Preemptive scheduling with finite capacity input buffers

In many scheduling problems, an arriving job is stored in an input buffer until it starts to be processed. Also, it may be necessary to hold a partially completed preempted job in an input buffer until processing of this job resumes. In the scheduling literature, most problems have been studied using the implicit assumption that the buffer has infinite capacity. We study preemptive single machine scheduling problems where the buffer capacity is finite. In this scheduling environment, jobs may be lost either because of insufficient input buffer capacity, or because due date requirements cannot be met. We examine problems where the objective is to minimize the weighted or unweighted number of lost jobs. Various assumptions about the generality of the data are examined. We present a complexity classification for various problems, either by deriving an efficient algorithm, or by proving that such an algorithm is unlikely to exist. Copyright Kluwer Academic Publishers 1997