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We consider single-machine on-line scheduling problems where jobs arrive over time. A set of independent jobs has to be scheduled on the machine, where preemption is not allowed and the number of jobs is unknown in advance. Each job becomes available at its release date, which is not known in advance, and its characteristics, e.g., processing requirement,… (More)

We investigate the computational complexity of scheduling multiprocessor tasks with pres-pecified processor allocations. We consider two criteria: minimizing schedule length and minimizing the sum of the task completion times. In addition, we investigate the complexity of problems when precedence constraints or release dates are involved.

We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless P = N P, none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by APX-hardness proofs. We show that, whereas… (More)

We consider the problem of preemptively scheduling a set of $n$ jobs on $m$ (identical , uniformly related, or unrelated) parallel machines. The scheduler may reject a subset of the jobs and thereby incur job-dependent penalties for each rejected job, and he must construct a schedule for the remaining jobs so as to optimize the preemptive makespan on the… (More)

Parallel machine scheduling problems concern the scheduling of n jobs on m machines to minimize some function of the job completion times. If preemption is not allowed, then most problems are not only NP-hard, but also very hard from a practical point of view. In this paper, we show that strong and fast linear programming lower bounds can be computed for an… (More)

We consider the open shop, job shop, and ow shop scheduling problems with integral processing times. We give polynomial-time algorithms to determine if an instance has a schedule of length at most 3, and show that deciding if there is a schedule of length at most 4 is N P-complete. The latter result implies that, unless P = N P, there does not exist a… (More)