发布时间 : 星期五 文章2013美国大学生数学建模大赛一等奖论文 - 图文更新完毕开始阅读24626e27eefdc8d376ee325c
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6.2 Sensitivity Analysis of Model 2
Allocation water resource of China is a complicated process. The final results can be influenced by many factors. Here, we choose two factors--balance degree and the cost of desalination to analyze the sensitivity of Model 2. We choose these two factors because they have more impact on our strategy. Balance degree Water resource remains unevenly distributed in the whole China which contributing to a small value of balance degree. Among the strategy we get before, there are four regions whose water resources just to meet the demand. This result is certainly not benefit to sustainable economic development and the stability of ecological environment. On the other hand, it is wasteful when we can not take full advantage of the large quantity of water in South and Southeast. Though using our Model can change the unbalance situation it will cost more. The purpose is that we try to find a strategy which is both satisfied with balance degree and cost. So it is necessary to analyze the relationship between balance degree and cost.
With the help of Matlab, we get a figure which illustrates the relationship:
Figure8: Relationship between balance degree and cost
From the figure above, we can feel the sensible change of cost with even little change of balance degree. In addition, we also find an interesting phenomenon: balance degree reaches its maximum value when cost is around 270 billion yuan, then it does not increase but decreases even though increasing cost. The two distribution of water resources shows as follows:
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Table 4: Two water resource distribution of lowest cost and largest balance degree
0 67.48 NR
0 9.89 IM
Water
0 12.82 CR Surplus
301.12 229.74 SR (billion m3)
75.15 75.15 SE
0 13.57 NE
From this table, we find that we can make an extra investment of 200 billion yuan to make water resources distribute uniformly in the whole China, which will contribute largely to economy and environment but the cost is “extremely” large. Government should take many things into consideration when establishing relevant policies. (we will discuss in detail whether government should spend 200 billion yuan in Verification and Discussion ) Cost of desalination There are three approaches to allocating water resources in the whole China, they are storage, movement and desalination. The cost of desalination has a big influence on how to allocate these three approaches. If the price is 5 yuan/m3 during we solve the problem. Desalination factories will not be built according to the results. However,with the advancement of technology, the price of desalination will be cheaper and cheaper. Now, we find when we should build desalination factories as the cost of desalination becomes cheaper and cheaper.
We continually change the cost of desalination so as to look for the “critical price”. Finally, we find that desalination factories of 28.09 billion m3 are built when the price is 1.5 yuan/m3. Meanwhile the total cost is 68.09 billion yuan, which is even smaller than the former strategy. So government is supposed to bring in desalination projects when the cost of desalination decreases to 1.5 yuan/m3.
The consequences of the sensitivity of Model 2 can be expressed vividly as the following figure:
Cost(billion yuan) Balance Degree 68.7 0.41 270 0.79
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Figure9: Consequence of sensitivity of model 2
7. Verification of Model
7.1 Economic Analysis
----Is it beneficial or not for China’s economy to improve balance degree with huge investment?
As is mentioned in the analysis of model 2, balanced distribution of water resources is be of great advantage for the balance of the ecosystem and sustainable development of economy. In the analysis of model 2, changing the value of balance degree from 0.4134 to 0.79411,we are surprised to find the total investment increase by 206.92 billion yuans. This expense looks like not worthy. Here we will have a further discussion about the impact of balance degree on economy in the whole country
From China Statistical Yearbook of 2011,every 10 thousand GDP Consumes 129
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cubic meter water [3]. Thus we use this index to transform surplus water of seven regions to GDP:
When the balance degree is 0.4134, GDPwater1?2.917?104 billion yuans; When the balance degree is 0.79411,GDPwater2?3.168?104 billion yuans.
Deducting the increase investment: 206.92 billion yuans. we obtain the Net income
GDPwater2net =3.148?104 billion yuans.
This result indicates the improvement of balance degree bring revenue of 2310 billion yuans straightly!
On the other hand when the total investment is 68.7 billion yuans, water resources in SR and SE are too surplus. Therefore it can be confirmed that the improvement of water resources in these two region will contribute less to GDP. But if transfer these water resources to water-deficient area,the contribution to GDP must be larger. So China may get more economic gain. In conclusion the essence of the improvement of balance degree is transferring “small value”water resources of NR and NE to water-deficient area and make “small value” become “large value”. This conclusion also explain more economic gain when improve balance degree.
7.2 Realistic Analysis
First of all, the transfer distance in model 2 is centroid distance between two regions, but it is not to fit the actual situation. Firstly , the transfer route might be changed by local terrain and geologic structure,which will bend the route and increase the distance. Secondly,
Rivers between two regions can shorten considerable amount of distance. Therefore owing to complex terrain of China, the transfer route should be based on meticulous fieldwork
For example , for NR, when transferring water from NE and SR, terrain and rivers of these three regions must be taken into consideration. As the following figure map shows. With the help of rivers and flatland we marked, the route can be better.