Algorithms for Parallel Machine Scheduling on Any Number of Machine

In this paper, we present algorithms for the problem of scheduling n independent jobs on m identical machines. As a generalization of the classical parallel machine scheduling problem each machine is available only at a machine dependent release time. For the problem of minimizing the make span, we develop a kind of linear time algorithm with a tight bound of 1+(m-1)/m. For the problem Pm|non-increasing job, known optimum|C
_max
, we develop a kind of algorithm with a tight bound of 5/4, when m=4, the algorithm has a tight bound of 6/5.