2013 HiMCM A题特等奖学生论文下载4421

2013 HiMCM A题特等奖学生论文下载4421

 

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论文摘要如下：

 

Summary Sheet: Group 4421 – Problem A

The patient must be reached before medical attention can be given, making minimizing the medical response time to reach a zone of population a societal concern. The purpose of this problem is to analyze the average time it takes an ambulance to travel from each zone to any zone in the county in order to maximize the population reached in the smallest amount of time. Using these results, we will form a plan for the Emergency Service Coordinator to direct ambulances.

Our solutions depend on the number of available ambulances and the number of emergencies the county has to deal with at a specific time. When three ambulances are available, 11 out of 20 combinations of ambulance placement will result in perfect coverage of the entire county within eight minutes. To determine which of these combinations resulted in optimal coverage we defined a new unit, people-minutes, which refers to the total amount of time required to reach every individual given a single arrangement of ambulances. Using this unit, we found the average time required to reach an individual by finding the total minimum people minutes for a given ambulance arrangement and dividing this by the total population of the county. In essence, it weighted the time needed to reach different zones by the relative proportion of the population in that zone. We wanted to make sure that not only were our ambulances quickly reaching citizens, they were also maximizing the number of citizens they could reach. We determined that zones 1, 2, and 5 were the optimal locations for ambulance placement, as this combination had the lowest average time, only 2.37 minutes. In the case where only two ambulances were available, perfect coverage could still be achieved, with ambulances in zones 2 and 5. With a single ambulance, it was impossible to cover every zone in eight minutes. We did determine that zone 2 would be the optimal zone for that single ambulance, because it would cover the most people within the time constraint. For each of these cases, we also considered situations where conditions may not be ideal and looked at the difference in coverage when the average travel time increased by ten percent. Our models were all relatively robust as a large proportion of the population could still be reached in eight minutes. We also wanted to consider other realistic

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