Open shop scheduling with makespan and total completion time criteria

In this paper we study the two machine open shop scheduling problem with a hierarchical objective: minimize the total completion time subject to minimum makespan. We show that this problem is distinct from the closely related problem of minimizing the total completion time. We develop polynomial-time algorithms for three special cases and an asymptotically optimal polynomial-time heuristic when a machine is dominant. We also extend some of our results to the three machine open shop case.