Computational Procedure For Large Scale GERT Network Using Graph Theory

Abstract

This paper presents an algorithm to analyze the calculation of a large scale GERT network by means of the method of graph theory. The detection of path is made by applying latin square multiplication and the detection of circuit and loop is made by applying the Boolean matrix, reachability matrix and strongly connected matrix. A method is shown to obtain the determinant of network Δ(s) by the matrix L of touching circuit and loop as well as latin multiplication, and further to obtain Δ_k(s) by the calculated HP_j of the matrix of touching path, circuit and loop by using the coefficient of (l - γ_ij). A numerical investigation demonstrates the applicability of the described method.