A note on the complexity of the concurrent open shop problem

The concurrent open shop problem is a relaxation of the well known open job shop problem, where the components of a job can be processed in parallel by dedicated, component specific machines. Recently, the problem has attracted the attention of a number of researchers. In particular, Leung et al. (2005) show, contrary to the assertion in Wagneur and Sriskandarajah (1993), that the problem of minimizing the average job completion time is not necessarily strongly NP-hard. Their finding has thus once again opened up the question of the problem’s complexity. This paper re-establishes that, even for two machines, the problem is NP-hard in the strong sense.