Scheduling with release times and rejection on two parallel machines

Abstract

In this paper we study scheduling with release times and job rejection on two parallel machines. In our scheduling model each job is either accepted and then processed by one of the two machines at or after its release time, or it is rejected and then a rejection penalty is paid. The objective is to minimize the makespan of the accepted job plus the total penalty of all rejected jobs. The scheduling problem is NP-hard in the ordinary sense. In this paper, we develop a 1.5 + -approximation algorithm for the problem, where is any given small positive constant.

Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty

“…where the second equality follows equality (6) and Lemma 4, and the last equality follows from π(B r * ) = 0. Therefore, Z = Z * , implying that the theorem holds.…”

“…where the second inequality follows from inequality (4) and the third inequality follows from inequality (6). Therefore, we have…”

“…where the second equality follows equality (6) and Lemma 4, and the last inequality follows from inequalities (5) and (7). To show that the bound is tight, consider the following instance with three jobs: Through the Process A(r), when r = r 0 = 0, the resulting schedule σ r 0 is to reject J 1 , J 2 , J 3 .…”

“…When there are exactly two machines. Zhong et al [6] developed a (3/2 + ε)-approximation algorithm for scheduling with release dates and rejection. When the number of machines is one, there are much more related results.…”

Scheduling with regular performance measures and optional job rejection on a single machine

“…Gerstl et al [6] explore minmax scheduling problems with acceptable lead-times, and propose extensions to position-dependent processing times, due-window and job-rejection. Zhong et al [23] address scheduling with release times and rejection on two parallel machines.…”