刘永祥 20060549 06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：从三家公司中选出一家订购电脑1、画出层次分析图W511W411W311W211W111主板硬盘内存电源CPU 丙乙甲2、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BP1P2P3P4P5P113351P21/31131/2P31/31131/2P41/311/311/3P512231 3 8 7.3 15 3.3BP1P2P3P4P5∑P10.33 0.38 0.41 0.33 0.30 1.76 P20.11 0.13 0.14 0.20 0.15 0.72 P30.11 0.13 0.14 0.20 0.15 0.72 P40.11 0.13 0.05 0.07 0.10 0.45 P50.33 0.25 0.27 0.20 0.30 1.36 ∑5.01 对向量W=(W1、W2、W3、W4、W5)t 归一化处理(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)=133511/31131.190.800.800.481.45=*1/21/31131/21/311/311/3122310.350.140.140.090.27计算判断矩阵最大特征跟λmax=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=0.023、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。