Batch scheduling with deadlines on parallel machines: An NP-hard case

The problem of scheduling groups of jobs on unrelated parallel machines in batches subject to group deadlines was studied by Brucker et al. (1997) and Kovalyov and Shafransky (1994). A classification of computational complexities of special cases was provided only for the situation when all groups have equal deadlines. We prove that the problem is strongly NP-hard for the case of different deadlines, identical machines, unit processing times and unit set-up times, and equal numbers of jobs in each group. The problem where machine deadlines are given instead of job deadlines is proved to be strongly NP-complete.