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Journal of Scheduling

, Volume 20, Issue 2, pp 147–164 | Cite as

Improved approaches to the exact solution of the machine covering problem

  • Rico WalterEmail author
  • Martin Wirth
  • Alexander Lawrinenko
Article

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.

Keywords

Identical parallel machines Machine covering Dominance criteria Branch-and-bound 

Notes

Acknowledgments

We would like to thank the two anonymous referees for their valuable comments that helped to improve the presentation of the paper and for suggesting shorter proofs of Theorem 4.1 and Lemma 3.5.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Rico Walter
    • 1
    Email author
  • Martin Wirth
    • 2
  • Alexander Lawrinenko
    • 3
  1. 1.Department of OptimizationFraunhofer Institute for Industrial Mathematics ITWMKaiserslauternGermany
  2. 2.Fachgebiet Management Science & Operations ResearchTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Lehrstuhl für ABWL/Management ScienceFriedrich-Schiller-Universität JenaJenaGermany

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