down due to technology development. The theory developed here provides a sound foundation for effective decision making policies on land use projects. Key words: economic cost , ecosystem service, ecological service assesment model, pollution. Team Control Number For office use only For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ Problem Chosen F3 ________________ T4 ________________ F4 ________________ E
点评：航空货运问题 一、基本参数 1、货机：假设均匀分布 每天三架货机。 2、工作时间5：00—20：00设置为 t ：[0，15]？ 每天货机到达时间：5：00—20：00； 一工作组装满装卸场：6小时；一货机装满：3小时； 装卸台的容量：1.5货机； 3、费用系数： 停机费（等待装货）：15000元/小时架 一工作组：每小时9000元；二工作组：每小时12000元 4、服务原则：假设先来先服务 二、模型建立：概率计算模型 （一）概率分布 1、三架货机到达的时刻3,2,1,=i t i 服从[0，15]上的均匀分布，则： 密度函数：()1 ,01515 f t t = ≤≤ 分布函数：(),01515 t F t t = ≤≤ 2、设τ,δ,ε分别是首架货机到达时刻、第一架与第二架间隔、第二架与第三架间隔，
（1）τ的分布函数 3 31321321321321321))(1(1))(1(1)()()(1),,(1) ()()},,(min{) ()(1t F t t P t t P t t P t t P t t t t t t P t t t t t t P t t t t t t P t t t t P t P t F t --=≤--=>>>-=>>>-=≤?≤?≤-Ω=≤?≤?≤=≤=≤=ττ τ 的密度函数： ()()()1125 15151)151(3]1[3)(')(2 22 11-=-=-==t t t f t F t F t f t t ττ ]15,0[∈t （2）其余两货机到达与第一个到达的货机的间隔21,t t ??在0到15-τ之间是均匀分布的 于是： τ -=?151)(t f i t , τ-≤≤150t ；τ-=?15)(t t F i t , τ-≤≤150t ，i =1,2 δ 的密度函数 /121212()()()1() 1()() F t P t P t t t t P t t t t P t t P t t δτδ=≤=?≤?≤=-?>?>=-?>?> 221)](1[1)](1[11t F t t P t ?--=≤?--= ()()2//15152)()](1[2)(')(11---= -==??τττδτδt t f t F t F t f t t （3）第三架货机到达与第二个到达的货机的间隔ε在0和15-δ-τ之间是均匀分布的， 于是： ε 的密度函数
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