2016 HiMCM B题特等奖学生论文下载6475

2016 HiMCM B题特等奖学生论文下载6475

 

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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: 6475 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.

Abstract Have you ever tried waiting forever for a UPS parcel to arrive? As the number of online stores rocketed around the world, it is getting increasingly crucial to smooth out online-offline connection. In our paper, we construct a mathematical model to determine the optimal numbers and locations of warehouses established to distribute merchandise purchased online by customers from 48 continental states in the USA.

 

In part 1, we assume that some particular trivial areas in some states are ignored. Then, we simplify the problem by constructing a 27-by-27 0-1 matrix. We fill the matrix with 1 or 0 according to whether the two concerned states can be mutually reached in a one-day ground shipping. On top of that, we apply Greedy Algorithm and computer analytic technique to give the optimal solution.

 

In part 2 and 3, we build the Vector Delivery Model. In the model, we use dots to demonstrate specific warehouse locations, and vectors to connect every warehouse with states within reach by the warehouse by one-day ground shipping. In conjunction with graph theory, we apply 0-1 programming to solve for the optimal solutions. Some adjustment by hand produces the optimal answer.

 

After building our model, we come up with specific answers to each question. Key Words: one-day ground shipping, 0-1 matrix, 0-1 Programming, Greedy Algorithm, Graph Theory, optimal solution, Vector Delivery Model

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