Batch scheduling of identical jobs on parallel identical machines

We study the classical batch scheduling problem with identical job processing times and identical setups on parallel identical machines. We show that, similar to the single machine case, the solution is given by a closed form, consisting of identical decreasing arithmetic sequences of batch sizes on the different machines. A very close-to-optimal integer solution is obtained in O(m+n) time, where m is the number of machines, and n is the number of jobs.