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 \(1.5+\epsilon \)-approximation algorithm for the problem, where \(\epsilon \) is any given small positive constant.
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Acknowledgments
The authors thank the AE and the anonymous referees for their helpful comments and suggestions. This research was supported by the National Natural Science Foundation of China (71501051), the Humanities and Social Sciences Research Foundation of Ministry of Education of China (13YJC630239), and the Foundation for Distinguished Young Teachers in Higher Education of Guangdong Province (YQ201403).
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Zhong, X., Pan, Z. & Jiang, D. Scheduling with release times and rejection on two parallel machines. J Comb Optim 33, 934–944 (2017). https://doi.org/10.1007/s10878-016-0016-x
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DOI: https://doi.org/10.1007/s10878-016-0016-x