Abstract:

The typical analytical algorithm for graphic evaluation and review technique (GERT) is based on the topological properties of the signal flow graph (Mason formula) and the moment generating function, whereas it is tremendously difficult to analyze the topological characteristics of the GERT network when the network consists of a large number of nodes and complex structure(including many loops). The complexity of GERT network may lead to misjudge and false negative of the loops. For this problem, the matrix representation of the GERT network is explored, the corresponding relationship between the Mason formula-based algorithm and the matrix transform is analyzed, and two kinds of algorithms based on matrix for GERT network are designed. The first method is to give the gain matrix of the signal flow graph and gain matrix of the flow graph for a given GERT network firstly, and then to study the relationship between the determinant of the gain matrix and the Mason formula, and to design the resolving algorithm finally. The other method is to utilize the transform operators on the matrix to represent the simplification operators of the signal flow graph including eliminating selfloop and some unconcerned nodes. As a consequence, the algorithm based on matrix transform is introduced. Finally, two illustrative examples are presented to demonstrate the convenience and accuracy of the proposed methods, which may provide a tool for the computer calculation of the GERT network.