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A two-agent single-machine scheduling problem to minimize the total cost with release dates

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Abstract

This paper considers a two-agent scheduling problem with arbitrary release dates on a single machine. The cost of the first agent is the maximum weighted completion time of its jobs while the cost of the second agent is the total weighted completion time of its jobs. The goal is to schedule the jobs such that the total cost of the two agents is minimized. The problem is known to be strongly NP-hard. Thus, as an alternative, a branch-and-bound algorithm incorporating several dominance properties and a lower bound is provided to derive the optimal solution and a largest- order-value method combined with proposed three initials is developed to derive the near-optimal solutions for the problem. Computational results are also presented to evaluate the performance of the proposed algorithms.

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Acknowledgments

We thank the Editor, an Associate Editor, and two anonymous referees for their helpful comments on the earlier version of our paper. This paper was supported in part by the National Natural Science Foundation of China (71301022); in part by the Personnel Training Fund of Kunming University of Science and Technology under Grant Number KKSY201407098; and in part by the Ministry of Science Technology (MOST) of Taiwan under Grant No. NSC 102-2221-E-035-070-MY3, Grant No. MOST 103-2410-H-035-022-MY2, and Grant No. NSC 102-2410-H-264-003.

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Authors and Affiliations

  1. School of Management Science and Engineering, Dalian University of Technology, Dalian, 116023, China

    Du-Juan Wang

  2. Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, China

    Yunqiang Yin

  3. Department of Healthcare Management, Yuanpei University, Hsinchu, Taiwan

    Wen-Hsiang Wu

  4. Department of Business Administration, Kang-Ning Junior College of Medical Care and Management, Taipei, Taiwan

    Wen-Hung Wu & Peng-Hsiang Hsu

  5. Department of Statistics, Feng Chia University, Taichung, Taiwan

    Chin-Chia Wu

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  1. Du-Juan Wang
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  2. Yunqiang Yin
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  3. Wen-Hsiang Wu
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  4. Wen-Hung Wu
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  5. Chin-Chia Wu
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  6. Peng-Hsiang Hsu
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Corresponding author

Correspondence to Peng-Hsiang Hsu.

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Communicated by V. Loia.

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Wang, DJ., Yin, Y., Wu, WH. et al. A two-agent single-machine scheduling problem to minimize the total cost with release dates. Soft Comput 21, 805–816 (2017). https://doi.org/10.1007/s00500-015-1817-z

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