Team # 52766
Team Control Number
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52766
Problem Chosen
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E
2016MCM/ICM
Summary Sheet
In order to predict the water scarcity and optimize the configuration reasonably, we analyze the situation of water scarcity by establishing a mathematical model, and propose the feasible suggestions on optimization. All the work is based on the sufficient data we collect.
Firstly, the local situation of water scarcity is estimated by introducing the water lacking rate index. Secondly, the local water consumption is predicted from personal living, industry, agriculture and ecology. Meanwhile, the local water consumption is predicted through establishing a compound model which based on an improved Logistic Model and the statistical regression analysis. Thirdly, the Gray Prediction Metabolism Model is used for predicting the amount of local water supply. At last, we comprehensively analyze the experimental results, and predict the ability of water supply in this local area.
To verify the availability of the model, we choose the North China as the object of study. We conclude that this area is seriously scarce before 2010 on the basis of mass data. The water scarcity will steadily remit and reach balance in 2025. This is due to China has finished the South-to-North Water Diversion and the North China gains large water resources from outside. The results call inside with the truth, so the model is reliable.
Then we try to optimize the water supplying and demanding structure in the North China, so that it can realize the internal self-sufficiency. We use analytic
hierarchy process (AHP) to assess the four schemes of water storage, water transfer, wastewater treatment and desalination from four aspects of timeliness, sustainability, economic, environmental benefits, so a more scientific water supplying system is developed. Finally, by means of adjusting the industrial structure, optimizing the mode of agricultural irrigation and improving the water conservation awareness of citizens, we propose a water resources allocation model to optimize the water supply system in the North China. In this way, the water scarcity in the North China can be solved five years ahead of the original schedule.
Key words
Water scarcity; water lacking rate index;improved Logistic Model;Gray Prediction Metabolism Model; statistical regression; analytic hierarchy process (AHP)
Team # 52766
Contents
1 INTRODUCTION & BACKGROUNDS ..................................................................................................... 1 2 PROBLEM ANALYSIS ........................................................................................................................... 1 2.1 Problem Restatement .................................................................................................................. 1 2.2 Problem solving.......................................................................................................................... 2 3 ASSUMPTIONS .................................................................................................................................... 2 4 NOTATIONS ......................................................................................................................................... 3 5 BASIC MODEL ..................................................................................................................................... 3 5.1 Model of the water consumption ................................................................................................ 3
5.1.1 Compound population Model based on Logistic Model ..................................................................... 4 5.1.2 Model of Industrial water consumption............................................................................................... 5 5.1.3 Model of total water consumption of a region..................................................................................... 6
5.2 Model of the Gray Metabolism Model GM (1, 1) ....................................................................... 6
5.2.1 Principle of common Gray GM (1, 1) Model ...................................................................................... 6 5.2.2 Principle of Gray Metabolism Model GM (1, 1)[2] .............................................................................. 8 5.2.3 Accuracy testing .................................................................................................................................. 8
5.3 Model of water supply capacity of a region ............................................................................... 9 5.4 Strengths & Weakness .............................................................................................................. 10 6 CHOOSE A REGION TO ANALYZE ........................................................................................................ 10 6.1 Brief introduction ..................................................................................................................... 10 6.2 Physical scarcity: ..................................................................................................................... 11 6.3 Economical scarcity: ................................................................................................................ 12 7 PREDICTION MODEL FOR THE NORTH CHINA .................................................................................... 12 7.1 Model of water consumption in North China. .......................................................................... 12 7.2 Water supply model in the North China ................................................................................... 17 7.3 The comprehensive evaluation to the future water resources in the North China .................... 18 7.4 Strengths and Weaknesses ........................................................................................................ 21 8 OPTIMIZATION OF WATER RESOURCES ALLOCATION ......................................................................... 21 8.1 Optimization of water supply allocation .................................................................................. 21
