In this paper, we address the scheduling problem with rejection in which we can choose a subset of jobs to process. Choosing not to process any job incurs a corresponding penalty. We consider the following problem for the first time: scheduling with rejection to minimize the total weighted completion time with the constraint of total penalties on identical parallel machines, where the number of...

We study classic scheduling problems on uniformly related machines. Efficient polynomial time approximation schemes (EPTAS’s) are fast and practical approximation schemes. New methods and techniques are essential in developing such improved approximation schemes, and their design is a primary goal of this research agenda. We present EPTAS’s for the scheduling problem of a set of jobs on uniform...

In this paper we present a new algorithm for the oo-line scheduling of parallel and independent jobs on a parallel processor system. To this end we introduce a machine model which is based on existing multiprocessors and accounts for the penalty of preemption. After examining the relation between the makespan and the total weighted completion time costs for the scheduling of parallel jobs it is...

This paper gives the positive answer to the question posed in the title for a wide class of minimization criteria including the maximum completion time, maximum lateness , total completion time, total weighted completion time, total tardiness, total weighted tardiness, number of late jobs and the weighted number of late jobs. That is any scheduling problem for m identical parallel machines to m...