In this paper, we investigate the m-machine permutation flowshop scheduling problem where exact time lags are defined between consecutive operations of every job. This generic model can be used for the study and analysis of various real situations, which may arise, for instance, in food-producing, pharmaceutical or steel industries. The objective is to minimize the maximum lateness. 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. Three branching schemes are proposed and compared. We perform a computational analysis to evaluate the efficiency of the developed method.