8.1.1 Construct the model of hierarchical structure .................................................................................... 21 8.1.2 Construction of comparison matrix of target-criterion layer. ............................................................ 22 8.1.3 Construction of comparison matrix criterion - target layer................................................................ 23 8.1.4 Total sorts of hierarchy and consistency check ................................................................................. 27 8.1.5 Interpretation of result ....................................................................................................................... 28
8.2Optimization of water consumption allocation ......................................................................... 29
8.2.1 Construction of water resources allocation model ............................................................................. 30 8.2.2 Main constraint equations ................................................................................................................. 30 8.2.3 Model Solution .................................................................................................................................. 32
CONCLUSIONS ..................................................................................................................................... 34 FURTHER DISCUSSIONS ........................................................................................................................ 34 REFERENCE ......................................................................................................................................... 34 APPENDIX ........................................................................................................................................... 35
Team # 52766
StrategyofConquering Thirst
Team #52766 Page 1of 42
1 Introduction & Backgrounds
An effective plan of solving the water scarcity problem is crucial to human society. According to the United Nations, today more than one billion people lack access to safe, clean drinking water, and just 10 countries share 60 percent of the world’s natural, renewable water resources; what’s more, water use has been growing at twice the rate of population over the last century. A model of water scarcity of the world shows the serious situation. (See Figure 1)
Figure 1: the map of the world’s water scarcity
At the same time, our societal and economic growth is largely driven by the productive use of water. Actually, the world tripled its water use in the last 50 years alone. Our world population is increasing, yet we still share one water resource – and it’s limited. If we’re going to meet the agricultural, industrial and residential needs of this growing world, we must use our water in effective, efficient ways.
2 Problem Analysis
2.1 Problem Restatement
Develop a model that provides a measure of the ability that a region cab provide clean water to meet the needs of its population. Doing all this work with considering the dynamic nature of the factors that affect both supply and demand.
Pick one country or region where water is either heavily or moderately overloaded. Explain why and how water is scarce in that region.
Show what the water situation will be in 15 years, and predict how this situation impact the lives of citizens of this region. Design an intervention plan taking all the drivers of water scarcity into account according to the situation, to help with the water scarcity and optimizing the model.
Estimate the optimized model and predict the results.
Team #52766 Page 2of 42
2.2Problem solving
We address the problem of optimizing water use of a region through analyzing the water situation, which provides a measure of the ability of a region to provide clean water to meet the needs of its population. The model consists of two big modules: water supply and water consumption. Water supply module is mainly composed of surface water and groundwater, the degree of environmental governance, storage capacity, precipitation, etc. Water module is mainly composed of personal living water, agricultural water, industrial water and ecological water use, etc.Finally we compare the model of water supply with the model of water consumption, then take a certain evaluation index to measure the region's water supply capacity.
Next, since the region of North China (include Beijing, Tianjin, Hebei, Shanxi, Inner Mongolia) meets the requirement of being heavily or moderately overloaded on using water, we choose the North China as the researching region. We explain the social and environmental reasons of the scarcity from physical and economical sides, to dissect what facts impact the water scarcity.
Then we make quantitative and qualitative analysis of the water supply and consumption in this region, to get what the characteristics of the situation in 15 years.
At last, according to the fourth and fifth question, we optimize the model from improving water supply and reducing water consumption, to solve the problem of water shortage. We consider about improving the water supply by the construction of reservoirs, water diversion works, water desalination, wastewater treatment, and political, economic and social considerations. On the other side, we reduce the water consumption from raising awareness about saving water and improving agricultural irrigation methods, adjusting the structure of industrial water, improving ecological aspects to consider autonomy ability. Then under the optimization of water supply and water consumption we set up a water allocation optimization model, which is used for exploitation and utilization planning of water resources, meanwhile predict the situation of water resources using in the future.
3 Assumptions
☆Ignore the impacts of the extreme disasters.
☆Ignore the impacts of the migration of population.
☆Ignore the administration cost in late period of water diversion project
☆Ignore the effects of the other polluting factors in the wastewater when consider about the polluted degree.
☆Ignore the transportation cost of the water supply when consider about the sea water desalination.
☆we assume that the gross of the population N(t) is large enough.
☆We assume that there is no big revolution in the configuration of water supply.
2016美赛E题参考答案 - 图文
