In this paper, we investigate the m-machine permutation flowshop scheduling problem where exact time lags are defined between consecutive operations of every job. The objective is to minimize the maximum lateness. We introduce different job types, depending on their time lags. We study polynomial special cases and provide a dominance relation. We derive lower and upper bounds that are integrated in a branch-and-bound procedure to solve the problem. We perform a computational analysis to evaluate the efficiency of the proposed method.