2016 HiMCM B题特等奖学生论文下载7037

2016 HiMCM B题特等奖学生论文下载7037

 

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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:  7037

Problem Chosen:  B

Please paste or type a summary of your results on this page. Please remember not to include  the name of your school, advisor,  or team members on this page.

Online shipping is a major booming business that is becoming a natural phenomenon through the increase of electronics in the United States. One of the major industries that has become proficient in this area of industry is UPS. At first, the team’s goal was to determine the minimum amount of warehouses needed to provide efficient one­day coverage throughout the continental United States. Some assumptions had to be made, particularly regarding seasonal weather conditions as well as traffic consistencies in the highway system. The time of the worst weather conditions was chosen, but that assumes no extraordinary events could slow down distribution. To accomplish this goal, certain criteria was needed to determine the location of the warehouses. The criteria used for the location was that optimal area covered by zipcode in one day (to meet the requirement of the one­day ground shipping with United Parcel Service), that the warehouse is located in a city with a major intersection of roads and highways, and that there was an overlap of one­day shipping capability reduced to a minimum. Using this criteria, it was determined that 28 warehouses was needed to effectively reach all the populated areas in the continental United States. Next, the team had to evaluate the effect of sale taxes on the amount of people with sale taxes based on the location of the warehouses. An equation was then created to score each of the 28 warehouses: S R=Po/(PI)(T). Using this equation, the warehouses with a score below the first quartile was found inefficient and was then attempted to be replaced with an another location. After solving this problem, clothing tax was factored into the location of the warehouses and so the equation changed to be SR=Po/(PI)(C). Using this equation, the locations that scored under the first quartile, 3.959, were determined to be inadequate and new locations were considered. The equation μT = ∑ ((Ti / R)(Ci)) was used to determine which map should be used as n i=1 the basis for the third map model. It was found that the second map was overall more efficient than the first and thus was used as the canvas for the clothing tax issue. The strengths for these models were that you could compare different warehouses and effectively determine efficiency. It also provides an accurate display of the ratios’ correspondence to the sales tax. Some weaknesses include its inaccuracy regarding warehouses with no taxes or out of state population. In such situations the score will be ∞ or 0 respectively and thus do not fully account for the other variables and their ratios.

 

 

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