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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Appendix: Detailed results on benchmark instances
Appendix: Detailed results on benchmark instances
Tables 7 and 8 contain detailed results for each of the 390 uniform and 390 non-uniform benchmark instances, respectively. Each row corresponds to a triple (n, m, Interval) and each column to one of the 10 instances per triple. For each instance, we record the best found objective function value (labeled as “Best”) as well as the best found upper bound value (labeled as “UB”). Bold entries indicate optimal values.
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Walter, R., Wirth, M. & Lawrinenko, A. Improved approaches to the exact solution of the machine covering problem. J Sched 20, 147–164 (2017). https://doi.org/10.1007/s10951-016-0477-x
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DOI: https://doi.org/10.1007/s10951-016-0477-x