Non-bottleneck machines in three-machine flow shops

The paper deals with the classical problem of minimizing the makespan in a three-machine flow shop. When any one of the three machines is a non-bottleneck machine, the problem is efficiently solvable by one of three algorithms from the literature. We show that even if one chooses the best solution, the worst-case performance ratio of these algorithms is 2, and the bound of 2 is tight. We also present a new sufficient condition for identifying the intermediate non-bottleneck machine which is weaker than all conditions proposed so far.