GERT网络的矩阵式表达及求解模型
发布时间：2019-04-27 19:47
【摘要】：图示评审技术(graphic evaluation and review technique,GERT)解析法一般利用信号流图的拓扑特征(梅森公式)和矩母函数进行求解,但当GERT网络节点较多且结构复杂(回路众多)时,拓扑结构特征的分析十分困难,易出现错判或遗漏情况。针对此问题,将GERT网络用矩阵形式进行表征,分析了以梅森公式为基础的解析法与矩阵变换的关系,设计了两类基于矩阵的GERT求解算法。首先给出GERT网络与信号流图增益矩阵、流图增益矩阵一一对应关系,分析增益矩阵行列式变换与信号流图求解公式的对应关系,设计GERT网络的增益矩阵行列式变换求解算法。另外,研究GERT网络(信号流图)化简操作(消除自环、消除节点)在信号流图增益矩阵上的变换形式,提出了GERT网络解析的矩阵变换方法。最后用两个例子说明矩阵表征及求解模型的简便性和正确性,为GERT解析的计算机操作奠定基础。
[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.
【作者单位】： 南京航空航天大学经济与管理学院;南京航空航天大学灰色系统研究所;英国De
【基金】：欧盟第7研究框架玛丽居里国际人才引进计划Fellow项目(FP7-PIIF-GA-2013-629051) 国家自然科学基金(91324003,71671090,71671091) 国家社科基金重点项目(12AZD102) 中央高校基本科研业务费专项资金(NJ20140032,NP2015208) 江苏省普通高校研究生科研创新计划项目(KYZZ15_0092)资助课题
【分类号】：C912.3
，
本文编号：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.
【作者单位】： 南京航空航天大学经济与管理学院;南京航空航天大学灰色系统研究所;英国De
【基金】：欧盟第7研究框架玛丽居里国际人才引进计划Fellow项目(FP7-PIIF-GA-2013-629051) 国家自然科学基金(91324003,71671090,71671091) 国家社科基金重点项目(12AZD102) 中央高校基本科研业务费专项资金(NJ20140032,NP2015208) 江苏省普通高校研究生科研创新计划项目(KYZZ15_0092)资助课题
【分类号】：C912.3
，
本文编号：2467261
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