順序優先法

順序優先法(OPA)是一種多準則決策分析方法英語Multiple-criteria decision analysis(multi-criteria decision-making ,MCDM),有助於解決具有偏好關係集體決策問題。

描述

大多數的多準則決策分析方法,如層次分析法(analytic hierarchy Process, AHP)和網絡分析法英語Analytic network process(Analytic Network Process, ANP),是以成對比較矩陣為基礎的[1]

 
決策問題[2]

該方法使用線性規劃方法同時計算專家、評價指標和備選方案的權重[2]。在OPA方法中使用序數數據英語Ordinal data的主要原因是與涉及人類的群體決策問題中使用的精確比例相比,序數數據的可及性和準確性[3]

在現實世界中,專家們可能對某一選擇或評價指標沒有足夠的了解。這種情況下,問題的輸入數據是不完整的,此時需要在OPA線性規劃模型中刪除與評價指標或備選方案相關的約束條件[4]

近年來,各種類型的數據歸一化方法被應用於多準則決策方法 (multi-criteria decision-making ,MCDM) 中。Palczewski和 Satabun表明,使用各種數據歸一化方法可以改變多準則決策方法的最終排名[5]。Javed 及其同事表明,可以通過避免數據歸一化來解決多準則決策問題[6]。不需要對偏好關係進行歸一化,因此,OPA方法不需要數據歸一化[7]

OPA方法

OPA模型是一個線性規劃模型,可以利用單純形法來解決。該方法的步驟如下:[8][9][2]

第一步: 確定專家,並根據工作經驗、教育資格等確定專家的優先次序。

第二步: 確定評價指標,並確定每個專家對指標的偏好。

第三步: 確定備選方案,並由每個專家確定在每一評價指標下備選方案的偏好。

第四步: 構建以下線性規劃模型,並通過適當的優化軟件如LINGO、GAMS、MATLAB等進行求解。

 

在上述模型中。 代表專家的等級 ,  代表指標的等級 , 代表備選方案的等級 。而 代表專家i在評價指標j下備選方案k的權重。在解決OPA線性規劃模型後,每個備選方案的權重由以下公式計算。

 

每個評價指標的權重按以下公式計算。

 

每個專家的權重按以下公式計算。

 

例子

 
例子的決策問題

假設要調查買房子的問題[10]。在這個決策問題中,有兩位專家,同時有兩個評價指標,即成本(c)和建築質量(q),為房屋的選擇提供標準。另一方面,有三所房子(h1,h2,h3)可供購買。第一個專家(x)有三年的工作經驗,第二個專家(y)有兩年的工作經驗。該問題的結構如圖所示。

第 1 步:第一位專家(x)比專家(y)有更多經驗,因此 x>y。

第 2 步:專家對評價指標的偏好總結在下表中。

專家對評價指標的意見
評價指標 專家(x) 專家(y)
c 1 2
q 2 1

第 3 步:專家對備選方案的偏好總結在下表中。

專家對備選方案的意見
備選方案 專家(x) 專家(y)
c q c q
h1 1 2 1 3
h2 3 1 2 1
h3 2 3 3 2

第 4 步:根據輸入數據形成 OPA 線性規劃模型,具體如下。

 

用優化軟件求解上述模型後,得到專家、評價指標和備選方案的權重如下。

 

因此,房子1(h1)被認為是最佳選擇。此外,可以認為,評價指標成本(c)比評價指標建築質量(q)更重要。另外,根據專家的權重,可以認為,與專家(y)相比,專家(x)對最終選擇的影響更大。

應用

OPA方法在各個研究領域的應用總結如下。

農業、製造業、服務業

建築行業

能源與環境

醫療保健

信息技術

交通運輸

延伸

以下是 OPA 方法的幾個擴展。

  • 灰色順序優先法 (OPA-G)[7]
  • 模糊順序優先法 (OPA-F)[28]
  • OPA 中的置信度測量[8]
  • 魯棒順序優先法 (OPA-R)[9]
  • 混合 OPA-模糊 EDAS[13]
  • 混合 DEA-OPA 模型[11]
  • 混合型 MULTIMOORA-OPA[38]
  • 團體加權順序優先法 (GWOPA)[39]

軟件

以下非盈利工具可用於解決使用 OPA 方法的 MCDM 問題。

  • 基於網絡的解算器[40]
  • 基於 Excel 的解算器[41]
  • 基於林格的解算器[42]
  • 基於 Matlab 的求解器[43]

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