Flow shop scheduling model (FSSM) is an important area of research in the field of Scheduling theory and it has many real applications in the industrial field. This study involves flow shop scheduling problem having machines on three levels in which utilization time of each task is considered as fuzzy triangular number. The concept of like parallel machines at each stage is also considered. Unit operational costs of jobs are also involved. The goal of this research is to recommend a heuristic approach inspired by Genetic algorithm (GA) which on implementation, provides an optimal or near-optimal schedule to reduce the make-span. Numerical example is also given to establish the usefulness of the proposed approach, and to approve the presentation, the results are compared with the existing methods like Branch and Bound (B & B).
