2016 HiMCM B题特等奖学生论文下载6829
2016 HiMCM B题特等奖学生论文下载6829
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论文摘要如下：
19th Annual High School Mathematical Contest in Modeling (HiMCM) Summary Sheet (Please make this the first page of your electronic Solution Paper.)
Team Control Number:6829 Problem Chosen:B
As online shopping become more and more popular in contemporary society, the increase demand for larger quantity of production as well as faster delivery time lead the recreation equipment company to build more warehouses in the U.S. Its goal is to make those new warehouses cover all the area within one-day ground shipping.
The two of the biggest problems of this question lie in the data extraction from the URLs and data analysis, especially when there are a lot of mismatched zip-codes existing on this website. It is not difficult to find that this is a typical set covering problem. So a more efficient algorithm is needed when doing analysis: approximation algorithm.
The essence of this model is derived from "greedy algorithm": instead of considering from the overall perspective, the approximation algorithm only looks for the current maximum cover-area increment (warehouse's location that can radiate the largest area). We are clearly aware that it is impossible to come up with all the answers with high precision due to the large amount of data needed to address. So sacrificing a little bit of precision of the results (as well as the number of results) to save a huge amount of computational time is worthwhile and extremely beneficial. We admit that the error is bigger than the brute force search, but the time we saved is definitely worth the precision.
One significant advantage of this model is the high efficiency. Although approximation algorithm could not compute the optimal result, its algorithm complexity can decrease from (! ⋅ ) to (2 ⋅ log2 ), as the time in other algorithms take up unimaginable amounts of time.
Furthermore, we optimized the approximation algorithm while solving part Ⅱ since tax rate had been taken into consideration. The same thinking pattern was employed in part Ⅲ.
Then we tested our model by calculating the land cover rate, as shown in table 3.
Lastly, the model analysis shows that our model has its stability when the tax rate of garment varies.
The paper will illustrate the ideas and results abovementioned specifically
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