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图与网络算法优秀论文31
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图与网络算法优秀论文31
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For office use only
T1
________________
T2
________________
T3
________________
T4
________________
Team Number
21185
Problem Chosen
B
For office use only
F1
________________
F2
________________
F3
________________
F4
________________
2013 Mathematical Contest in Modeling (MCM) Summary Sheet
Summary
There are mainly three water problems in China: too little water in northern and northwestern part;
too much floods in southern part; and too dirty water produced by industry and agricultural
pollutants.
In order to address problems above and provide a thirteen-year water strategy (2013-2025) for the
leadership of China, we conclude five sub-problems and its solution in our paper: 1)Prediction of
the supply and demand of water in a period of thirteen years based on historical data;2) Model
building of national water storage and movement strategy to solve China’s uneven distribution of
water in time and space; 3)Model designing of regional water de-salinization strategy to increase
the total amount of available water;4)Model building of water conservation strategy, including
regional water pollution treatment and national water-saving; 5)Long run cost-benefit analysis of
four water strategies above and the discussion of the optimal combination of water strategies.
In first model, we choose the most appropriate Fitting Function. Using Grey Predicted Model, we
can get the correlation degree between water consumption and population, industrial GDP and
agriculture output. Then we successfully finger out the water demand in 2025 is 6770 hundred million
m^3
by using GM prediction. In our second model, we use CV (coefficient of Variation) and water
supply pressure as the decision-making index and work out a water storage project list by using
Goal Programming. Based on cost and benefits analysis, we build Minimum Spanning Tree to
work out the optimal water transfer plan. That is, we should transfer water from Yangtze watershed
to Yellow watershed and Hai watershed. Besides, we devise a local water transfer strategy. In the
third model, we build a set of parameters to describe the degree of water purification demand of
each city and successfully get the water de-salinization plant building scheme. In the fifth model,
we do long run cost-benefit analysis of four water strategies above. We first analyze weights of
economic, physical, environmental implications by using AHP (analytic hierarchy process). Then
we use Neural Network Algorithm to classify the quality of each strategy and finally get a
reasonable strategy evaluation model.
In the whole modeling process, we give full consideration to validity, feasibility and cost-efficiency
of our model.
Five Models for China's Water Scarcitys
Contents
1 Introduction ................................................................................................................. 1
2 Nomenclatures ............................................................................................................. 2
3 Model one: Water demand and supply Forecast (2013-2025) ................................. 3
3.1 Introduction ........................................................................................................ 3
3.2 Assumptions ....................................................................................................... 3
3.3 Function Fit Model ............................................................................................. 3
3.3.1Analysis of China’s water use ..................................................................... 4
3.3.2Model Testing .............................................................................................. 6
3.3.3Prediction Results and Conclusion ............................................................. 6
3.4 Grey Forecasting Model ..................................................................................... 7
3.4.1Reasons for Improvement ........................................................................... 7
3.4.2Correlation Degree Analysis ....................................................................... 8
3.4.3Thirteen-year water forecast based on Verhulst Model............................... 9
3.4.4Model Solution .......................................................................................... 10
3.4.5Model Testing ............................................................................................ 10
4 Model Two: Water Storage and Movement ............................................................ 12
4.1 Terminology...................................................................................................... 12
4.2 Water Storage Model: Time Balancing Strategy of Water Resources .............. 13
4.2.1Introduction ............................................................................................... 13
4.2.2Analysis ..................................................................................................... 13
4.2.3Model Solution .......................................................................................... 14
4.2.4Conclusion ................................................................................................ 16
4.3 Water Transfer Model: Spatial Balancing of Water Resources Strategy .......... 16
4.3.1Introduction ............................................................................................... 16
4.3.2Backgrounds and Water Movement Principles ......................................... 17
4.3.3Model Analysis ......................................................................................... 18
4.3.4Objective Function of water transfer strategy ........................................... 21
4.3.5Model Testing ............................................................................................ 21
4.3.6National water transfer strategy ................................................................ 21
4.3.7Conclusion ................................................................................................ 22
5 Model Three: Water De-salinization Strategy ........................................................ 23
5.1 Introduction ...................................................................................................... 23
5.2 Terminology...................................................................................................... 23
5.3 Assumptions ..................................................................................................... 23
