Comparative Study to Find the Critical Path Using Triangular Fuzzy Number

Abstract

The “Shortest path” problem which is a well-known and elemental problem in “Operational Research” associated to finding a path between two vertices (i.e. nodes) of a graph such that the sum of the weights ( like Cost, time and Distance) of its connecting edges is minimize. This problem is associated with many real-world applications.The Critical path problem is a classic and significant network optimization problem that appears in many applications, particularly in project planning and control the complex project, to implement the CPM we want clear determination of time duration. The out come of a conventional critical path approach computation does not accurately reflect the real-world situation. In this paper we developed a fuzzy critical path approach when the collected data’s are expressed in terms of triangular fuzzy numbers. In this article we presents a network based on critical path environment. The primary contribution of the work is to find the critical path by ranking method. A numerical example is shown to highlight the procedure of the proposed method at the end of this paper.