2017 HiMCM B题特等奖学生论文下载8124

2017 HiMCM B题特等奖学生论文下载8124

 

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论文摘要如下：

Abstract: ​ ​​ ​​ ​​ ​​ ​

 

As​ ​the​ ​2018​ ​Winter​ ​Olympics​ ​is​ ​approaching,​ ​skiing​ ​fans​ ​are​ ​excited​ ​and​ ​prompted​ ​to construct​ ​a​ ​new​ ​ski​ ​resorts​ ​in​ ​Wasatch​ ​Peaks​ ​Ranch.​ ​Upon​ ​their​ ​request,​ ​we​ ​construct​ ​21​ ​skiing routes​ ​with​ ​1-2-2​ ​difficulty​ ​level​ ​distribution​ ​and​ ​a​ ​total​ ​slope​ ​length​ ​over​ ​160​ ​kilometers. ​ ​​ ​​ ​​

 

​In​ ​part​ ​1,​ ​we​ ​simplify​ ​the​ ​problem​ ​by​ ​constructing​ ​a​ ​13-by-13​ ​0-1​ ​matrix,​ ​seeking​ ​all​ ​the potential​ ​ski​ ​slopes​ ​as​ ​decision​ ​variables.​ ​To​ ​construct​ ​a​ ​topological​ ​structure​ ​for​ ​the​ ​routes,​ ​we find​ ​the​ ​nodes​ ​on​ ​the​ ​smooth​ ​terrains​ ​by​ ​comparing​ ​the​ ​normal​ ​vectors.​ ​We​ ​fill​ ​the​ ​matrix​ ​with​ ​1 or​ ​0​ ​to​ ​show​ ​whether​ ​the​ ​node​ ​is​ ​used​ ​after​ ​optimizing​ ​the​ ​solution​ ​using​ ​Lingo.​ ​On​ ​top​ ​of​ ​that, we​ ​apply​ ​Cluster​ ​Analysis​ ​to​ ​group​ ​the​ ​peaks​ ​into​ ​different​ ​groups​ ​to​ ​find​ ​the​ ​typical​ ​peaks​ ​and bowls​ ​that​ ​can​ ​be​ ​applied​ ​to​ ​the​ ​Linear​ ​Programming​ ​(0-1​ ​matrix)​ ​Model. ​ ​​ ​​ ​​ ​​ ​

 

In​ ​part​ ​2,​ ​we​ ​evaluate​ ​all​ ​the​ ​given​ ​data​ ​by​ ​employing​ ​multiple-criteria​ ​decision​ ​analysis.​ ​Our design​ ​of​ ​the​ ​resort​ ​is​ ​within​ ​the​ ​top​ ​5​ ​resorts​ ​among​ ​the​ ​given​ ​resorts.​ ​After​ ​processing​ ​the​ ​data, we​ ​go​ ​through​ ​an​ ​analytic​ ​hierarchy​ ​process​ ​to​ ​construct​ ​a​ ​clear​ ​criteria​ ​and​ ​apply​ ​it​ ​to​ ​our design.​ ​The​ ​major​ ​criteria​ ​include​ ​the​ ​total​ ​distance,​ ​skiable​ ​acres,​ ​vertical​ ​drop,​ ​number​ ​of​ ​runs, distribution​ ​of​ ​difficulty,​ ​number​ ​of​ ​lifts,​ ​and​ ​annual​ ​snowfall. ​ ​​ ​​ ​​

 

​After​ ​building​ ​our​ ​model,​ ​we​ ​come​ ​up​ ​with​ ​specific​ ​solution​ ​and​ ​design​ ​to​ ​each​ ​question.

 

Keywords:​ ​0-1​ ​matrix,​ ​multiple-criteria​ ​decision​ ​analysis,​ ​optimal​ ​solution,​ ​analytical hierarchy​ ​process,​ ​pairwise​ ​comparison.

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