购车问题的数学模型

购车问题的数学模型

摘要

本文针对不同人群购车的考虑因素，以及市场上几款典型用车的各项性能指标，使用层次分析法（AHP）建立数学模型分析各种汽车的市场前景。层次分析法是对1些较为复杂、较为模糊的问题作出决策的简易方法，它特别适用于那些难于完全定量分析的问题。模型分为3个层次：目标层（购车），准则层（汽车性能指标）和方案层（汽车购买选择）。目标层是分析问题的预定目标，也就是购车。准则层包含了为实现目标所涉及的中间环节，根据不同人群在购车时所考虑因素，建立正互反矩阵，计算出权重向量，得出不同人群购车时的偏重因素。方案层包括了为实现目标可供选择的各种措施或决策方案，也是通过计算权重向量，得出各种汽车在同1指标中的优劣。最后将准则层和方案层进行整合，即可得出不同人群可供选择的车型。把模型得出的结论和搜集的资料进行对比，可以发现两者的结论基本1致，说明该模型和实际比较贴近，结果比较合理。

关键词：购车问题；决策；层次分析；1致性；权重向量。
 
                                   Abstract

  The article is concerning consideration automobiles and various function targets of above typical cars , I established Maths model to analyze market prospects of different cars by use of AHP . It fives easy solutions to some complex and unclear problems , and is suitable for those problems not solved by quantitative analysis in particular . This model consists of three gradations : Aim(purchasing the car) , principle(capability target) and plan(choosing the car) . The aim is a predetermined one for problem analysis , which is automobile purchase . The principle includes middle segments involved for the realization of goals . According to adequate consideration of different consumer needs , setting up matrix , counting vectors ,I get the preferred elements of them to purchase a car . The plan includes kinds of suggestions for choices . Then advantages and disadvantages of the car are concluded under the models are finished for buyers to choose . Through the comparison between the conclusion from the model and material collected if the result is mostly the same , that means the model is close to reality and the the result is reasonable .

Key words : purchasing , decisopn , consistency , matrix