# Improved algorithms for single machine scheduling with release dates and rejections

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## Abstract

We consider bi-criteria scheduling problems on a single machine with release dates and rejections and both the makespan and the total rejection cost have to be minimized. We consider three scenarios: (1) minimize the sum of the two objectives: makespan and total rejection cost, (2) minimize the makespan subject to a bound on the total rejection cost and (3) minimize the total rejection cost subject to a bound on the makespan. We summarize the results obtained in the literature and provide for several cases improved approximation algorithms and FPTASs.

## Keywords

Scheduling Release date Rejection Makespan Total rejection penalty Approximation algorithm## Mathematics Subject Classification

90B35 Scheduling theory, deterministic 68W25 Approximation algorithms## Notes

### Acknowledgments

Cheng He was supported in part by NSFC Grant 11201121 and CSC 201309895008 and young backbone teachers of Henan colleges 2013GGJS-079. Kangbok Lee was supported in part by PSC CUNY (The City University of New York) Grant TRADA-46-477.

### Compliance with ethical standards

### Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

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