DETERMINATION OF CRITICAL PATH IN PROJECT NETWORK WITH IMPRECISE INFORMATION

Abstract

The purpose of the critical path method (CPM) is to identify the critical activities on the critical path of a project network. The successful implementation of CPM required the availability of clearly determined time duration for each activity in the project. But in real situations, for many projects we may use human judgments for estimating the duration of activities, leading to uncertainty or vagueness about the time duration for activities on a project network. This has to lead the development of the fuzzy critical path method (FCPM). In the FCPM, there is a way to deal with the imprecise data by employing the concept of fuzziness, where the vague activity times can be represented by fuzzy sets. In this study, a new method has been developed based upon the concepts of fuzzy sets, linear programming formulation, and different fuzzy ranking methods to solve and determine the fuzzy critical path of project network scheduling problems under imprecise environment. We assume that the duration of activities in the project network are given a new representation of triangular fuzzy numbers. In the proposed method of FCPM problem, we use fuzzy arithmetic operations and different ranking methods to identify the FCP of the fuzzy project network by computing and comparing project characteristics such as the Earliest start, Latest finish and Total floats of fuzzy activity times. Example is provided to show the efficiency of the proposed method.