A new approach for solving fuzzy critical path problem using analysis of events

This paper deals with a novel project scheduling approach considering fuzzy duration. Hereby, duration of activity has assumed to follow L–R fuzzy number. The solution methodology is to apply a combination of linear programming formulation and Zadeh’s extension principle. Two LP models are proposed in order to calculate earliest and latest events time in project scheduling problem. The membership function of earliest and latest times of events are derived by calculating lower and upper bounds of earliest and latest times considering different α-cuts of fuzzy duration. Critical events in which some part of project should be timely accomplished are also determined. The resulting approach avoids generating negative and infeasible solution while backward pass calculation conducted. Finally, a numerical illustration is given to demonstrate superiority of proposed approach over existing methods in the literature.