Abstract
We study the online batch scheduling of equal-length jobs on two identical batch machines. Each batch machine can process up to b jobs simultaneously as a batch (where b is called the capacity of the machines). The goal is to determine a schedule that maximises the (weighted) number of early jobs. For the non-preemptive model, we first present an upper bound that depends on the machine capacity b, and then we provide a greedy online algorithm with a competitive ratio of 1/(b + 1). For the preemption-restart model with b = ∞, we first show that no online algorithm has a competitive ratio greater than 0.595, and then we design an online algorithm with a competitive ratio of .
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