Appropriate scheduling and sequencing of tasks on machines is one of the basic and significant problems that a shop or a factory manager encounters; this is why in recent decades extensive studies have been done on scheduling issues. One type of scheduling problems is just-in-time (JIT) scheduling and in this area, motivated by JIT manufacturing, this study investigates a mathematical model for appraising a multi-objective programing that minimize total weighted tardiness, earliness and total flowtime with fuzzy parameters on parallel machines, simultaneously with respect to the impact of machine deterioration. Besides, in this paper attempted to present a defuzzification approach and a heuristic method based on genetic algorithm (GA) to solve the proposed model. Finally, several dominant properties of optimal solutions are demonstrated in comparison with the results of a state-of-the-art commercial solver and the simulated annealing method that is followed by illustrating some instances for indicating validity and efficiency of the method. Manuscript profile