2013 HiMCM A题特等奖学生论文下载4185

2013 HiMCM A题特等奖学生论文下载4185

 

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论文摘要如下：

2013
16th Annual High School Mathematical Contest in Modeling (HiMCM)
Summary Sheet
(Please attach a copy of this page to each copy of your Solution Paper.)
Team Control Number: 4185
Problem Chosen: A

Summary

The goal of our model is to help Emergency Service Coordinator (ESC) maximize the number of residents in the six population zones that can be reached within 8 minutes of an emergency call in a country by determining where the county should station its ambulances.

At first, we determined the best location to place one, two or three ambulances by using the Boolean model, which assigns a “true” or “false” property for an ambulance’s ability to reach a zone in 8 minutes. Then by examining the combinations closely, we obtain the maximum value of population coverage: there were 11 solutions for total coverage with 3 ambulances, a unique solution for total coverage with 2 ambulances, and a maximum of 160,000 people covered with only one. This model is useful due to its zero-tolerance restrictions on the solutions, but cannot differentiate between acceptable solutions.

Second, we improved our model by minimizing transit time, while taking population into consideration. This model uses weighted averages to find the average amount of time a system of ambulances takes to rescue a random patient from any zone, which are more likely to come from populous zones. We obtained the most optimal locations for different situations: a lone ambulance is best stationed in zone 2, a pair of ambulances are best stationed in zones 2 and 5, and three ambulances are best stationed in zones 1, 2, and 5.

Third, we created two models to examine the optimal solution for dealing with catastrophic situations, where many people from different zones make 911 calls. The first method was the nearest neighbor method, in which we create a near-optimal route shared by 3 ambulances, passing through all zones. Then in this route, we placed hospitals at every other point. Using this method, we can on average rescue a person every 2.722 minutes.

The second method, split-cycle method, takes a more complicated approach: it divides the six zones evenly into three areas, with one ambulance responsible for one area. By comparing different combinations produced, we are able to find an optimal solution where ambulances are stationed in zones 2, 4, and 5. This method is both more effective and practical: it averaged only 2.118 minutes to rescue a person.

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