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Team #22887 Page 1 of 33

For office use only

________________

Team Control Number

22887

Problem Chosen

For office use only

________________

2013

Mathematical Contest in Modeling (MCM/ICM) Summary Sheet

(Attach a copy of this page to your solution paper.)

The utilization of water resources would be greatly improved and the issue of

water shortage would be addressed if reasonable and effective water

strategies can be established. Our work is to provide a non-technical position

paper to governmental leadership with the help of mathematical deduce. This

paper presents the descriptions of several models to develop it.

The first model divides China into nine river basins and predicts the water

supply and its demand. Stationary Time Series is used for the supply forecast,

and the exponential curve fitting is built to predict the demand by using the

Non-stationary Time Series Trend Analysis. The results show the accuracy of

the model.

The next model provides the account of giving priority to promoting agricultural

water saving. The Game Theory helps to solve it.

The third model is generally committed to the plan of water transfer. Cost

–profit equations are established after some scientific and effective

simplify .Linear programming is used to work out it.

The fourth model offers the method and functions to calculate the cost of

desalination. Synthetically considering the effect on environment and physics,

a suggestion about desalination has been offered.

The fifth model simulates the relationship between the consumption and price

of water. A piecewise water price model has been set up and well used.

The sixth model puts forward a estimation about the cost and profit of glacier

transport from the Antarctic Circle to China .It has been regarded as an

alternative after considering the effect on environment and China's national

conditions.

The last model discussed the economic, physical, and environmental

implications of the strategy by using Analytic Hierarchy Process.

Last but not least, a non-technical position paper to governmental leadership

has been offered after summarizing all the work done.

Team #22887    Page 2 of 33 
 
Introduction .............................................................................................................................4 
  The Description of Problem..................................................................................................5 
1    What problem we are confronting................................................................................5 
2 What we do to solve these problems ..............................................................................5 
Terms and Definitions ............................................................................................................6 
Basic Assumptions ..................................................................................................................6 
     Models ...............................................................................................................................7 
1      Model 1 .......................................................................................................................7 
1.1    The model Description ...........................................................................................7 
1.2    Additional    Assumptions ......................................................................................7 
1.3    Symbols ..................................................................................................................8 
1.4  Model Establishment ................................................................................................8 
1.5      Results and Analyse ........................................................................................... 12 
2      Model 2 .................................................................................................................... 12 
2.1    The model Description ........................................................................................ 13 
2.2    Additional Assumptions ...................................................................................... 13 
2.3    Symbols ............................................................................................................... 13 
2.4    Model Establishment .......................................................................................... 13 
2.5      Results and Analyse ........................................................................................... 15 
3      Model 3 .................................................................................................................... 15 
3.1    The model Description ........................................................................................ 15 
3.2 Additional Assumptions.......................................................................................... 15 
3.4    Model Establishment .......................................................................................... 16 
4    Model 4 ...................................................................................................................... 22 
4.1    The Model Description ........................................................................................ 22 
4.2 Additional Asumptions ........................................................................................... 22 
4.3    Symbols ............................................................................................................... 22 

Team #22887    Page 3 of 33 
4.4    Model Establishment .......................................................................................... 23 
4.5      Results and Analyse ........................................................................................... 23 
5    Model 5
[11]
 .................................................................................................................. 24 
5.1 The Model Description ........................................................................................... 24 
5.2 Additional Assumptions.......................................................................................... 24 
5.3    Symbols： ........................................................................................................... 24 
5.4 Model Establishment .............................................................................................. 24 
6 Model 6 ......................................................................................................................... 26 
6.1 Model Description: ................................................................................................. 26 
6.2   Additional Asumptions： ..................................................................................... 26 
6.3    Symbols： ........................................................................................................... 26 
6.4 Model Establishment .............................................................................................. 27 
6.5 Model Analyse： .................................................................................................... 27 
Analytic Hierarchy Processof Model Evaluation
[12]
 ............................................................. 28 
1    Model    Descripton .................................................................................................... 28 
2    Symbols ...................................................................................................................... 28 
3 Model Establishment ..................................................................................................... 29 
3.1 Construct a Comparison Matrix ............................................................................. 29 
3.2    Results of Model .................................................................................................. 31 
3.3    Model analysis ..................................................................................................... 31 
3.4Models pros and cons ............................................................................................. 31 
Appendix .............................................................................................................................. 32 
1 Reference ...................................................................................................................... 32 
2.Position Paper for the China Congress .......................................................................... 33 
 ................................................................................................................................................. 33 
 
 
   