Best possible algorithms for online scheduling on identical batch machines with periodic pulse interruptions

Abstract

We consider an online scheduling problem on identical batch machines to minimize the makespan with periodic pulse interruptions. Periodic pulse interruptions are machine unavailable intervals with negligible length and divide the scheduling horizon into available intervals. Jobs are released online over time and processed simultaneously as batches with the same processing times on identical batch machines. Every batch must be entirely processed in an available interval without any preemption. For unbounded machine capacity, we design best possible online algorithms with the competitive ratios of 1+η and 2m for a single machine (m=1) and m identical parallel machines (m≥2), respectively, where η≈0.8019 is the positive root of η3+2η2−η=1. For bounded machine capacity, we derive a best possible online algorithm with a competitive ratio of 1+η.