2015美赛特等奖原版论文集38996

For office use only T1 _ T2 _ T3 _ T4 _ Team Control Number 38996 Problem Chosen D For office use only F1 _ F2 _ F3 _ F4 _ 2015 Mathematical Contest in Modeling (MCM/ICM) Summary Sheet Sustainable Development Evaluation System Summary Sustainable development has attracted plenty of attention from all over the word for recent decades. While the definition of sustainable development is very comprehensive. To evaluate sustainability of a country, devise an evaluation model for sustainable development. Based on our analysis of sustainable development, we depart the meaning of sustainable development into two dimension: social-economic development and environment- resource development. We design the index system by expanding ecological footprint into our model, and then we invoke entropy evaluation method and the subject-object weighting method based on CRITIC to derive the calculation process of two overall indices. By scaling the indices in coordinate system and calculate the direction by regression analysis, we devise the harmonious development (included angle between actual development direction and ideal development direction) and valid development (projection of actual development on standard development pattern) of a country to evaluate the sustainability thought two aspects. Their product, a hyperbolic sustainable distance, is the final result of our model, which represent the hyperbolic distance between the current development and goal development point. We show an implementation of our model that takes America, China, France, Nepal and South Africa as example. It turns out that America, France (the Best one) and South Africa are all sustainable, while the others are not. We also compare our model with other possible approaches, which turns out that our model is more appropriate for sustainable development. We choose Nepal in our further investigation, where we invoke ARIMA model to forecast without intervention and system dynamics to forecast with intervention. Because of the limited data resources, we estimate the parameters of structure equations in each subsystem by Three-Stage Least Squares method, then we list the exact formulas of dynamic equations. After exploring the current development situation and geological characteristics of Nepal, we utilize sensitivity analysis and our forecast results to propose a sustainable development plan for Nepal, among which modernization program performs best according to our system- dynamics simulation results. Finally, we discuss the strengths and weaknesses of our model. Team # 38996 Page 1 of 20 Contents 1. Introduction . 2 1.1. Background . 2 1.2. Our Work . 2 2. Assumption . 3 3. Sustainability of a Country and Policy . 4 3.1. Analysis of Sustainable Development . 4 3.2. Ecological Footprint . 5 3.2.1. Calculation . 5 3.2.2. Discussion on EF Model . 5 3.3. The Model . 6 3.3.1. Index System . 6 3.3.2. Sustainability Measurement . 8 3.3.3. An Implementation of Our model . 10 3.3.4. Further Discussion . 12 4. Sustainability Development Plan . 13 4.1. Current Situation and Forecast without intervention. 13 4.2. Details of the Plan . 14 4.2.1. Effectiveness Judgment by Sensitivity Analysis . 14 4.2.2. Reasonability Judgment by Actual Conditions . 15 4.2.3. Ultimate Plan for Sustainable development . 15 5. Dynamic Improvement . 16 5.1. System Dynamics and Structure Equations . 16 5.2. Simulation Run and Results . 18 5.3. Conclusion. 19 6. Analysis of the Model . 19 6.1. Strengths . 19 6.2. Weaknesses . 20 References . 20 Team # 38996 Page 2 of 20 1. Introduction 1.1. Background Broadly speaking, Defined by the 1987 Brundtland Report Our Common World 1, sustainable development meets the needs of the present without compromising the ability of future generations to meet their own needs. Sustainable development can we developed into various aspect such as nature, society, ecology, policy and so on. To be specific, sustainable development is to balance the development of nature, society, ecology, population and economy. In terms of the profound definition of sustainable development, scientist have already come up with some essential principal of sustainable develop, and they are principal of equality, principal of sustainability and principal of commonality. The principal of equality refers to the fair and equitable resources between generations, intergenerational equity allocation and utilization. While the principal of sustainability indicates that economic and social development of mankind cannot exceed the carrying capacity of resources and the environment. And the principal of commonality represents that although national sustainable development patterns are different, the principles of equality and sustainability are common. Unfortunately, many developing countries are suffering from the unsustainable development as they lack sufficient international aids and technological path pattern to cope with the intense contradiction between the pressing needs of contemporary citizens and the responsibility of protecting the environment. Meanwhile, numerous international organizations do not equip with scientific enough methods to evaluate the sustainability of each country. Nor can they efficiently figure out which country is most worth providing aids to. The International Conglomerate of Money (ICM) wants to use their extensive financial resources and influence to create a more sustainable world. They are particularly interested in developing countries, where they believe they can see the greatest results of their investments. 1.2. Our Work We devise a mathematical model to measure the sustainability of given countries and policy after analyzing the concept of sustainable development. To be specific, we invoke the emergy based ecological footprint in our model after finding its drawbacks while measuring the sustainability of a country. Then we design a new evaluation system to perfect the objects that have been taken into consider. We also show our model results in a coordinate system so that they can be understood by any people who are interested in the issue but do not equip with much background knowledge. The model can tell when and how a country is sustainable or unsustainable explicitly. We also have some further discussion on approaches to sharpen our model. Team # 38996 Page 3 of 20 Having devised a model for sustainability, we investigate Nepal from 48 LDC list. We first explore the current situation of Nepal by means of non-interference prediction with ARIMA model. Base on the results we derived from the analysis, we propose a 20-year sustainable development plan for Nepal, and the plan includes programs, policies, and a direction that indicates what ICM should do according to a specific state within Nepal. We eventually devise a dynamic version of our model for the purpose to forecast the effect of each program and policy. The improved model comes back to the previous one if no programs or policies are carried out. We run the simulation each program and policy and draw the conclusion about which suggestions we had given are the highly effective strategies to be implemented by ICM. Finally, we test the sensitivity of our model and discuss the strengths and weakness of our model. 