In todays globalized environment,the company heavily emphasise reducing carbon emission, therefore this study examines carbon emission within the context of production scheduling.In this study, a revised multi-start simulated-annealing algorithm (RMSA) is presented for permutation flowshop scheduling problems with the objectives of minimizing the carbon emission and total weighted tardiness. To evaluate the performance of the RMSA, computational experiments were conducted on the well-known benchmark problem set provided by Taillard. The non-dominated sets obtained from each of the different experimental combination parameters and the RMSA were compared, and then combined to form a net non-dominated front. As shown by experimental results, highly effective when compared to another methods.