This research extends the hybrid particle swarm optimization-based metaheuristic to solve the fuzzy parallel machine scheduling problems with bell-shaped fuzzy processing times. In this paper, we propose a discrete particle swarm optimization (DPSO) which comprises two components: a particle swarm optimization and genetic algorithm. In this paper, fuzzy arithmetic on bell-shaped fuzzy numbers is used to determine the completion time of jobs. We also use a defuzzification function to rank the fuzzy numbers. Under this ranking concept among fuzzy numbers, we plan to minimize the fuzzy makespan. An extensive numerical study on large-scale scheduling problems up to 100 jobs is conducted to assess the performance of the DPSO algorithm. The results show the proposed algorithm in comparison with lower bound to be very efficient for different structure instances.
