Scheduling jobs with release times on a machine with finite storage

Abstract

Consider a single machine with a buffer which can store up to b waiting jobs for some fixed b. Given the release times, the weights and the processing times of n consecutive jobs, a maximum weight subset of jobs is to be found that is schedulable without violating the buffer's capacity constraint. A polynomial algorithm for the unweighted loss-delay problem is presented. The weighted case is shown to be NP-hard as well as an unweighted two-machine version.

Untitled

“…Proof Nawijn et al [8] prove that the recognition version of problem 1|b I = b, r j , d j = ∞, s j = 1|∑w j U j is binary NP-complete. Examination of their constructed instance of that problem shows that the use of preemptions does not reduce the optimal cost.…”

“…Nawijn [7] studies a nonpreemptive, finite capacity input buffer problem in which the jobs that are not lost are processed in their order of arrival. Also, Nawijn et al [8] derive a polynomial time algorithm for the nonpreemptive problem of minimizing the number of lost jobs when the buffer capacity is a positive constant. They prove that the problem of minimizing the weighted number of lost jobs is binary NPhard.…”