AHP层次分析法--实例

刘永祥2006054906级工商5班一、用AHP分析法解答“公司从联想、华硕、同方三个品牌中选择一家，订购价位在5000元的台式机”的问题。用到的五个相关属性是：CPU、内存、硬盘、电源、主板，分别用P1、P2、P3、P4、P5来表示。判断矩阵B：CPU内存硬盘电源主板BP1P2P3P4P5P113351P21/31131/2P31/31131/2P41/311/311/3P512231二、公司给三家公司（以“甲、乙、丙”表示）的单个目标的属性进行打分。1、CPUB1甲乙丙甲132乙1/311/2丙1/2212、内存B2甲乙丙甲131/2乙1/311/6丙2613、硬盘B3甲乙丙甲135乙1/313丙1/51/314、电源B4甲乙丙甲11/32乙316丙1/21/615、主板B5甲乙丙甲11/23乙216丙1/31/61解：1、画出层次分析图从三家公司中选出一家订购电脑CPU内存硬盘电源主板甲乙丙W111W211W311W411W5112、求出目标层的权重估计用“和积法”计算其最大特征向量判断矩阵B：CPU内存硬盘电源主板BP1P2P3P4P5P113351P21/31131/2P31/31131/2P41/311/311/3P512231387.3153.3BP1P2P3P4P5∑P10.330.380.410.330.301.76P20.110.130.140.200.150.72P30.110.130.140.200.150.72P40.110.130.050.070.100.45P50.330.250.270.200.301.36∑5.01对向量W=(W1、W2、W3、W4、W5)t归一化处理1iinii(i=1,2,……n)Wt=(0.35,0.14,0.14,0.09,0.27)W=(W1、W2、W3、W4、W5)T=(0.35,0.14,0.14,0.09,0.27)T(BW)=133511/31131/21/31131/21/311/311/312231计算判断矩阵最大特征跟λmaxmax1()niiiBWnW=1.19/5*0.35+0.8/5*0.14+0.8/5*0.14+0.48/5*0.09+1.45/5*0.27=5.11C.I.=(λmax-N)/(N-1)=(5.11-5)/(5-1)=0.03C.R.=0.03/1.12=0.020.350.140.140.090.27*=1.190.800.800.481.453、求出方案层对目标层的最大特征向量（同2），求得：(W11W21W31)=(0.54,0.16,0.30)(W12W22W23)=(0.30,0.10,0.60)(W13W23W33)=(0.63,0.26,0.11)(W14W24W34)=(0.22,0.67,0.11)(W15W25W35)=(0.30,0.60,0.10)4、求得三家公司的总得分：甲的得分=Wi*Wi1=0.35*0.54+0.14*0.3+0.14*0.63+0.09*0.22+0.27*0.3=0.42乙的得分=Wi*Wi2=0.35*0.16+0.14*0.1+0.14*0.26+0.09*0.67+0.27*0.6=0.33丙的得分=Wi*Wi3=0.35*0.30+0.14*0.6+0.14*0.11+0.09*0.11+0.27*0.1=0.24所以应该选择甲（联想）公司进行电脑订购。