5.4 Model Building ................................................................................................. 24
5.5 Model Solving .................................................................................................. 24
5.6 Analysis and Conclusion .................................................................................. 25
6 Model Four: Water Conservation Strategy ............................................................ 25
6.1 Introduction ...................................................................................................... 25
6.2 Water Pollution Control Model ........................................................................ 25
6.2.1 Introduction .............................................................................................. 25
6.2.2 Assumptions ............................................................................................. 25
6.2.3 Terminology ............................................................................................. 26
6.2.5 Model solution: ........................................................................................ 27
6.2.6 Model analysis: ........................................................................................ 28
6.3 Water-saving Model.......................................................................................... 29
6.3.1 The water consumption per unit GDP ................................................. 29
6.3.2 Analysis and Conclusion .......................................................................... 30
7 Model Five: Impacts Evaluation Model .................................................................. 31
7.1 Introduction ...................................................................................................... 31
7.2 The Comparison of η (the actual benefit of a project)...................................... 31
7.3 Evaluation of Economic, Physical, and Environmental impacts using AHP ... 31
7.4 Neural Network Evaluation Algorithm ............................................................ 33
7.4.1 Analysis .................................................................................................... 33
7.4.2 Conclusion ............................................................................................... 34
8 Strengths and Weaknesses ........................................................................................ 35
8.1 Strengths .................................................................................................... 35
8.2 Weaknesses ................................................................................................ 35
9 Position paper for the Governmental leadership of China ................................... 36
10 References .................................................................................................................. 36
11 Appendix and Supporting Datas ............................................................................. 37
Team # 21185 Page 1 of 42
1 Introduction
Water, the magic encounter between one hydrogen and two oxygen atoms, is vital for all kinds of
life forms in the earth. The human body, myriad ecological systems and the big biosphere of our
entire planet, all of these can’t live without the beautiful gift from our Almighty God. However, in
many parts of the world nowadays, we human are facing severe water problems.
Take China for example. With more than 20 percent of world’s population but less than 7 percent of
its freshwater, China is continuously facing issues associated with water. There are mainly three
problems in China: too little water in northern and northwestern part of country; too much floods
in southern part; and too dirty water produced by industry and agricultural pollutants. Furthermore,
being a developing country, China has the responsibility to deal both the soaring water demand
caused by booming economy and the increasing need to improve water consumption efficiency.
In order to address problems above and provide a thirteen-year water strategy (2013-2025) for the
leadership of China, we conclude five sub-problems to tackle in our paper.
Prediction of the supply and demand of water in a period of thirteen years (2013-2025)
based on historical data
Model building of national water storage and movement strategy to solve China’s uneven
distribution of water in time and space
Model designing of regional water de-salinization strategy to increase the total amount of
available water
Model building of water conservation strategy, including regional water pollution treatment
and national water-saving
Long run cost-benefit analysis of four water strategies above and the discussion of the
optimal combination of water strategies
In the whole modeling process, we give full consideration to validity, feasibility and cost-efficiency
of our model.
Team # 21185 Page 2 of 42
2 Nomenclatures
D
The fresh water demand of a region
S
The fresh water supply of a region
W
The total amount of water resources of a region
nation
The fresh water demand of whole nation
The fresh water demand of whole nation
U
The groundwater resources of a region
O
The surface water resources of a region
N
The population size of a region
GDP
Gross Domestic Products
g
Real GDP per capita
The water supply pressure of a region
0
The national average water supply pressure
The water consumption per unit GDP
C
The capacity of a reservoir
E
The average construction costs of a reservoir
η
The actual benefit of a project
The range of water resource in a certain period of time
The number of a certain province in model two
The amount of water a region can’t provide by itself
The watershed attribute of the number i province
The terrace attribute of the number i province
(x, y)
The geographical coordinates of a region’s capital city
The distance between region i and j
r
The Earth Radius
The edge weights of national water transferring network
The estimated water consumption in 2013
The growth rate of water consumption
p
The desalinization cost of tons of seawater
p
The desalinization cost of tons of seawater in 2013
The optimal time to build water purification plant
The measurement of the seawater’s desalination cost
Demand for water-pollution control degree of number k
watershed
The water supply pressure of a watershed
Ⅰ
The highest level of water quality
Ⅱ
The middle level of water quality
Ⅲ
The lowest level of water quality
The ratio between the sum of
Ⅰ
,
Ⅱ
and
Ⅲ
water of
resources to the total water resources
,
Demand for Water-pollution Control Degree of the
number j city in number k watershed
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