This paper addresses the multiobjective permutation flow shop scheduling problem, where makespan and total flow time are to be minimized simultaneously. We solve the problem by an extended version of the multiobjective evolutionary algorithm based on decomposition (MOEA/D). We investigate the effects of scalarization functions and the replacement mechanism. We also incorporate local search into MOEA/D and investigate design issues including individuals to do local search and resource allocation. Experiments are conducted on 90 public problem instances with different scale, and research findings are reported. Comparing with the state of the art, our algorithm shows competitive performance on small-scale instances and superior performance on medium- and large-scale instances.