We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive over time at their release dates. The task is to determine feasible preemptive schedule on single or multiple possibly unrelated machines that maximizes the number of complete before deadline. Due strong impossibility results for competitive analysis machine, we require contain some slac...

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 jobdependent penalties for each rejected job, and he must construct a schedule for the remaining jobs so as to optimize the preemptive makespan on the m machines plus the sum of the penalties of th...

A classical scheduling problem is to find schedules that minimize average weighted completion time of jobs with release dates. When multiple machines are available, the machine environments may range from identical machines (the processing time required by a job is invariant across the machines) at one end, to unrelated machines (the processing time required by a job on any machine is an arbitr...

We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine...

We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine...