(1) Department of Industrial and Systems Engineering, Florida International University, Miami, FL, USA;(2) Department of Industrial Engineering and Management, Mingchi University of Technology, Taipei, Taiwan
Abstract:
We consider the problem of minimizing the makespan on a batch processing machine, in which jobs are not all compatible. Only
compatible jobs can be included into the same batch. This relation of compatibility is represented by a split graph. All jobs
are available at the same date. The capacity of the batch processing machine is finite or infinite. The processing time of
a batch is given by the processing time of the longest job in the batch. We establish the NP-hardness of the general problem
and present polynomial algorithms for several special cases.