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We consider the on-line problem of scheduling jobs with precedence constraints on m machines. We concentrate in two models, the model of uniformly related machines and the model of restricted assignment. For the related machines model, we show a lower bound of ( √ m) for the competitive ratio of deterministic and randomized on-line algorithms, with or without preemptions even for known running times. This matches the deterministic upper bound of O( √ m) given by Ja e. The lower bound should bedoi:10.1016/s0166-218x(01)00272-4 fatcat:yqprd2y7ujgzhdxn7ps7a6x7zq