发布时间 : 星期日 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
Team #20300 Page 16 of 28
w2??ck?cp
k?16w3??pk?pp,k?2,4,6
k
In general, Model 2 is Expressed as follows:
Decision variables:
?t11t12?T??t21t22?t31t32?
The Objective function:
t13??t23?；c(k?1,2...6)；p(k?2,4,6)
kk?t33?minW?w1?w2?w3
Constraints:
?ck?rk??1?raink,k?1,2,L,6???pk??2?coastk,k?2,4,6??3??oi?ci?pi??xij,i?1,2,3?j?1?s.t.?3??xij?cj?pj?sj,j?1,2,3 ?i?1??1?B???6?bk??62k=1?(b?)?k?6k?1?
5.2.3 Solution And Analysis of Model 2
Solution
Before solving the problem, there are 5 parameters in model 2 which we should ascertain.(These paraments are mentioned in Establishment of Model 2) They are:
Team #20300 Page 17 of 28
General cost of transfer:tp?5.858?10?4yuan/m3?km; Extra cost of transfer:hp?0.0157yuan/m3?m; Cost of building a reservoir:cp?3.4093yuan/m3; Cost of desalination:pp?5yuan/m3;
We get the values of 4 paraments with the help of some relevant information. Besides, there is another parament--balance degree, whose size suggests the balance situation of water supply and demand in different regions. The larger the parament is, the better balance of different regions’ water supply and demand is. When solving the problem, we might as well set:
?0?0.2
We will discuss the relationship between balance degree and water strategy in detail in Verification and Analysis. We obtain the solution of the problem with the help of Lingo:
? Total cost:68.75 billion yuan
? Transfer:NE to NR, 3.894 billion m3; SR to NR, 28.09 billion m3 ? Construction of reservoir:IM, 5.018 billion m3; CR,1.892 billion m3 ? Construction of desalination factory:NONE
The whole allocation of water resources is shown below: Unit:billion m3
Figure 7: The whole allocation of water resources
Analysis
Model 2 gives a solution--an investment of 68.7 billion yuan on condition that we use the paraments confirmed above. This strategy can meet the water needs of six regions in the whole China in 2025. Because of the least cost, we can be sure that the strategy is the best solution under this circumstance.
As for the regions with water surplus such as NE, SR and SE, there are two regions
Team #20300 Page 18 of 28
transferring water to the same region--NR. This result is accordance with reality: there is a huge water shortage in NR, considering the factors of distance and altitude, the optimization results are supposed to make full use of the water in short distance and high altitude.
Regions like IM and MR should build reservoirs, note that these two regions both use reservoirs to meet their water demand, that is they do not choose water transferred from SR or SE. Because of the high altitude in IM and the long distance to SR. It costs much more if IM uses the water transferred from SR; for MR, however, it has a smaller water shortage.It is also more convenient and cheaper for MR to building reservoirs than to use transferred water to meet its water demand. So the final results shows the same approach--building reservoirs for the two regions to meet their water demand.
The results also indicate we need not build desalination factories on that condition, only using two methods--movement and storage can totally solve water demands in China in 2025. Why not building desalination factories? We find out that the price of desalination is 5 yuan/m3 in 2012, which is much more expensive when compared with the price of transferring water or building reservoirs. Our model is based on the minimum cost, so the method--Building desalination factories will not be included in the optimized results. But we can predict that with the rapid development of science and technology, cost of seawater desalination will decrease largely. Then it can be cheaper and practical to use this method.
5.2.4 Water Resource Allocation in West Region
Provinces like Qinghai, Xinjiang and Tibet belong to west region. There are some same features of these three regions. For example, they are all with vast area, high altitude and small population, which contributes to a large quantity of total water resource but a lower utilization ratio of water resource per capita. Water resource also remains unevenly distributed in time and space. For these three regions, it is especially necessary to exploit and use water resource reasonably.
The rainfall is mainly concentrated in the southeast in Qinghai as well as its lakes[11]. It makes for a large quantity of water resource but a difficulty in utilization. In view of this situation, we suggest to build some canal to transfer water to the region with water shortfall.
Water resource is also unevenly distributed in Xinjiang, rainfall is mainly distribute in South of Mount Tianshan[12]. According to this phenomenon, we can build some reservoirs in water-deficient area, changing its situation of water shortage.
Tibet has the largest potential of water exploitation. It has largest quantity of total water resource and water resource per capita[13]. As for Tibet, we should address on how to take advantage of the largest water resource. In our opinion, there are at least several ways. Firstly, building some large hydropower station to make electricity. Secondly, building large hydraulic engineering, transferring a large amount of water to where the regions need. However, it is not so easy to achieve this goal for its
Team #20300 Page 19 of 28
extremly high altitude, that is why the water allocation of Tibet is not included in our Model 2 though it has rich water resource. With the development of science and technology, we believe we can make full use of water resource in Tibet.
6. Sensitivity Analysis of Our Model
According to China’s demand of water in 2025, we set up 2 models. Model 1 finds a way to exploit water resource reasonably. Model 2 gives us a best solution to allocate water resources for different regions with lowest cost. These 2 models provide us with an approach to solve the allocation of water resources in the whole China. However, when we consider the problem deeply, factors like economic,
environment and balance degree also have significant impact on our strategy of using water resources.
6.1 Sensitivity Analysis of Model 1
When considering the differences of every region in geography, season and the global climate change. Paraments like?1,?2 can be different, whose value can reflect the efforts we make to protect environment. The larger the value is, the more effort we make to protect environment. For example, if China get addicted to development of economy but regarding less of environment protection, the value of ?1,?2 can increase to 0.9,0.4. Then the results compared with the former are as below:
Table3: Sensitivity analysis of model 1
Approach From STO.R From SUR.R From CA.G Total δ1=0.9 δ2=0.4 30.13 8.224 20.79 59.14 δ1=0.8 δ2=0.3 26.78 6.168 20.79 53.74 Variation 12.50% 33.30% 0 10.00% SUR.R:Surface runoff; STO.R:Storage of reservoir;
CA.G:Compensation amount of groundwater
From the table above, we can see the rainfall of NR increases by 10%. This
increasing part of water is mainly used in industry to prove that China concentrates much on economic development. However, China may pay the price for its regarding less of environment. This situation we should try our best to avoid.