Possibilistic Moments for the Task Duration in Fuzzy PERT

Abstract

Program (or project) evaluation review technique (PERT) has remained a modern method in project scheduling for decades. Since its invention, numerous authors have tried modifications to its basic method in an attempt to overcome its intrinsic drawbacks. In this paper, the authors research improvements to the Fuzzy version of PERT. The initial motivation is the avoidance of the backward recursion problem in Fuzzy PERT, with fuzzy input data for the task durations through an alternative approach. Furthermore, the authors propose various membership functions for the representation of the fuzzy task duration in accordance with the nature of each task. This approach is intended to give more realistic results. The tools for this operation are the possibilistic mean and the possibilistic variance of fuzzy numbers. The possibilistic method acts as a defuzzification method that results in a crisp value as an outcome both for the task times (earliest/latest start - earliest/latest finish) and for the floats (total/free/safety). The authors also base this study on estimates of experts in project scheduling who are experienced in time management. A practical application is also provided for a better comprehension of the proposed method.