, Volume 14, Issue 1, pp 41–55 | Cite as

Improved algorithms for single machine scheduling with release dates and rejections

  • Cheng He
  • Joseph Y.-T. Leung
  • Kangbok Lee
  • Michael L. PinedoEmail author
Research paper


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.


Scheduling Release date Rejection Makespan  Total rejection penalty Approximation algorithm 

Mathematics Subject Classification

90B35 Scheduling theory, deterministic 68W25 Approximation algorithms 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Cheng He
    • 1
  • Joseph Y.-T. Leung
    • 2
  • Kangbok Lee
    • 3
  • Michael L. Pinedo
    • 4
    Email author
  1. 1.School of ScienceHenan University of TechnologyZhengzhouChina
  2. 2.Department of Computer ScienceNew Jersey Institute of TechnologyNewarkUSA
  3. 3.Department of Business and Economics, York CollegeThe City University of New YorkJamaicaUSA
  4. 4.Department of Information, Operations and Management Sciences, Stern School of BusinessNew York UniversityNew YorkUSA

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