This article considers two- and three-machine flowshop scheduling problems, where the operation on the last machine may or may not be omitted. The objective is to minimize maximum lateness for the two-machine flowshop and makespan for the three-machine flowshop, having the above-mentioned option, designated as
, respectively. Given that both problems are NP-hard, a heuristic and a branch and ... [Show full abstract] bound algorithm are proposed to solve each problem. Dominance properties are proposed and worse case performances under certain conditions are provided. Computational results show that the heuristic algorithm for each problem consistently generates good schedules.