2. Assumption The consumption of resources and production of waste are determined and can be measured by statistic method. As the consumption of resources and production of waste includes countless details which is hard to measure accurately, and the main purpose of our model is to measure the sustainability of a country or policy instead of measuring the explicit statistic data. The country measured is relatively stable. That is to say, extremely dramatic change does not happen in the chosen country while we are measuring its sustainability. For example, devastating natural disasters and devastating war which might possibly exterminate the country will not be taken into consideration. The economic state, demographics, resource consumption data and environment data of each the chosen country is available. The complicated situations in all developing country make it impracticable to investigate one by one, so we mainly focus on using these data to estimate whether a country is sustainably developing. The statistical data is valid. We suppose that the true value of every index locates right nearby the statistic data. Consequently, we assume that the data is believable. The operating property and mechanism of a country is relatively independent from others. We hypothesize that every country all over the world respects the state sovereignty each other. In another word, the institutional structure and the operating mechanism within each country depends on the country itself only and will not be interfered by others. It is because every country has its sovereignty to determine which economic structure or political system to implement. And the inner political and economic structure will, to a great extent, determines various economic operating property and mechanism. Team # 38996 Page 4 of 20 3. Sustainability of a Country and Policy 3.1. Analysis of Sustainable Development Sustainable development should takes care of two basic concepts: the contemporary peoples need and their descendants ability to meet their needs. To meet the requirement, we should economize natural resource, protect the environment and develop our society and economic at the same time. What is more important is to keep these aspects in a relatively balanced relation and position. Only if we succeed in balance them all, can we satisfy contemporary needs without depriving our offspring of their ability to meet their needs in the future, and make sure of the development of our posterity without sacrificing contemporary social and economic development. In a word, three dimensions of human development (economic, society, and environment) should develop in a balance state. Recall the fishing model which derives an ideal point of fishing amount. At this point, the fish will keep reproducing at a highest rate so that the entire fishing industry can keep doing so for a long time. We can actually regard this point as a situation that meets a sustainable development. It is because both contemporary peoples needs and the interest of their posterity are satisfied as much as possible. That is to say, with the highest reproduction of fish, people can get most amount of fish from fishing, and the entire ecosystem is protect from ecological degradation. In another word, the fish ecosystem and fishing economic (which fosters and flourishes social development) keeps a balance relationship. We can also say the three dimensions meet an equilibrium state at this good point. It is, however, very hard to find this balanced point in reality. We can merely describe this situation in a fuzzy word. Therefore, we must clarify some main factors that typically contribute to these three dimensions. To start with, we explore social development of a country. It is clear that the population (including gross, density, and rate of change), public service (including medical treatment and public health, telecom service, transport service, etc.), and culture (including education, science, and technology) all contribute to level of social development. The higher level of the public service and culture, the better social development, while the population is a crucial control variate that provides the average level of these two components above. We also seek principal factors that represent the development of social economy, which is the foundation of social development. We invoke some basic results of economics, and we figure the principal elements as follow: Gross Domestic Product, added value of agriculture, industry (including heavy industry, manufacture, service, and investment), laboring population, technology and so on. The more prosperous these elements are, the better a countrys economy is. Last but not least, we will discuss some variates that can well indicate the level of environment and natural resources consumption in Section 3.2 in detail. Team # 38996 Page 5 of 20 Now we are discussing the relation between these aspects of a countrys development and sustainability. In terms of two meanings of sustainable development, we divide these aspects into two parts respectively. What calls for special attention is that the division is not absolutely clear, and we devise the division only for explanation purpose. For contemporary people, the essential needs are to promote the culture and boom the production as much and fast as possible, which can be explained by social and economy development. As for posterity, the amount of remained natural resources and the friendliness of environment at that time would definitely determine their ability to meet their needs. 3.2. Ecological Footprint Ecological footprint (EF) is originally proposed by Rees (1992) and improved by Wackernagel 2 to measure the sustainability. According to the thought of ecological footprint, every individual or group of units can consume natural resources and produce waste back into ecology system. The natural resources consumption and produced waste can be converse into biologically productive area. Subtracting appropriated carrying capacity, the positive result indicates sustainable development while the negative one means the development is unsustainable and the ecology is in a deficit state (ecological deficit). 3.2.1. Calculation The computational formula of ecological footprint is = = = ,( = 1,2,) where is ecological footprint; is per capita ecological footprint; is consumption item; is per capita biologically productive areas output for item per annum; is the conversed per capita biological productive areas output for item per annum; is the production amount of item per annum; is the import volume of item ; is the export volume of item ; is population; and is balance factor. The computational formula of appropriated carrying capacity is = = ,( = 1,2,) where is total appropriated carrying capacity; is per capita EC; is per capita biologically productive area; is equivalence factor; is productive factor. Let = , then EF model evaluates the sustainability by value of . If 0, then the country is sustainable, otherwise unsustainable. 3.2.2. Discussion on EF Model The balance factor lacks enough explanation From the computational formula, we find that the balancing factor represents ratio of the productivity of a certain biologically productive area to overall average productivity Team # 38996 Page 6 of 20 biologically productive area. That means different type of land with similar balance factor can replace each other. Whats more, the balance factors are constant which is obviously irrational. The calculation of EF may be extremely hard and may lead to huge error For example, EF model converts the consumption of fossil fuel into the area that can absorb the CO2 produced by burning them. However, the waste gas produced while burning the fossil fuel is not merely limited to carbon dioxide, and SO2 is another important pollutant that cannot be neglected. In order to make the computational process more accurate, we can invoke the thought of emergy analysis. Emergy analysis t