Online batch scheduling of equal-length jobs on two identical batch machines to maximise the number of early jobs.

We study the online batch scheduling of equal-length jobs on two identical batch machines. Each batch machine can process up tobjobs simultaneously as a batch (wherebis 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 capacityb, and then we provide a greedy online algorithm with a competitive ratio of 1/(b+ 1). For the preemption-restart model withb= ∞, 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. [ABSTRACT FROM PUBLISHER]