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The unbounded parallel-batch scheduling with rejection

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Journal of the Operational Research Society

Abstract

In this paper, we consider the unbounded parallel-batch scheduling with rejection. A job is either rejected, in which case a certain penalty has to be paid, or accepted and processed in batches on a machine. The processing time of a batch is defined as the longest processing time of the jobs contained in it. Four problems are considered: (1) to minimize the sum of the total completion time of the accepted jobs and the total rejection penalty of the rejected jobs; (2) to minimize the total completion time of the accepted jobs subject to an upper bound on the total rejection penalty of the rejected jobs; (3) to minimize the total rejection penalty of the rejected jobs subject to an upper bound on the total completion time of the accepted jobs; (4) to find the set of all the Pareto optimal schedules. We provide a polynomial-time algorithm for the first problem. Furthermore, we show that all the other three problems are binary NP-hard and present a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for them.

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Acknowledgements

We thank two anonymous referees for their helpful comments on an earlier version of our paper. This research was supported in part by The Hong Kong Polytechnic University under Grant Number J-BB7J. Zhang and Lu were also supported in part by grants NSFC (10971201), NSFC (10901142) and NSFC-RGC (70731160633).

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Authors and Affiliations

  1. Zhengzhou University, Henan, Zhengzhou, People's Republic of China

    L Q Zhang & L F Lu

  2. The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    L F Lu & C T Ng

Authors
  1. L Q Zhang
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  2. L F Lu
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  3. C T Ng
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Correspondence to C T Ng.

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Zhang, L., Lu, L. & Ng, C. The unbounded parallel-batch scheduling with rejection. J Oper Res Soc 63, 293–298 (2012). https://doi.org/10.1057/jors.2011.31

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  • DOI: https://doi.org/10.1057/jors.2011.31

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