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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,第五章案例：层次分析法在选择第三方物流供应商中的应用,2008.3.18,1,层次分析法的基本原理,层次分析法,(The Analytic Hierarchy Process,，简称,AHP),是美国著名运筹学家，匹兹堡大学教授,T,L,Sauty,于,20,世纪,70,年代中期提出的一种系统分析决策方法。,具有,定量与定性,结合的特点,1,层次分析法的基本原理,原理：,首先把问题层次化，然后根据问题的性质和要达到的总目标，将问题分解为不同的组成因素，并按照因素间的相互关联影响以及隶属关系将因素按不同层次聚集组合，形成一个层次分析模型，并最终把系统分析归结为最低层相对最高层的相对重要性权值的确定或相对优劣次序的排序问题。,2,建模,2,建模,特征向量权重,2,建模,Cs,p,1,p,2,p,n,p,1,a,11,a,12,a,1n,p,2,a,21,a,22,a,2n,p,n,a,n1,a,n2,a,nn,判断矩阵,2,建模,2,建模,根据正矩阵理论，,A,矩阵具有如下特点：,2,建模,2,建模,2,建模,矩阵最大特征值和特征向量求解方法：,线性代数,近似方法：,和积法,方根法（略）,2,建模,和积法计算其最大特征向量,A,p,1,p,2,p,3,p,4,p,5,p,6,p,1,1,1,1,4,1,1/2,p,2,1,1,2,4,1,1/2,p,3,1,1/2,1,5,3,1/2,p,4,1/4,1/4,1/5,1,1/3,1/3,p,5,1,1,1/3,3,1,1,p,6,2,2,2,3,1,1,判断矩阵,和积法具体计算步骤：,将判断矩阵的每一列元素作归一化处理，其元素的一般项为：,a,ij,=,a,ij,1,n,a,ij,(i,j=1,2,.n),A,p,1,p,2,p,3,p,4,p,5,p,6,p,1,1,1,1,4,1,1/2,p,2,1,1,2,4,1,1/2,p,3,1,1/2,1,5,3,1/2,p,4,1/4,1/4,1/5,1,1/3,1/3,p,5,1,1,1/3,3,1,1,p,6,2,2,2,3,1,1,6.25 5.75 6.53 20 7.33 3.83,A,p,1,p,2,p,3,p,4,p,5,p,6,p,1,0.16,0.17,0.15,0.20,0.14,0.13,p,2,0.16,0.17,0.30,0.20,0.14,0.13,p,3,0.16,0.09,0.15,0.25,0.42,0.13,p,4,0.04,0.04,0.03,0.05,0.05,0.09,p,5,0.16,0.17,0.05,0.15,0.14,0.26,p,6,0.32,0.34,0.30,0.15,0.14,0.26,6.25 5.75 6.53 20 7.33 3.83,将每一列经归一化处理后的判断矩阵按行相加为：,W,i,=,1,n,a,ij,(i=1,2,.n),A,p,1,p,2,p,3,p,4,p,5,p,6,p,1,0.16,0.17,0.15,0.20,0.14,0.13,p,2,0.16,0.17,0.30,0.20,0.14,0.13,p,3,0.16,0.09,0.15,0.25,0.42,0.13,p,4,0.04,0.04,0.03,0.05,0.05,0.09,p,5,0.16,0.17,0.05,0.15,0.14,0.26,p,6,0.32,0.34,0.30,0.15,0.14,0.26,0.951.101.200.300.931.51,A,p,1,p,2,p,3,p,4,p,5,p,6,p,1,0.16,0.17,0.15,0.20,0.14,0.13,p,2,0.16,0.17,0.30,0.20,0.14,0.13,p,3,0.16,0.09,0.15,0.25,0.42,0.13,p,4,0.04,0.04,0.03,0.05,0.05,0.09,p,5,0.16,0.17,0.05,0.15,0.14,0.26,p,6,0.32,0.