顺序优先法

顺序优先法(OPA)是一种多准则决策分析方法英语Multiple-criteria decision analysis(multi-criteria decision-making ,MCDM),有助于解决具有偏好关系集体决策问题。

描述

大多数的多准则决策分析方法,如层次分析法(analytic hierarchy Process, AHP)和网络分析法英语Analytic network process(Analytic Network Process, ANP),是以成对比较矩阵为基础的[1]

 
决策问题[2]

该方法使用线性规划方法同时计算专家、评价指标和备选方案的权重[2]。在OPA方法中使用序数数据英语Ordinal data的主要原因是与涉及人类的群体决策问题中使用的精确比例相比,序数数据的可及性和准确性[3]

在现实世界中,专家们可能对某一选择或评价指标没有足够的了解。这种情况下,问题的输入数据是不完整的,此时需要在OPA线性规划模型中删除与评价指标或备选方案相关的约束条件[4]

近年来,各种类型的数据归一化方法被应用于多准则决策方法 (multi-criteria decision-making ,MCDM) 中。Palczewski和 Satabun表明,使用各种数据归一化方法可以改变多准则决策方法的最终排名[5]。Javed 及其同事表明,可以通过避免数据归一化来解决多准则决策问题[6]。不需要对偏好关系进行归一化,因此,OPA方法不需要数据归一化[7]

OPA方法

OPA模型是一个线性规划模型,可以利用单纯形法来解决。该方法的步骤如下:[8][9][2]

第一步: 确定专家,并根据工作经验、教育资格等确定专家的优先次序。

第二步: 确定评价指标,并确定每个专家对指标的偏好。

第三步: 确定备选方案,并由每个专家确定在每一评价指标下备选方案的偏好。

第四步: 构建以下线性规划模型,并通过适当的优化软件如LINGO、GAMS、MATLAB等进行求解。

 

在上述模型中。 代表专家的等级 ,  代表指标的等级 , 代表备选方案的等级 。而 代表专家i在评价指标j下备选方案k的权重。在解决OPA线性规划模型后,每个备选方案的权重由以下公式计算。

 

每个评价指标的权重按以下公式计算。

 

每个专家的权重按以下公式计算。

 

例子

 
例子的决策问题

假设要调查买房子的问题[10]。在这个决策问题中,有两位专家,同时有两个评价指标,即成本(c)和建筑质量(q),为房屋的选择提供标准。另一方面,有三所房子(h1,h2,h3)可供购买。第一个专家(x)有三年的工作经验,第二个专家(y)有两年的工作经验。该问题的结构如图所示。

第 1 步:第一位专家(x)比专家(y)有更多经验,因此 x>y。

第 2 步:专家对评价指标的偏好总结在下表中。

专家对评价指标的意见
评价指标 专家(x) 专家(y)
c 1 2
q 2 1

第 3 步:专家对备选方案的偏好总结在下表中。

专家对备选方案的意见
备选方案 专家(x) 专家(y)
c q c q
h1 1 2 1 3
h2 3 1 2 1
h3 2 3 3 2

第 4 步:根据输入数据形成 OPA 线性规划模型,具体如下。

 

用优化软件求解上述模型后,得到专家、评价指标和备选方案的权重如下。

 

因此,房子1(h1)被认为是最佳选择。此外,可以认为,评价指标成本(c)比评价指标建筑质量(q)更重要。另外,根据专家的权重,可以认为,与专家(y)相比,专家(x)对最终选择的影响更大。

应用

OPA方法在各个研究领域的应用总结如下。

农业、制造业、服务业

建筑行业

能源与环境

医疗保健

信息技术

交通运输

延伸

以下是 OPA 方法的几个扩展。

  • 灰色顺序优先法 (OPA-G)[7]
  • 模糊顺序优先法 (OPA-F)[28]
  • OPA 中的置信度测量[8]
  • 鲁棒顺序优先法 (OPA-R)[9]
  • 混合 OPA-模糊 EDAS[13]
  • 混合 DEA-OPA 模型[11]
  • 混合型 MULTIMOORA-OPA[38]
  • 团体加权顺序优先法 (GWOPA)[39]

软件

以下非盈利工具可用于解决使用 OPA 方法的 MCDM 问题。

  • 基于网络的解算器[40]
  • 基于 Excel 的解算器[41]
  • 基于林格的解算器[42]
  • 基于 Matlab 的求解器[43]

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