2012 HiMCM B题特等奖学生论文下载3681

2012 HiMCM B题特等奖学生论文下载3681

 

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论文摘要如下：

15th 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: 3681 Problem Chosen: B

Please 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.

The average American family spent $368 per month, or $4416 per year, on gasoline in 2011. Gas has gone up by an average of 19 cents per year over the past 9 years. For our model city (New York City), our model saved 1.75% over normal consumers when driving 200 miles a week. This would translate to $77.45 savings per year for the average American family just from optimizing the timing of gas purchases. These numbers explain the immediate importance of this problem to all Americans.

Our model is a multiple regression for the change in price of gas, given past weeks change in gas, past change prices of crude oil, and the displacement of the current price of gas from the average. It uses all linear combinations between past weeks change in gas, and all linear combinations of past change prices of crude oil. The R2 of our model for our model city, or the percentage of variance in the output variable that is explained by variance in the input variables, is .784. More importantly, the model correctly forecasted the direction of change in price of gas in 40 out of 45 weeks in 2012 after being trained on data from 2011.

We also investigated other methods of calculating the change, finding that a simple Markov process could make many effective predictions. We included this model in our analysis, and used it in our letter to the editor, as it is easy to understand and simple to implement in actual gas buying routine.

We then calculated the savings garnered using the multivariate linear model in 2012 and compared it to the simple Markov model, the model that buys gasoline whenever the tank is empty, the model that fills the tank every week, and the optimal solution, found using Dijkstra's Algorithm. Our model saved more than the simple Markov model in most cases. Variance in savings can be attributed to the severity of errors in the model's predictions.

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