34,0.30,0.15,0.14,0.26,0.951.101.200.300.931.51,5.99,B,p,1,p,2,p,3,p,4,p,5,p,6,p,1,0.16,0.17,0.15,0.20,0.14,0.13,p,2,0.16,0.17,0.30,0.20,0.14,0.13,p,3,0.16,0.09,0.15,0.25,0.42,0.13,p,4,0.04,0.04,0.03,0.05,0.05,0.09,p,5,0.16,0.17,0.05,0.15,0.14,0.26,p,6,0.32,0.34,0.30,0.15,0.14,0.26,0.16,0.18,0.20,0.05,0.16,0.25,W,权重,用和积法计算其最大特征向量为：,W=,（,W,1,，,W,2,W,n,),t,=,（,0.16,0.18,0.20,0.05,0.16,0.25,),t,即为所求的特征向量的近似解。,计算判断矩阵最大特征根,max,max,=,1,n,(BW),i,nW,i,(BW)=,1,1,1,4,1,1/2,1,1,2,4,1,1/2,1,1/2,1,5,3,1/2,1/4,1/4,1/5,1,1/3,1/3,1,1,1/3,3,1,1,2,2,2,3,1,1,0.16,0.18,0.20,0.05,0.16,0.25,=,1.025,1.225,1.305,0.309,1.066,1.64,max,=,1,n,(BW),i,nW,i,=,1.068,0.858,1.110,1.134,1.0875,1.093,+,+,+,+,+,=6.35,判断矩阵一致性指标,C.I.(Consistency Index),C.I.=,max,-n,n-1,判断矩阵一致性指标,C.I.(Consistency Index),C.I.=,6.35-6,6-1,=0.07,随机一致性比率,C.R.(Consistency Ratio),。,C.R.=,C.I,R.I.,0.07,1.24,=,=0.056 0.10,3,应用,AHP,选择第三方物流供应商,3.1,决策问题分析,（,1,）按总目标，子目标，评价标准直至具体措施的顺序分解为不同层次；,（,2,）先求出每一层次上各元素间的对比量化判断矩阵，进而求出每一层次的各元素对其上一层次某一元素的权重；,（,3,）最后再用加权和的方法递阶归并，以求出各方案对总目标的权重,（,4,）愈重要的目标权重愈大，权重值最大者即为最优方案。,3,应用,AHP,选择第三方物流供应商,3.2,确定层数及各层目标,3,应用,AHP,选择第三方物流供应商,3,应用,AHP,选择第三方物流供应商,3.3,模型及其求解,如图,1,所示。,根据各因素的重要性比较构造判断矩阵并进行计算，所得判断矩阵及相应计算结果如下：,3,应用,AHP,选择第三方物流供应商,3,应用,AHP,选择第三方物流供应商,3,应用,AHP,选择第三方物流供应商,3,应用,AHP,选择第三方物流供应商,3,应用,AHP,选择第三方物流供应商,3,应用,AHP,选择第三方物流供应商,3,应用,AHP,选择第三方物流供应商,按照上述计算和分析的结果，,应该选择第三方物流供应商,P,1,为最佳方案,。,应用层次分析法将对第三方物流供应商的定性选择转化为定性与定量分析选择相结合，为企业管理者从众多第三方物流供应商中选择最佳的第三方物流供应商提供了比较可靠和科学的依据，从而增加了企业战略决策的有效性和权威性。,AHP,局限性,1,）,AHP,方法也有致命的缺点，它,只能在给定的策略中去选择最优的,，而不能给出新的策略；,2,）,AHP,方法中所用的,指标体系需要有专家系统,的支持，如果给出的指标不合理则得到的结果也就不准确；,3,）,AHP,方法中进行多层比较的时候需要给出,一致性比较,，如果不满足一致性指标要求，则,AHP,方法方法就失去了作用；,4,）,AHP,方法需要求矩阵的特征值，但是在,AHP,方法中一般用的是求,平均值,（可以算术、几何、协调平均）的方法来求特征值，这对于一些病态矩阵是有系统误差的。,
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