Scheduling on a batch machine with job compatibilities

We consider the problem of minimizing the makespan on a single batch processing machine, in which jobs are not all compatible, i.e. there are at least two jobs that can not be processed simultaneously in the same batch. The capacity of the batch processing machine can be finite or infinite. The processing time of a batch is given by the processing time of the longest jobs in the batch. We prove NP-hardness of the general problem and present polynomial algorithms for several special cases.