Optimal Batch Schedules for Parallel Machines

We consider the problem of batch scheduling on parallel machines where jobs have release times, deadlines, and identical processing times. The goal is to schedule these jobs in batches of size at most B on m identical machines. Previous work on this problem primarily focused on finding feasible schedules. Motivated by the problem of minimizing energy, we consider problems where the number of batches is significant. Minimizing the number of batches on a single processor previously required an impractical O(n) dynamic programming algorithm. We present a O(n) algorithm for simultaneously minimizing the number of batches and maximum completion time, and give improved guarantees for variants with infinite size batches, agreeable release times, and batch “budgets”. Finally, we give a pseudo-polynomial algorithm for general batch-count-sensitive objective functions and correct errors in previous results.