This paper studies the identical parallel machine scheduling problem with family set-up times and an objective of minimizing total weighted completion time (weighted flowtime). The family set-up time is incurred whenever there is a switch of processing from a job in one family to a job in another family. A heuristic is proposed in this paper for the problem. Computational results show that the proposed heuristic outperforms an existing heuristic, especially for large-sized problems, in terms of both solution quality and computation times. The improvement of solution quality is as high as 4.753% for six-machine problem and 7.822% for nine-machine problem, while the proposed heuristic runs three times faster than the existing one.
