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The unbounded parallel-batch scheduling with rejection

Author

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  • L Q Zhang

    (Zhengzhou University, Zhengzhou, Henan, People's Republic of China)

  • L F Lu

    (1] Zhengzhou University, Zhengzhou, Henan, People's Republic of China[2] The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

  • C T Ng

    (The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

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.

Suggested Citation

  • L Q Zhang & L F Lu & C T Ng, 2012. "The unbounded parallel-batch scheduling with rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(3), pages 293-298, March.
    • Handle: RePEc:pal:jorsoc:v:63:y:2012:i:3:p:293-298
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    Citations

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    Cited by:

    1. Jinwen Ou, 2020. "Near-linear-time approximation algorithms for scheduling a batch-processing machine with setups and job rejection," Journal of Scheduling, Springer, vol. 23(5), pages 525-538, October.
    2. Baruch Mor & Gur Mosheiov, 2016. "Minimizing maximum cost on a single machine with two competing agents and job rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1524-1531, December.
    3. Ou, Jinwen & Lu, Lingfa & Zhong, Xueling, 2023. "Parallel-batch scheduling with rejection: Structural properties and approximation algorithms," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1017-1032.

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