Scheduling with finite capacity input buffers

In many scheduling problems, a newly released job must be stored in an input buffer while it waits to begin processing. The lack of attention given to these buffers in the classical scheduling literature results from the implicit assumption that they have infinite capacity. In modern manufacturing environments, however, there are several important reasons for limiting buffer capacity. We study nonpreemptive single machine dynamic scheduling problems under the assumption that some jobs may be lost, either because of insufficient input buffer capacity, or because due dates cannot be met. The objective is to minimize the weighted or unweighted number of lost jobs. We study problems with zero, fixed or arbitrary buffer capacity, with unit or arbitrary processing times, and with unit or arbitrary buffer storage requirements. We present a complexity classification in which, for each problem, either an efficient algorithm is derived, or a proof is given that such an algorithm is unlikely to exist.