Scheduling on Batch Processing Machines with Constraints of Compatibility Between Jobs

Abstract We consider the problem of minimizing the makespan on batch processing machines, 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. Each job has a processing time and the capacity of batch processing machines can be finite or infinite. The processing time of a batch is given by the processing time of the longest job in the batch. We prove the NP-hardness of the general problem and present heuristics and exact algorithms for its solution.