美赛e题参考答案

For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________

Team Control Number

For office use only F1 ________________ F2 ________________

52766

Problem Chosen

F3 ________________ F4 ________________

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)

Contents

1 INTRODUCTION & BACKGROUNDS ........................................ 错误!未定义书签。 2 PROBLEM ANALYSIS ................................................ 错误!未定义书签。

Problem Restatement ......................................... 错误!未定义书签。 Problem solving ............................................. 错误!未定义书签。

3 ASSUMPTIONS .................................................... 错误!未定义书签。 4 NOTATIONS ..................................................... 错误!未定义书签。 5 BASIC MODEL .................................................... 错误!未定义书签。

Model of the water consumption .............................. 错误!未定义书签。

Compound population Model based on Logistic Model ................. 错误!未定义书签。 Model of Industrial water consumption ............................. 错误!未定义书签。 Model of total water consumption of a region ...................... 错误!未定义书签。

Model of the Gray Metabolism Model GM (1, 1) ................ 错误!未定义书签。

Principle of common Gray GM (1, 1) Model .......................... 错误!未定义书签。 Principle of Gray Metabolism Model GM (1, 1) ..................... 错误!未定义书签。

[2] Accuracy testing .................................................. 错误!未定义书签。

Model of water supply capacity of a region .................. 错误!未定义书签。 Strengths & Weakness ........................................ 错误!未定义书签。

6 CHOOSE A REGION TO ANALYZE ........................................ 错误!未定义书签。

Brief introduction .......................................... 错误!未定义书签。 Physical scarcity: .......................................... 错误!未定义书签。 Economical scarcity: ........................................ 错误!未定义书签。

7 PREDICTION MODEL FOR THE NORTH CHINA ................................ 错误!未定义书签。

Model of water consumption in North China. .................. 错误!未定义书签。 Water supply model in the North China ....................... 错误!未定义书签。 The comprehensive evaluation to the future water resources in the North China ............................................................ 错误!未定义书签。 Strengths and Weaknesses .................................... 错误!未定义书签。

8 OPTIMIZATION OF WATER RESOURCES ALLOCATION ........................... 错误!未定义书签。

Optimization of water supply allocation ..................... 错误!未定义书签。

Construct the model of hierarchical structure ..................... 错误!未定义书签。 Construction of comparison matrix of target-criterion layer. ....... 错误!未定义书签。 Construction of comparison matrix criterion - target layer ......... 错误!未定义书签。 Total sorts of hierarchy and consistency check .................... 错误!未定义书签。 Interpretation of result .......................................... 错误!未定义书签。

Optimization of water consumption allocation ................ 错误!未定义书签。

Construction of water resources allocation model .................. 错误!未定义书签。 Main constraint equations ......................................... 错误!未定义书签。 Model Solution .................................................... 错误!未定义书签。

CONCLUSIONS ...................................................... 错误!未定义书签。 FURTHER DISCUSSIONS ............................................... 错误!未定义书签。 REFERENCE ....................................................... 错误!未定义书签。 APPENDIX ........................................................ 错误!未定义书签。

Strategy of Conquering Thirst