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Improved approaches to the exact solution of the machine covering problem

Author

Listed:
  • Rico Walter

    (Fraunhofer Institute for Industrial Mathematics ITWM)

  • Martin Wirth

    (Technische Universität Darmstadt)

  • Alexander Lawrinenko

    (Friedrich-Schiller-Universität Jena)

Abstract

For the basic problem of scheduling a set of n independent jobs on a set of m identical parallel machines with the objective of maximizing the minimum machine completion time—also referred to as machine covering—we propose a new exact branch-and-bound algorithm. Its most distinctive components are a different symmetry-breaking solution representation, enhanced lower and upper bounds, and effective novel dominance criteria derived from structural patterns of optimal schedules. Results of a comprehensive computational study conducted on benchmark instances attest to the effectiveness of our approach, particularly for small ratios of n to m.

Suggested Citation

  • Rico Walter & Martin Wirth & Alexander Lawrinenko, 2017. "Improved approaches to the exact solution of the machine covering problem," Journal of Scheduling, Springer, vol. 20(2), pages 147-164, April.
    • Handle: RePEc:spr:jsched:v:20:y:2017:i:2:d:10.1007_s10951-016-0477-x
    DOI: 10.1007/s10951-016-0477-x
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    References listed on IDEAS

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    1. Ravindra K. Ahuja & James B. Orlin, 2001. "Inverse Optimization," Operations Research, INFORMS, vol. 49(5), pages 771-783, October.
    2. Rico Walter, 2013. "Comparing the minimum completion times of two longest-first scheduling-heuristics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 125-139, January.
    3. Yong He & Zhiyi Tan, 2002. "Ordinal On-Line Scheduling for Maximizing the Minimum Machine Completion Time," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 199-206, June.
    4. Sheng-Yi Cai, 2007. "Semi-Online Machine Covering," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 373-382.
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    Cited by:

    1. Alexander Lawrinenko & Stefan Schwerdfeger & Rico Walter, 2018. "Reduction criteria, upper bounds, and a dynamic programming based heuristic for the max–min $$k_i$$ k i -partitioning problem," Journal of Heuristics, Springer, vol. 24(2), pages 173-203, April.
    2. Rico Walter & Alexander Lawrinenko, 2020. "A characterization of optimal multiprocessor schedules and new dominance rules," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 876-900, November.

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