Abstract
This article studies online scheduling of equal length jobs with precedence constraints on m parallel batching machines. The jobs arrive over time. The objective is to minimise the total weighted completion time of jobs. Denote the size of each batch by b with b = ∞ in the unbounded batching and b < ∞ in the bounded batching. For the unbounded batching version, we provide an online algorithm with a best possible competitive ratio of ρ m , where ρ m is the positive solution of ρ m+1 − ρ = 1. The algorithm is also best possible when the jobs have identical weights. For the bounded batching version with identical weights of jobs, we provide an online algorithm with a competitive ratio of 2.
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