2013 HiMCM A题特等奖学生论文下载4155

2013 HiMCM A题特等奖学生论文下载4155

 

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论文摘要如下：

 

Summary

 

The first quintessential problem we face is to determine the shortest time it takes to commute between different zones, which we solved by employing both the Dijkstra's Algorithm and the Floyd–Warshall Algorithm, favoring the latter in practice.

Having reasoned that an ambulance arrangement that effectively covers the whole county is one that maximizes the population coverage, we applied the Tree Traversal programming method to Questions 1&2, and obtained solutions that succeeded in covering the entire region. We then analyzed the given data and answered Question 3 by putting 1 ambulance in the location with the largest population coverage and calculated the number of people left without coverage.

We optimized the basic model from 2 different angles, building matrixes and making accurate mathematic calculations to achieve both the most efficient way to cover the population and the fastest way to respond to emergency calls. We concluded that if ambulances are arranged in such a way so that the regions they cover overlap, they can provide more secure care in case one of them is dispatched, while the shorter the average time it takes an ambulance to reach designated areas is, the faster its response. Therefore we came up with 2 optimization plans, one to increase coverage overlap, and another to ensure fastest contact. We used standard deviation as a method of determining the best solutions among the optimized ones.

To solve the problem concerning catastrophic scenarios we approached it from 3 perspectives depending on the nature of the catastrophe, and proceeded to discuss 3 different plans on how to station the ambulances so that they most substantially boost rescue rates. In case of sporadic outbreaks in random areas, we applied the aforementioned plan with large area overlaps so that enough ambulances will be on standby once 1 has been dispatched to deal with a crisis case. Our second plan is to have the ambulances repeatedly dispatched and retrieved all over the county, but found that this does not provide satisfactory coverage. Most notably, in cases where 3 ambulances are involved and needs to reach all areas as fast as possible, we used the method of overall planning to determine several ways to station ambulances so that they can travel through all 6 zones within 8 minutes.

 

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