Scheduling jobs with release dates on parallel batch processing machines
Discrete Applied Mathematics
Short Communication: On scheduling unbounded batch processing machine(s)
Computers and Industrial Engineering
An asymptotic PTAS for batch scheduling with nonidentical job sizes to minimize makespan
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Scheduling an unbounded batching machine with job processing time compatibilities
Discrete Applied Mathematics
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
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We consider batch processing jobs to minimize the mean completion time. A batch processing machine can handle up to $B$ jobs simultaneously. Each job is represented by an arrival time and a processing time. Jobs processed in a batch have the same completion time, i.e., their common starting time plus the processing time of their longest job. For batch processing, non-preemptive scheduling is usually required and we discuss this case. The batch processing problem reduces to the ordinary uniprocessor system scheduling problem if $B=1$. We focus on the other extreme case $B=+\infty$. Even for this seemingly simple extreme case, we are able to show that the problem is NP-hard for the weighted version. In addition, we establish a polynomial time algorithm for a special case when there are only a constant number of job processing times. Finally, we give a polynomial time approximation scheme for the general case.