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.
