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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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    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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