GERT網(wǎng)絡的矩陣式表達及求解模型
發(fā)布時間：2019-04-27 19:47
【摘要】：圖示評審技術(graphic evaluation and review technique,GERT)解析法一般利用信號流圖的拓撲特征(梅森公式)和矩母函數(shù)進行求解,但當GERT網(wǎng)絡節(jié)點較多且結構復雜(回路眾多)時,拓撲結構特征的分析十分困難,易出現(xiàn)錯判或遺漏情況。針對此問題,將GERT網(wǎng)絡用矩陣形式進行表征,分析了以梅森公式為基礎的解析法與矩陣變換的關系,設計了兩類基于矩陣的GERT求解算法。首先給出GERT網(wǎng)絡與信號流圖增益矩陣、流圖增益矩陣一一對應關系,分析增益矩陣行列式變換與信號流圖求解公式的對應關系,設計GERT網(wǎng)絡的增益矩陣行列式變換求解算法。另外,研究GERT網(wǎng)絡(信號流圖)化簡操作(消除自環(huán)、消除節(jié)點)在信號流圖增益矩陣上的變換形式,提出了GERT網(wǎng)絡解析的矩陣變換方法。最后用兩個例子說明矩陣表征及求解模型的簡便性和正確性,為GERT解析的計算機操作奠定基礎。
[Abstract]:(graphic evaluation and review technique,GERT (graphical evaluation technique) analytical method usually uses topological characteristics of signal flow diagram (Mason formula) and moment generating function to solve, but when GERT network has more nodes and complex structure (numerous loops), The analysis of topological features is very difficult, and it is easy to misjudge or omit. In order to solve this problem, the GERT network is represented in the form of matrix, the relationship between analytic method based on Mason formula and matrix transformation is analyzed, and two kinds of matrix-based GERT algorithms are designed. Firstly, the corresponding relation between GERT network and signal flow graph gain matrix, flow graph gain matrix one-to-one correspondence is given. The corresponding relation between gain matrix determinant transformation and signal flow graph solving formula is analyzed, and the algorithm of GERT network gain matrix determinant transformation is designed. In addition, the transformation form of GERT network (signal flow graph) simplification operation (eliminating self-loop and eliminating node) on the gain matrix of signal flow graph is studied, and the analytic matrix transformation method of GERT network is proposed. Finally, two examples are given to illustrate the simplicity and correctness of the matrix representation and solution model, which lays the foundation for the computer operation of GERT analysis.
【作者單位】： 南京航空航天大學經(jīng)濟與管理學院;南京航空航天大學灰色系統(tǒng)研究所;英國De
【基金】：歐盟第7研究框架瑪麗居里國際人才引進計劃Fellow項目(FP7-PIIF-GA-2013-629051) 國家自然科學基金(91324003,71671090,71671091) 國家社科基金重點項目(12AZD102) 中央高�；究蒲袠I(yè)務費專項資金(NJ20140032,NP2015208) 江蘇省普通高校研究生科研創(chuàng)新計劃項目(KYZZ15_0092)資助課題
【分類號】：C912.3
，
本文編號：2467261
[Abstract]:(graphic evaluation and review technique,GERT (graphical evaluation technique) analytical method usually uses topological characteristics of signal flow diagram (Mason formula) and moment generating function to solve, but when GERT network has more nodes and complex structure (numerous loops), The analysis of topological features is very difficult, and it is easy to misjudge or omit. In order to solve this problem, the GERT network is represented in the form of matrix, the relationship between analytic method based on Mason formula and matrix transformation is analyzed, and two kinds of matrix-based GERT algorithms are designed. Firstly, the corresponding relation between GERT network and signal flow graph gain matrix, flow graph gain matrix one-to-one correspondence is given. The corresponding relation between gain matrix determinant transformation and signal flow graph solving formula is analyzed, and the algorithm of GERT network gain matrix determinant transformation is designed. In addition, the transformation form of GERT network (signal flow graph) simplification operation (eliminating self-loop and eliminating node) on the gain matrix of signal flow graph is studied, and the analytic matrix transformation method of GERT network is proposed. Finally, two examples are given to illustrate the simplicity and correctness of the matrix representation and solution model, which lays the foundation for the computer operation of GERT analysis.
【作者單位】： 南京航空航天大學經(jīng)濟與管理學院;南京航空航天大學灰色系統(tǒng)研究所;英國De
【基金】：歐盟第7研究框架瑪麗居里國際人才引進計劃Fellow項目(FP7-PIIF-GA-2013-629051) 國家自然科學基金(91324003,71671090,71671091) 國家社科基金重點項目(12AZD102) 中央高�；究蒲袠I(yè)務費專項資金(NJ20140032,NP2015208) 江蘇省普通高校研究生科研創(chuàng)新計劃項目(KYZZ15_0092)資助課題
【分類號】：C912.3
，
本文編號：2467261
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