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Improved approaches to the exact solution of the machine covering problem

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  • Walter, Rico
  • Wirth, Martin
  • Lawrinenko, Alexander

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.

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  • Walter, Rico & Wirth, Martin & Lawrinenko, Alexander, 2017. "Improved approaches to the exact solution of the machine covering problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 80530, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    • Handle: RePEc:dar:wpaper:80530
    DOI: 10.1007/s10951-016-0477-x
    Note: for complete metadata visit http://tubiblio.ulb.tu-darmstadt.de/80530/
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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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